"Compressed" Compressed Sensing
Reeves, Galen
2010-01-01
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller number of samples is sufficient when there exists prior knowledge about the distribution of the unknown vector, or when only partial recovery is needed. An information-theoretic lower bound with connections to free probability theory and an upper bound corresponding to a computationally simple thresholding estimator are derived. It is shown that in certain cases (e.g. discrete valued vectors or large distortions) the number of samples can be decreased. Interestingly though, it is also shown that in many cases no reduction is possible.
Compressive Sensing Over Networks
Feizi, Soheil; Effros, Michelle
2010-01-01
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide an explicit trade-off between the rate and the decoding complexity. The key difference of compressive sensing and traditional information theoretic approaches is at their decoding side. Although optimal decoders to recover the original signal, compressed by source coding have high complexity, the compressive sensing decoder is a linear or convex optimization. First, we investigate applications of compressive sensing on distributed compression of correlated sources. Here, by using compressive sensing, we propose a compression scheme for a family of correlated sources with a modularized decoder, providing a trade-off between the compression rate and the decoding complexity. We call this scheme Sparse Distributed Compression. We use this compression scheme for a general multi...
Compressed sensing & sparse filtering
Carmi, Avishy Y; Godsill, Simon J
2013-01-01
This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.Â Apart from compressed sensing this book contains other related app
Beamforming Using Compressive Sensing
2011-10-01
dB to align the peak at 7.3o. Comparing peaks to val- leys , compressive sensing provides a greater main to interference (and noise) ratio...elements. Acknowledgments This research was supported by the Office of Naval Research. The authors would like to especially thank of Roger Gauss and Joseph
Zhou, Tianyi
2011-01-01
Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals and require time consuming recovery. In this paper, we introduce \\textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit quantized signal of dimensional $n$ from its 1-bit measurements via invoking $n$ times of Kullback-Leibler divergence based nearest neighbor search. Compared with CS and 1-bit CS, HCS allows the signal to be dense, takes considerably less (linear) recovery time and requires substantially less measurements ($\\mathcal O(\\log n)$). Moreover, HCS recovery can accelerate the subsequent 1-bit CS dequantizer. We study a quantized recovery error bound of HCS for general signals and "HCS+dequantizer" recovery error bound for sparse signals. Extensive numerical simulations verify the appealing accuracy, robustness, efficiency and consistency of HCS.
Stevens, Andrew J.; Kovarik, Libor; Abellan, Patricia; Yuan, Xin; Carin, Lawrence; Browning, Nigel D.
2015-08-02
One of the main limitations of imaging at high spatial and temporal resolution during in-situ TEM experiments is the frame rate of the camera being used to image the dynamic process. While the recent development of direct detectors has provided the hardware to achieve frame rates approaching 0.1ms, the cameras are expensive and must replace existing detectors. In this paper, we examine the use of coded aperture compressive sensing methods [1, 2, 3, 4] to increase the framerate of any camera with simple, low-cost hardware modifications. The coded aperture approach allows multiple sub-frames to be coded and integrated into a single camera frame during the acquisition process, and then extracted upon readout using statistical compressive sensing inversion. Our simulations show that it should be possible to increase the speed of any camera by at least an order of magnitude. Compressive Sensing (CS) combines sensing and compression in one operation, and thus provides an approach that could further improve the temporal resolution while correspondingly reducing the electron dose rate. Because the signal is measured in a compressive manner, fewer total measurements are required. When applied to TEM video capture, compressive imaging couled improve acquisition speed and reduce the electron dose rate. CS is a recent concept, and has come to the forefront due the seminal work of Candès [5]. Since the publication of Candès, there has been enormous growth in the application of CS and development of CS variants. For electron microscopy applications, the concept of CS has also been recently applied to electron tomography [6], and reduction of electron dose in scanning transmission electron microscopy (STEM) imaging [7]. To demonstrate the applicability of coded aperture CS video reconstruction for atomic level imaging, we simulate compressive sensing on observations of Pd nanoparticles and Ag nanoparticles during exposure to high temperatures and other environmental
Mroueh, Youssef; Rosasco, Lorenzo
2013-01-01
We introduce q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically and empirically. Results in 1-bit compressive sensing are recovered as a special case. Our theoretical results suggest a tradeoff between the quantization parameter q, and the number of measurements m in the control of the error of the resulting recovery a...
Compressed sensing electron tomography
Leary, Rowan, E-mail: rkl26@cam.ac.uk [Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ (United Kingdom); Saghi, Zineb; Midgley, Paul A. [Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ (United Kingdom); Holland, Daniel J. [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA (United Kingdom)
2013-08-15
The recent mathematical concept of compressed sensing (CS) asserts that a small number of well-chosen measurements can suffice to reconstruct signals that are amenable to sparse or compressible representation. In addition to powerful theoretical results, the principles of CS are being exploited increasingly across a range of experiments to yield substantial performance gains relative to conventional approaches. In this work we describe the application of CS to electron tomography (ET) reconstruction and demonstrate the efficacy of CS–ET with several example studies. Artefacts present in conventional ET reconstructions such as streaking, blurring of object boundaries and elongation are markedly reduced, and robust reconstruction is shown to be possible from far fewer projections than are normally used. The CS–ET approach enables more reliable quantitative analysis of the reconstructions as well as novel 3D studies from extremely limited data. - Highlights: • Compressed sensing (CS) theory and its application to electron tomography (ET) is described. • The practical implementation of CS–ET is outlined and its efficacy demonstrated with examples. • High fidelity tomographic reconstruction is possible from a small number of images. • The CS–ET reconstructions can be more reliably segmented and analysed quantitatively. • CS–ET is applicable to different image content by choice of an appropriate sparsifying transform.
S. Abhishek
2016-07-01
Full Text Available It is well understood that in any data acquisition system reduction in the amount of data reduces the time and energy, but the major trade-off here is the quality of outcome normally, lesser the amount of data sensed, lower the quality. Compressed Sensing (CS allows a solution, for sampling below the Nyquist rate. The challenging problem of increasing the reconstruction quality with less number of samples from an unprocessed data set is addressed here by the use of representative coordinate selected from different orders of splines. We have made a detailed comparison with 10 orthogonal and 6 biorthogonal wavelets with two sets of data from MIT Arrhythmia database and our results prove that the Spline coordinates work better than the wavelets. The generation of two new types of splines such as exponential and double exponential are also briefed here .We believe that this is one of the very first attempts made in Compressed Sensing based ECG reconstruction problems using raw data.
Beamforming using compressive sensing.
Edelmann, Geoffrey F; Gaumond, Charles F
2011-10-01
Compressive sensing (CS) is compared with conventional beamforming using horizontal beamforming of at-sea, towed-array data. They are compared qualitatively using bearing time records and quantitatively using signal-to-interference ratio. Qualitatively, CS exhibits lower levels of background interference than conventional beamforming. Furthermore, bearing time records show increasing, but tolerable, levels of background interference when the number of elements is decreased. For the full array, CS generates signal-to-interference ratio of 12 dB, but conventional beamforming only 8 dB. The superiority of CS over conventional beamforming is much more pronounced with undersampling.
Compressive Sensing DNA Microarrays
Richard G. Baraniuk
2009-01-01
Full Text Available Compressive sensing microarrays (CSMs are DNA-based sensors that operate using group testing and compressive sensing (CS principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed.
Compressive light field sensing.
Babacan, S Derin; Ansorge, Reto; Luessi, Martin; Matarán, Pablo Ruiz; Molina, Rafael; Katsaggelos, Aggelos K
2012-12-01
We propose a novel design for light field image acquisition based on compressive sensing principles. By placing a randomly coded mask at the aperture of a camera, incoherent measurements of the light passing through different parts of the lens are encoded in the captured images. Each captured image is a random linear combination of different angular views of a scene. The encoded images are then used to recover the original light field image via a novel Bayesian reconstruction algorithm. Using the principles of compressive sensing, we show that light field images with a large number of angular views can be recovered from only a few acquisitions. Moreover, the proposed acquisition and recovery method provides light field images with high spatial resolution and signal-to-noise-ratio, and therefore is not affected by limitations common to existing light field camera designs. We present a prototype camera design based on the proposed framework by modifying a regular digital camera. Finally, we demonstrate the effectiveness of the proposed system using experimental results with both synthetic and real images.
Compressive sensing in medical imaging.
Graff, Christian G; Sidky, Emil Y
2015-03-10
The promise of compressive sensing, exploitation of compressibility to achieve high quality image reconstructions with less data, has attracted a great deal of attention in the medical imaging community. At the Compressed Sensing Incubator meeting held in April 2014 at OSA Headquarters in Washington, DC, presentations were given summarizing some of the research efforts ongoing in compressive sensing for x-ray computed tomography and magnetic resonance imaging systems. This article provides an expanded version of these presentations. Sparsity-exploiting reconstruction algorithms that have gained popularity in the medical imaging community are studied, and examples of clinical applications that could benefit from compressive sensing ideas are provided. The current and potential future impact of compressive sensing on the medical imaging field is discussed.
Compressive sensing for urban radar
Amin, Moeness
2014-01-01
With the emergence of compressive sensing and sparse signal reconstruction, approaches to urban radar have shifted toward relaxed constraints on signal sampling schemes in time and space, and to effectively address logistic difficulties in data acquisition. Traditionally, these challenges have hindered high resolution imaging by restricting both bandwidth and aperture, and by imposing uniformity and bounds on sampling rates.Compressive Sensing for Urban Radar is the first book to focus on a hybrid of two key areas: compressive sensing and urban sensing. It explains how reliable imaging, tracki
Compressed sensing for body MRI.
Feng, Li; Benkert, Thomas; Block, Kai Tobias; Sodickson, Daniel K; Otazo, Ricardo; Chandarana, Hersh
2017-04-01
The introduction of compressed sensing for increasing imaging speed in magnetic resonance imaging (MRI) has raised significant interest among researchers and clinicians, and has initiated a large body of research across multiple clinical applications over the last decade. Compressed sensing aims to reconstruct unaliased images from fewer measurements than are traditionally required in MRI by exploiting image compressibility or sparsity. Moreover, appropriate combinations of compressed sensing with previously introduced fast imaging approaches, such as parallel imaging, have demonstrated further improved performance. The advent of compressed sensing marks the prelude to a new era of rapid MRI, where the focus of data acquisition has changed from sampling based on the nominal number of voxels and/or frames to sampling based on the desired information content. This article presents a brief overview of the application of compressed sensing techniques in body MRI, where imaging speed is crucial due to the presence of respiratory motion along with stringent constraints on spatial and temporal resolution. The first section provides an overview of the basic compressed sensing methodology, including the notion of sparsity, incoherence, and nonlinear reconstruction. The second section reviews state-of-the-art compressed sensing techniques that have been demonstrated for various clinical body MRI applications. In the final section, the article discusses current challenges and future opportunities. 5 J. Magn. Reson. Imaging 2017;45:966-987. © 2016 International Society for Magnetic Resonance in Medicine.
Adaptive compressive sensing camera
Hsu, Charles; Hsu, Ming K.; Cha, Jae; Iwamura, Tomo; Landa, Joseph; Nguyen, Charles; Szu, Harold
2013-05-01
We have embedded Adaptive Compressive Sensing (ACS) algorithm on Charge-Coupled-Device (CCD) camera based on the simplest concept that each pixel is a charge bucket, and the charges comes from Einstein photoelectric conversion effect. Applying the manufactory design principle, we only allow altering each working component at a minimum one step. We then simulated what would be such a camera can do for real world persistent surveillance taking into account of diurnal, all weather, and seasonal variations. The data storage has saved immensely, and the order of magnitude of saving is inversely proportional to target angular speed. We did design two new components of CCD camera. Due to the matured CMOS (Complementary metal-oxide-semiconductor) technology, the on-chip Sample and Hold (SAH) circuitry can be designed for a dual Photon Detector (PD) analog circuitry for changedetection that predicts skipping or going forward at a sufficient sampling frame rate. For an admitted frame, there is a purely random sparse matrix [Φ] which is implemented at each bucket pixel level the charge transport bias voltage toward its neighborhood buckets or not, and if not, it goes to the ground drainage. Since the snapshot image is not a video, we could not apply the usual MPEG video compression and Hoffman entropy codec as well as powerful WaveNet Wrapper on sensor level. We shall compare (i) Pre-Processing FFT and a threshold of significant Fourier mode components and inverse FFT to check PSNR; (ii) Post-Processing image recovery will be selectively done by CDT&D adaptive version of linear programming at L1 minimization and L2 similarity. For (ii) we need to determine in new frames selection by SAH circuitry (i) the degree of information (d.o.i) K(t) dictates the purely random linear sparse combination of measurement data a la [Φ]M,N M(t) = K(t) Log N(t).
Designing experiments through compressed sensing.
Young, Joseph G.; Ridzal, Denis
2013-06-01
In the following paper, we discuss how to design an ensemble of experiments through the use of compressed sensing. Specifically, we show how to conduct a small number of physical experiments and then use compressed sensing to reconstruct a larger set of data. In order to accomplish this, we organize our results into four sections. We begin by extending the theory of compressed sensing to a finite product of Hilbert spaces. Then, we show how these results apply to experiment design. Next, we develop an efficient reconstruction algorithm that allows us to reconstruct experimental data projected onto a finite element basis. Finally, we verify our approach with two computational experiments.
Compressive sensing of sparse tensors.
Friedland, Shmuel; Li, Qun; Schonfeld, Dan
2014-10-01
Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.
Compressive Sensing for Quantum Imaging
Howland, Gregory A.
This thesis describes the application of compressive sensing to several challenging problems in quantum imaging with practical and fundamental implications. Compressive sensing is a measurement technique that compresses a signal during measurement such that it can be dramatically undersampled. Compressive sensing has been shown to be an extremely efficient measurement technique for imaging, particularly when detector arrays are not available. The thesis first reviews compressive sensing through the lens of quantum imaging and quantum measurement. Four important applications and their corresponding experiments are then described in detail. The first application is a compressive sensing, photon-counting lidar system. A novel depth mapping technique that uses standard, linear compressive sensing is described. Depth maps up to 256 x 256 pixel transverse resolution are recovered with depth resolution less than 2.54 cm. The first three-dimensional, photon counting video is recorded at 32 x 32 pixel resolution and 14 frames-per-second. The second application is the use of compressive sensing for complementary imaging---simultaneously imaging the transverse-position and transverse-momentum distributions of optical photons. This is accomplished by taking random, partial projections of position followed by imaging the momentum distribution on a cooled CCD camera. The projections are shown to not significantly perturb the photons' momenta while allowing high resolution position images to be reconstructed using compressive sensing. A variety of objects and their diffraction patterns are imaged including the double slit, triple slit, alphanumeric characters, and the University of Rochester logo. The third application is the use of compressive sensing to characterize spatial entanglement of photon pairs produced by spontaneous parametric downconversion. The technique gives a theoretical speedup N2/log N for N-dimensional entanglement over the standard raster scanning technique
Compressed sensing for distributed systems
Coluccia, Giulio; Magli, Enrico
2015-01-01
This book presents a survey of the state-of-the art in the exciting and timely topic of compressed sensing for distributed systems. It has to be noted that, while compressed sensing has been studied for some time now, its distributed applications are relatively new. Remarkably, such applications are ideally suited to exploit all the benefits that compressed sensing can provide. The objective of this book is to provide the reader with a comprehensive survey of this topic, from the basic concepts to different classes of centralized and distributed reconstruction algorithms, as well as a comparison of these techniques. This book collects different contributions on these aspects. It presents the underlying theory in a complete and unified way for the first time, presenting various signal models and their use cases. It contains a theoretical part collecting latest results in rate-distortion analysis of distributed compressed sensing, as well as practical implementations of algorithms obtaining performance close to...
Singh, Shikha; Singhal, Vanika; Majumdar, Angshul
2016-01-01
This work addresses the problem of extracting deeply learned features directly from compressive measurements. There has been no work in this area. Existing deep learning tools only give good results when applied on the full signal, that too usually after preprocessing. These techniques require the signal to be reconstructed first. In this work we show that by learning directly from the compressed domain, considerably better results can be obtained. This work extends the recently proposed fram...
Compressive Sensing in Communication Systems
Fyhn, Karsten
2013-01-01
Wireless communication is omnipresent today, but this development has led to frequency spectrum becoming a limited resource. Furthermore, wireless devices become more and more energy-limited, due to the demand for continual wireless communication of higher and higher amounts of information....... The need for cheaper, smarter and more energy efficient wireless devices is greater now than ever. This thesis addresses this problem and concerns the application of the recently developed sampling theory of compressive sensing in communication systems. Compressive sensing is the merging of signal...... acquisition and compression. It allows for sampling a signal with a rate below the bound dictated by the celebrated Shannon-Nyquist sampling theorem. In some communication systems this necessary minimum sample rate, dictated by the Shannon-Nyquist sampling theorem, is so high it is at the limit of what...
Compressive Sensing with Optical Chaos
Rontani, D.; Choi, D.; Chang, C.-Y.; Locquet, A.; Citrin, D. S.
2016-12-01
Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.
Deterministic sensing matrices in compressive sensing: a survey.
Nguyen, Thu L N; Shin, Yoan
2013-01-01
Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensing matrices have been considered. These matrices are highly desirable on structure which allows fast implementation with reduced storage requirements. In this paper, a survey of deterministic sensing matrices for compressive sensing is presented. We introduce a basic problem in compressive sensing and some disadvantage of the random sensing matrices. Some recent results on construction of the deterministic sensing matrices are discussed.
LDPC Codes for Compressed Sensing
Dimakis, Alexandros G; Vontobel, Pascal O
2010-01-01
We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, \\emph{channel coding linear programming decoding (CC-LPD)}, which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, \\emph{compressed sensing linear programming decoding (CS-LPD)}, also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an under-determined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement ...
Blind compressive sensing dynamic MRI.
Lingala, Sajan Goud; Jacob, Mathews
2013-06-01
We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting l1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize-minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the l1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the l0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our
Compressed sensing traction force microscopy.
Brask, Jonatan Bohr; Singla-Buxarrais, Guillem; Uroz, Marina; Vincent, Romaric; Trepat, Xavier
2015-10-01
Adherent cells exert traction forces on their substrate, and these forces play important roles in biological functions such as mechanosensing, cell differentiation and cancer invasion. The method of choice to assess these active forces is traction force microscopy (TFM). Despite recent advances, TFM remains highly sensitive to measurement noise and exhibits limited spatial resolution. To improve the resolution and noise robustness of TFM, here we adapt techniques from compressed sensing (CS) to the reconstruction of the traction field from the substrate displacement field. CS enables the recovery of sparse signals at higher resolution from lower resolution data. Focal adhesions (FAs) of adherent cells are spatially sparse implying that traction fields are also sparse. Here we show, by simulation and by experiment, that the CS approach enables circumventing the Nyquist-Shannon sampling theorem to faithfully reconstruct the traction field at a higher resolution than that of the displacement field. This allows reaching state-of-the-art resolution using only a medium magnification objective. We also find that CS improves reconstruction quality in the presence of noise. A great scientific advance of the past decade is the recognition that physical forces determine an increasing list of biological processes. Traction force microscopy which measures the forces that cells exert on their surroundings has seen significant recent improvements, however the technique remains sensitive to measurement noise and severely limited in spatial resolution. We exploit the fact that the force fields are sparse to boost the spatial resolution and noise robustness by applying ideas from compressed sensing. The novel method allows high resolution on a larger field of view. This may in turn allow better understanding of the cell forces at the multicellular level, which are known to be important in wound healing and cancer invasion. Copyright © 2015 Acta Materialia Inc. Published by Elsevier
Xiangwei Li
2014-12-01
Full Text Available Compressive Sensing Imaging (CSI is a new framework for image acquisition, which enables the simultaneous acquisition and compression of a scene. Since the characteristics of Compressive Sensing (CS acquisition are very different from traditional image acquisition, the general image compression solution may not work well. In this paper, we propose an efficient lossy compression solution for CS acquisition of images by considering the distinctive features of the CSI. First, we design an adaptive compressive sensing acquisition method for images according to the sampling rate, which could achieve better CS reconstruction quality for the acquired image. Second, we develop a universal quantization for the obtained CS measurements from CS acquisition without knowing any a priori information about the captured image. Finally, we apply these two methods in the CSI system for efficient lossy compression of CS acquisition. Simulation results demonstrate that the proposed solution improves the rate-distortion performance by 0.4~2 dB comparing with current state-of-the-art, while maintaining a low computational complexity.
Li, Xiangwei; Lan, Xuguang; Yang, Meng; Xue, Jianru; Zheng, Nanning
2014-12-05
Compressive Sensing Imaging (CSI) is a new framework for image acquisition, which enables the simultaneous acquisition and compression of a scene. Since the characteristics of Compressive Sensing (CS) acquisition are very different from traditional image acquisition, the general image compression solution may not work well. In this paper, we propose an efficient lossy compression solution for CS acquisition of images by considering the distinctive features of the CSI. First, we design an adaptive compressive sensing acquisition method for images according to the sampling rate, which could achieve better CS reconstruction quality for the acquired image. Second, we develop a universal quantization for the obtained CS measurements from CS acquisition without knowing any a priori information about the captured image. Finally, we apply these two methods in the CSI system for efficient lossy compression of CS acquisition. Simulation results demonstrate that the proposed solution improves the rate-distortion performance by 0.4~2 dB comparing with current state-of-the-art, while maintaining a low computational complexity.
New Theory and Algorithms for Compressive Sensing
2009-03-06
are compressed by a factor of 10 or more when expressed in terms of their largest Fourier or wavelet coefficients. The usual approach to acquiring a...information conversion 2.2.1 Compressive sensing background Compressive Sensing (CS) provides a framework for acquisition of an N × 1 discrete -time signal...1) This optimization problem, also known as Basis Pursuit with Denoising (BPDN) [10] can be solved with tradi- tional convex programming techniques
Statistical Mechanical Analysis of Compressed Sensing Utilizing Correlated Compression Matrix
Takeda, Koujin
2010-01-01
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multi-input multi-output wireless communication systems. We found that strong one-dimensional correlations between expansion bases of original information slightly degrade reconstruction performance.
Compressed Sensing with Rank Deficient Dictionaries
Hansen, Thomas Lundgaard; Johansen, Daniel Højrup; Jørgensen, Peter Bjørn
2012-01-01
In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio...... (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C....../A) step in a GPS receiver. Simulations show that for this application the proposed choice of measurement matrix yields an increase in SNR performance of up to 5 − 10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared...
Compressive sensing for nuclear security.
Gestner, Brian Joseph
2013-12-01
Special nuclear material (SNM) detection has applications in nuclear material control, treaty verification, and national security. The neutron and gamma-ray radiation signature of SNMs can be indirectly observed in scintillator materials, which fluoresce when exposed to this radiation. A photomultiplier tube (PMT) coupled to the scintillator material is often used to convert this weak fluorescence to an electrical output signal. The fluorescence produced by a neutron interaction event differs from that of a gamma-ray interaction event, leading to a slightly different pulse in the PMT output signal. The ability to distinguish between these pulse types, i.e., pulse shape discrimination (PSD), has enabled applications such as neutron spectroscopy, neutron scatter cameras, and dual-mode neutron/gamma-ray imagers. In this research, we explore the use of compressive sensing to guide the development of novel mixed-signal hardware for PMT output signal acquisition. Effectively, we explore smart digitizers that extract sufficient information for PSD while requiring a considerably lower sample rate than conventional digitizers. Given that we determine the feasibility of realizing these designs in custom low-power analog integrated circuits, this research enables the incorporation of SNM detection into wireless sensor networks.
Compressed sensing and sparsity in photoacoustic tomography
Haltmeier, Markus; Moon, Sunghwan; Burgholzer, Peter
2016-01-01
Increasing the imaging speed is a central aim in photoacoustic tomography. In this work we address this issue using techniques of compressed sensing. We demonstrate that the number of measurements can significantly be reduced by allowing general linear measurements instead of point wise pressure values. A main requirement in compressed sensing is the sparsity of the unknowns to be recovered. For that purpose we develop the concept of sparsifying temporal transforms for three dimensional photoacoustic tomography. Reconstruction results for simulated and for experimental data verify that the proposed compressed sensing scheme allows to significantly reducing the number of spatial measurements without reducing the spatial resolution.
Video compressive sensing using Gaussian mixture models.
Yang, Jianbo; Yuan, Xin; Liao, Xuejun; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2014-11-01
A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.
Compressive sensing based algorithms for electronic defence
Mishra, Amit Kumar
2017-01-01
This book details some of the major developments in the implementation of compressive sensing in radio applications for electronic defense and warfare communication use. It provides a comprehensive background to the subject and at the same time describes some novel algorithms. It also investigates application value and performance-related parameters of compressive sensing in scenarios such as direction finding, spectrum monitoring, detection, and classification.
Compressed Sensing-Based Multiuser Cooperative Networks
付晓梅; 崔阳然
2016-01-01
To avoid interference, compressed sensing is introduced into multiuser cooperative network. A coopera-tive compressed sensing and amplify-and-forward(CCS-AF)scheme is proposed, and it is proved that the channel capacity increases compared with the traditional cooperative scheme by considering the CCS-AF transmission ma-trix as the measurement matrix. Moreover, a new power allocation algorithm among the relays is proposed to im-prove the channel capacity. Numerical results validate the effectiveness of the proposed scheme.
Compressive Sensing Using the Entropy Functional
Kose, Kivanc
2011-01-01
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregman's row action D-projection method for compressive sensing applications. Simulation examples are presented.
Application of Compressive Sensing to Digital Holography
2015-05-01
AFRL-RY-WP-TR-2015-0071 APPLICATION OF COMPRESSIVE SENSING TO DIGITAL HOLOGRAPHY Mark Neifeld University of Arizona...From - To) May 2015 Final 3 September 2013 – 27 February 2015 4. TITLE AND SUBTITLE APPLICATION OF COMPRESSIVE SENSING TO DIGITAL HOLOGRAPHY 5a...from under- sampled data. This work presents a new reconstruction algorithm for use with under-sampled digital holography measurements and yields
Spectral Compressive Sensing with Polar Interpolation
Fyhn, Karsten; Dadkhahi, Hamid; F. Duarte, Marco
2013-01-01
Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space....... In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing...
An underwater acoustic data compression method based on compressed sensing
郭晓乐; 杨坤德; 史阳; 段睿
2016-01-01
The use of underwater acoustic data has rapidly expanded with the application of multichannel, large-aperture underwater detection arrays. This study presents an underwater acoustic data compression method that is based on compressed sensing. Underwater acoustic signals are transformed into the sparse domain for data storage at a receiving terminal, and the improved orthogonal matching pursuit (IOMP) algorithm is used to reconstruct the original underwater acoustic signals at a data processing terminal. When an increase in sidelobe level occasionally causes a direction of arrival estimation error, the proposed compression method can achieve a 10 times stronger compression for narrowband signals and a 5 times stronger compression for wideband signals than the orthogonal matching pursuit (OMP) algorithm. The IOMP algorithm also reduces the computing time by about 20% more than the original OMP algorithm. The simulation and experimental results are discussed.
Compressive Sensing for MIMO Radar
Yu, Yao; Poor, H Vincent
2009-01-01
Multiple-input multiple-output (MIMO) radar systems have been shown to achieve superior resolution as compared to traditional radar systems with the same number of transmit and receive antennas. This paper considers a distributed MIMO radar scenario, in which each transmit element is a node in a wireless network, and investigates the use of compressive sampling for direction-of-arrival (DOA) estimation. According to the theory of compressive sampling, a signal that is sparse in some domain can be recovered based on far fewer samples than required by the Nyquist sampling theorem. The DOA of targets form a sparse vector in the angle space, and therefore, compressive sampling can be applied for DOA estimation. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than other approaches. This is particularly useful in a distributed scenario, in which the results at each receive node need to be transmitted to a fusion center for further processing.
The possibilities of compressed sensing based migration
Aldawood, Ali
2013-09-22
Linearized waveform inversion or Least-square migration helps reduce migration artifacts caused by limited acquisition aperture, coarse sampling of sources and receivers, and low subsurface illumination. However, leastsquare migration, based on L2-norm minimization of the misfit function, tends to produce a smeared (smoothed) depiction of the true subsurface reflectivity. Assuming that the subsurface reflectivity distribution is a sparse signal, we use a compressed-sensing (Basis Pursuit) algorithm to retrieve this sparse distribution from a small number of linear measurements. We applied a compressed-sensing algorithm to image a synthetic fault model using dense and sparse acquisition geometries. Tests on synthetic data demonstrate the ability of compressed-sensing to produce highly resolved migrated images. We, also, studied the robustness of the Basis Pursuit algorithm in the presence of Gaussian random noise.
Gated viewing laser imaging with compressive sensing.
Li, Li; Wu, Lei; Wang, Xingbin; Dang, Ersheng
2012-05-10
We present a prototype of gated viewing laser imaging with compressive sensing (GVLICS). By a new framework named compressive sensing, it is possible for us to perform laser imaging using a single-pixel detector where the transverse spatial resolution is obtained. Moreover, combining compressive sensing with gated viewing, the three-dimensional (3D) scene can be reconstructed by the time-slicing technique. The simulations are accomplished to evaluate the characteristics of the proposed GVLICS prototype. Qualitative analysis of Lissajous-type eye-pattern figures indicates that the range accuracy of the reconstructed 3D images is affected by the sampling rate, the image's noise, and the complexity of the scenes.
Pitfalls and possibilities of radar compressive sensing.
Goodman, Nathan A; Potter, Lee C
2015-03-10
In this paper, we consider the application of compressive sensing (CS) to radar remote sensing applications. We survey a suite of practical system-level issues related to the compression of radar measurements, and we advocate the consideration of these issues by researchers exploring potential gains of CS in radar applications. We also give abbreviated examples of decades-old radio-frequency (RF) practices that already embody elements of CS for relevant applications. In addition to the cautionary implications of system-level issues and historical precedents, we identify several promising results that RF practitioners may gain from the recent explosion of CS literature.
Compressive wavefront sensing with weak values.
Howland, Gregory A; Lum, Daniel J; Howell, John C
2014-08-11
We demonstrate a wavefront sensor that unites weak measurement and the compressive-sensing, single-pixel camera. Using a high-resolution spatial light modulator (SLM) as a variable waveplate, we weakly couple an optical field's transverse-position and polarization degrees of freedom. By placing random, binary patterns on the SLM, polarization serves as a meter for directly measuring random projections of the wavefront's real and imaginary components. Compressive-sensing optimization techniques can then recover the wavefront. We acquire high quality, 256 × 256 pixel images of the wavefront from only 10,000 projections. Photon-counting detectors give sub-picowatt sensitivity.
Fast electron microscopy via compressive sensing
Larson, Kurt W; Anderson, Hyrum S; Wheeler, Jason W
2014-12-09
Various technologies described herein pertain to compressive sensing electron microscopy. A compressive sensing electron microscope includes a multi-beam generator and a detector. The multi-beam generator emits a sequence of electron patterns over time. Each of the electron patterns can include a plurality of electron beams, where the plurality of electron beams is configured to impart a spatially varying electron density on a sample. Further, the spatially varying electron density varies between each of the electron patterns in the sequence. Moreover, the detector collects signals respectively corresponding to interactions between the sample and each of the electron patterns in the sequence.
Graphical Models Concepts in Compressed Sensing
Montanari, Andrea
2010-01-01
This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via $\\ell_1$ penalized least-squares (known as LASSO or BPDN). We discuss how to derive fast approximate message passing algorithms to solve this problem. Surprisingly, the analysis of such algorithms allows to prove exact high-dimensional limit results for the LASSO risk. This paper will appear as a chapter in a book on âCompressed Sensingâ edited by Yonina Eldar and Gitta Kutyniok.
Compressive sensing with a microwave photonic filter
Chen, Ying; Yu, Xianbin; Chi, Hao
2015-01-01
In this letter, we present a novel approach to realizing photonics-assisted compressive sensing (CS) with the technique of microwave photonic fi ltering. In the proposed system, an input spectrally sparse signal to be captured and a random sequence are modulated on an optical carrier via two Mach...... to a frequency- dependent power fading, low-pass fi ltering required in the CS is then realized. A proof-of-concept ex- periment for compressive sampling and recovery of a signal containing three tones at 310 MHz, 1 GHz and 2 GHz with a compression factor up to 10 is successfully demonstrated. More simulation...
Adaptive Remote Sensing Texture Compression on GPU
Xiao-Xia Lu
2010-11-01
Full Text Available Considering the properties of remote sensing texture such as strong randomness and weak local correlation, a novel adaptive compression method based on vector quantizer is presented and implemented on GPU. Utilizing the property of Human Visual System (HVS, a new similarity measurement function is designed instead of using Euclid distance. Correlated threshold between blocks can be obtained adaptively according to the property of different images without artificial auxiliary. Furthermore, a self-adaptive threshold adjustment during the compression is designed to improve the reconstruct quality. Experiments show that the method can handle various resolution images adaptively. It can achieve satisfied compression rate and reconstruct quality at the same time. Index is coded to further increase the compression rate. The coding way is designed to guarantee accessing the index randomly too. Furthermore, the compression and decompression process is speed up with the usage of GPU, on account of their parallelism.
Statistical Compressive Sensing of Gaussian Mixture Models
Yu, Guoshen
2010-01-01
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is introduced. For signals following a Gaussian distribution, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS, where N is the signal dimension, and with an optimal decoder implemented with linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the k-best term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the k-best term approximation with probability one, and the ...
Statistical Compressed Sensing of Gaussian Mixture Models
Yu, Guoshen
2011-01-01
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is u...
Spectral analysis based on compressive sensing in nanophotonic structures.
Wang, Zhu; Yu, Zongfu
2014-10-20
A method of spectral sensing based on compressive sensing is shown to have the potential to achieve high resolution in a compact device size. The random bases used in compressive sensing are created by the optical response of a set of different nanophotonic structures, such as photonic crystal slabs. The complex interferences in these nanostructures offer diverse spectral features suitable for compressive sensing.
Whole brain susceptibility mapping using compressed sensing.
Wu, Bing; Li, Wei; Guidon, Arnaud; Liu, Chunlei
2012-01-01
The derivation of susceptibility from image phase is hampered by the ill-conditioned filter inversion in certain k-space regions. In this article, compressed sensing is used to compensate for the k-space regions where direct filter inversion is unstable. A significantly lower level of streaking artifacts is produced in the resulting susceptibility maps for both simulated and in vivo data sets compared to outcomes obtained using the direct threshold method. It is also demonstrated that the compressed sensing based method outperforms regularization based methods. The key difference between the regularized inversions and compressed sensing compensated inversions is that, in the former case, the entire k-space spectrum estimation is affected by the ill-conditioned filter inversion in certain k-space regions, whereas in the compressed sensing based method only the ill-conditioned k-space regions are estimated. In the susceptibility map calculated from the phase measurement obtained using a 3T scanner, not only are the iron-rich regions well depicted, but good contrast between white and gray matter interfaces that feature a low level of susceptibility variations are also obtained. The correlation between the iron content and the susceptibility levels in iron-rich deep nucleus regions is studied, and strong linear relationships are observed which agree with previous findings.
Compressive sensing for high resolution radar imaging
Anitori, L.; Otten, M.P.G.; Hoogeboom, P.
2010-01-01
In this paper we present some preliminary results on the application of Compressive Sensing (CS) to high resolution radar imaging. CS is a recently developed theory which allows reconstruction of sparse signals with a number of measurements much lower than what is required by the Shannon sampling th
Compressive sensing with a spherical microphone array
Fernandez Grande, Efren; Xenaki, Angeliki
2016-01-01
A wave expansion method is proposed in this work, based on measurements with a spherical microphone array, and formulated in the framework provided by Compressive Sensing. The method promotes sparse solutions via ‘1-norm minimization, so that the measured data are represented by few basis functions...
Compressed Sensing-Based Direct Conversion Receiver
Pierzchlewski, Jacek; Arildsen, Thomas; Larsen, Torben
2012-01-01
Due to the continuously increasing computational power of modern data receivers it is possible to move more and more processing from the analog to the digital domain. This paper presents a compressed sensing approach to relaxing the analog filtering requirements prior to the ADCs in a direct...
Compressive Sensing for Spread Spectrum Receivers
Fyhn, Karsten; Jensen, Tobias Lindstrøm; Larsen, Torben
2013-01-01
With the advent of ubiquitous computing there are two design parameters of wireless communication devices that become very important: power efficiency and production cost. Compressive sensing enables the receiver in such devices to sample below the Shannon-Nyquist sampling rate, which may lead...... to a decrease in the two design parameters. This paper investigates the use of Compressive Sensing (CS) in a general Code Division Multiple Access (CDMA) receiver. We show that when using spread spectrum codes in the signal domain, the CS measurement matrix may be simplified. This measurement scheme, named...... Compressive Spread Spectrum (CSS), allows for a simple, effective receiver design. Furthermore, we numerically evaluate the proposed receiver in terms of bit error rate under different signal to noise ratio conditions and compare it with other receiver structures. These numerical experiments show that though...
Spatial Compressive Sensing for Strain Data Reconstruction from Sparse Sensors
2014-10-01
Spatial Compressive Sensing for Strain Data Reconstruction from Sparse Sensors by Mulugeta A Haile ARL-TR-7126 October 2014...Spatial Compressive Sensing for Strain Data Reconstruction from Sparse Sensors Mulugeta A Haile Vehicle Technology Directorate, ARL...
Coding Strategies and Implementations of Compressive Sensing
Tsai, Tsung-Han
This dissertation studies the coding strategies of computational imaging to overcome the limitation of conventional sensing techniques. The information capacity of conventional sensing is limited by the physical properties of optics, such as aperture size, detector pixels, quantum efficiency, and sampling rate. These parameters determine the spatial, depth, spectral, temporal, and polarization sensitivity of each imager. To increase sensitivity in any dimension can significantly compromise the others. This research implements various coding strategies subject to optical multidimensional imaging and acoustic sensing in order to extend their sensing abilities. The proposed coding strategies combine hardware modification and signal processing to exploiting bandwidth and sensitivity from conventional sensors. We discuss the hardware architecture, compression strategies, sensing process modeling, and reconstruction algorithm of each sensing system. Optical multidimensional imaging measures three or more dimensional information of the optical signal. Traditional multidimensional imagers acquire extra dimensional information at the cost of degrading temporal or spatial resolution. Compressive multidimensional imaging multiplexes the transverse spatial, spectral, temporal, and polarization information on a two-dimensional (2D) detector. The corresponding spectral, temporal and polarization coding strategies adapt optics, electronic devices, and designed modulation techniques for multiplex measurement. This computational imaging technique provides multispectral, temporal super-resolution, and polarization imaging abilities with minimal loss in spatial resolution and noise level while maintaining or gaining higher temporal resolution. The experimental results prove that the appropriate coding strategies may improve hundreds times more sensing capacity. Human auditory system has the astonishing ability in localizing, tracking, and filtering the selected sound sources or
Compressive sensing in the EO/IR.
Gehm, M E; Brady, D J
2015-03-10
We investigate the utility of compressive sensing (CS) to electro-optic and infrared (EO/IR) applications. We introduce the field through a discussion of historical antecedents and the development of the modern CS framework. Basic economic arguments (in the broadest sense) are presented regarding the applicability of CS to the EO/IR and used to draw conclusions regarding application areas where CS would be most viable. A number of experimental success stories are presented to demonstrate the overall feasibility of the approaches, and we conclude with a discussion of open challenges to practical adoption of CS methods.
A Compressed Sensing Wire-Tap Channel
Reeves, Galen; Milosavljevic, Nebojsa; Gastpar, Michael
2011-01-01
A multiplicative Gaussian wire-tap channel inspired by compressed sensing is studied. Lower and upper bounds on the secrecy capacity are derived, and shown to be relatively tight in the large system limit for a large class of compressed sensing matrices. Surprisingly, it is shown that the secrecy capacity of this channel is nearly equal to the capacity without any secrecy constraint provided that the channel of the eavesdropper is strictly worse than the channel of the intended receiver. In other words, the eavesdropper can see almost everything and yet learn almost nothing. This behavior, which contrasts sharply with that of many commonly studied wiretap channels, is made possible by the fact that a small number of linear projections can make a crucial difference in the ability to estimate sparse vectors.
Compressive sensing and entropy in seismic signals
Marinho, Eberton S.; Rocha, Tiago C.; Corso, Gilberto; Lucena, Liacir S.
2017-09-01
This work analyzes the correlation between the seismic signal entropy and the Compressive Sensing (CS) recovery index. The recovery index measures the quality of a signal reconstructed by the CS method. We analyze the performance of two CS algorithms: the ℓ1-MAGIC and the Fast Bayesian Compressive Sensing (BCS). We have observed a negative correlation between the performance of CS and seismic signal entropy. Signals with low entropy have small recovery index in their reconstruction by CS. The rationale behind our finding is: a sparse signal is easy to recover by CS and, besides, a sparse signal has low entropy. In addition, ℓ1-MAGIC shows a more significant correlation between entropy and CS performance than Fast BCS.
Compressed sensing performance bounds under Poisson noise
Raginsky, Maxim; Marcia, Roummel F; Willett, Rebecca M
2009-01-01
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this setting, standard CS techniques cannot be applied directly for several reasons. First, the usual signal-independent and/or bounded noise models do not apply to Poisson noise, which is non-additive and signal-dependent. Second, the CS matrices typically considered are not feasible in real optical systems because they do not adhere to important constraints, such as nonnegativity and photon flux preservation. Third, the typical $\\ell_2$--$\\ell_1$ minimization leads to overfitting in the high-intensity regions and oversmoothing in the low-intensity areas. In this paper, we describe how a feasible positivity- and flux-preserving sensing matrix can be constructed, and then analyze the performance of a CS reconstruction approach for Poisson data that minimizes an objective functi...
Compressive Sensing Image Sensors-Hardware Implementation
Shahram Shirani
2013-04-01
Full Text Available The compressive sensing (CS paradigm uses simultaneous sensing and compression to provide an efficient image acquisition technique. The main advantages of the CS method include high resolution imaging using low resolution sensor arrays and faster image acquisition. Since the imaging philosophy in CS imagers is different from conventional imaging systems, new physical structures have been developed for cameras that use the CS technique. In this paper, a review of different hardware implementations of CS encoding in optical and electrical domains is presented. Considering the recent advances in CMOS (complementary metal–oxide–semiconductor technologies and the feasibility of performing on-chip signal processing, important practical issues in the implementation of CS in CMOS sensors are emphasized. In addition, the CS coding for video capture is discussed.
Multichannel Compressive Sensing MRI Using Noiselet Encoding
Pawar, Kamlesh; Zhang, Jingxin
2014-01-01
The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI, and presents a method to design the pulse sequence for the noiselet encoding. This novel encoding scheme is combined with the multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. An empirical RIP a...
Dynamic Spectrum Detection Via Compressive Sensing
Michael Odeyomi
2012-04-01
Full Text Available Spectrum congestion is a major concern in both military and commercial wireless networks. To support growing demand for ubiquitous spectrum usage, Cognitive Radio is a new paradigm in wireless communication that can be used to exploit unused part of the spectrum by dynamically adjusting its operating parameters. While cognitive radio technology is a promising solution to the spectral congestion problem, efficient methods for detecting white spaces in wideband radio spectrum remain a challenge. Conventional methods of detection are forced to use the high sampling rate requirement of Nyquist criterion. In this paper, the feasibility and efficacy of using compressive sensing (CS algorithms inconjunction with Haar wavelet for identifying spectrum holes in the wideband spectrum is explored. Compressive sensing is an emerging theory that shows that it’s possible to achieve good reconstruction, at sampling rates lower than that specified by Nyquist. CS approach is robust in AWGN and fading channel.
Restricted Conformal Property of Compressive Sensing
Cheng, Tao
2014-01-01
Energy and direction are tow basic properties of a vector. A discrete signal is a vector in nature. RIP of compressive sensing can not show the direction information of a signal but show the energy information of a signal. Hence, RIP is not complete. Orthogonal matrices can preserve angles and lengths. Preservation of length can show energies of signals like RIP do; and preservation of angle can show directions of signals. Therefore, Restricted Conformal Property (RCP) is proposed according t...
Designing robust sensing matrix for image compression.
Li, Gang; Li, Xiao; Li, Sheng; Bai, Huang; Jiang, Qianru; He, Xiongxiong
2015-12-01
This paper deals with designing sensing matrix for compressive sensing systems. Traditionally, the optimal sensing matrix is designed so that the Gram of the equivalent dictionary is as close as possible to a target Gram with small mutual coherence. A novel design strategy is proposed, in which, unlike the traditional approaches, the measure considers of mutual coherence behavior of the equivalent dictionary as well as sparse representation errors of the signals. The optimal sensing matrix is defined as the one that minimizes this measure and hence is expected to be more robust against sparse representation errors. A closed-form solution is derived for the optimal sensing matrix with a given target Gram. An alternating minimization-based algorithm is also proposed for addressing the same problem with the target Gram searched within a set of relaxed equiangular tight frame Grams. The experiments are carried out and the results show that the sensing matrix obtained using the proposed approach outperforms those existing ones using a fixed dictionary in terms of signal reconstruction accuracy for synthetic data and peak signal-to-noise ratio for real images.
Biomedical sensor design using analog compressed sensing
Balouchestani, Mohammadreza; Krishnan, Sridhar
2015-05-01
The main drawback of current healthcare systems is the location-specific nature of the system due to the use of fixed/wired biomedical sensors. Since biomedical sensors are usually driven by a battery, power consumption is the most important factor determining the life of a biomedical sensor. They are also restricted by size, cost, and transmission capacity. Therefore, it is important to reduce the load of sampling by merging the sampling and compression steps to reduce the storage usage, transmission times, and power consumption in order to expand the current healthcare systems to Wireless Healthcare Systems (WHSs). In this work, we present an implementation of a low-power biomedical sensor using analog Compressed Sensing (CS) framework for sparse biomedical signals that addresses both the energy and telemetry bandwidth constraints of wearable and wireless Body-Area Networks (BANs). This architecture enables continuous data acquisition and compression of biomedical signals that are suitable for a variety of diagnostic and treatment purposes. At the transmitter side, an analog-CS framework is applied at the sensing step before Analog to Digital Converter (ADC) in order to generate the compressed version of the input analog bio-signal. At the receiver side, a reconstruction algorithm based on Restricted Isometry Property (RIP) condition is applied in order to reconstruct the original bio-signals form the compressed bio-signals with high probability and enough accuracy. We examine the proposed algorithm with healthy and neuropathy surface Electromyography (sEMG) signals. The proposed algorithm achieves a good level for Average Recognition Rate (ARR) at 93% and reconstruction accuracy at 98.9%. In addition, The proposed architecture reduces total computation time from 32 to 11.5 seconds at sampling-rate=29 % of Nyquist rate, Percentage Residual Difference (PRD)=26 %, Root Mean Squared Error (RMSE)=3 %.
Parallel hyperspectral compressive sensing method on GPU
Bernabé, Sergio; Martín, Gabriel; Nascimento, José M. P.
2015-10-01
Remote hyperspectral sensors collect large amounts of data per flight usually with low spatial resolution. It is known that the bandwidth connection between the satellite/airborne platform and the ground station is reduced, thus a compression onboard method is desirable to reduce the amount of data to be transmitted. This paper presents a parallel implementation of an compressive sensing method, called parallel hyperspectral coded aperture (P-HYCA), for graphics processing units (GPU) using the compute unified device architecture (CUDA). This method takes into account two main properties of hyperspectral dataset, namely the high correlation existing among the spectral bands and the generally low number of endmembers needed to explain the data, which largely reduces the number of measurements necessary to correctly reconstruct the original data. Experimental results conducted using synthetic and real hyperspectral datasets on two different GPU architectures by NVIDIA: GeForce GTX 590 and GeForce GTX TITAN, reveal that the use of GPUs can provide real-time compressive sensing performance. The achieved speedup is up to 20 times when compared with the processing time of HYCA running on one core of the Intel i7-2600 CPU (3.4GHz), with 16 Gbyte memory.
Speech Enhancement based on Compressive Sensing Algorithm
Sulong, Amart; Gunawan, Teddy S.; Khalifa, Othman O.; Chebil, Jalel
2013-12-01
There are various methods, in performance of speech enhancement, have been proposed over the years. The accurate method for the speech enhancement design mainly focuses on quality and intelligibility. The method proposed with high performance level. A novel speech enhancement by using compressive sensing (CS) is a new paradigm of acquiring signals, fundamentally different from uniform rate digitization followed by compression, often used for transmission or storage. Using CS can reduce the number of degrees of freedom of a sparse/compressible signal by permitting only certain configurations of the large and zero/small coefficients, and structured sparsity models. Therefore, CS is significantly provides a way of reconstructing a compressed version of the speech in the original signal by taking only a small amount of linear and non-adaptive measurement. The performance of overall algorithms will be evaluated based on the speech quality by optimise using informal listening test and Perceptual Evaluation of Speech Quality (PESQ). Experimental results show that the CS algorithm perform very well in a wide range of speech test and being significantly given good performance for speech enhancement method with better noise suppression ability over conventional approaches without obvious degradation of speech quality.
Compressed sensing imaging techniques for radio interferometry
Wiaux, Y; Puy, G; Scaife, A M M; Vandergheynst, P
2009-01-01
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave backgroun...
Compressed sensing for phase contrast CT
Gaass, Thomas; Potdevin, Guillaume; Noeel, Peter B.; Tapfer, Arne; Willner, Marian; Herzen, Julia; Bech, Martin; Pfeiffer, Franz; Haase, Axel [Zentralinstitut fuer Medizintechnik, Technische Universitaet Muenchen, Garching (Germany); Department of Physics, Technische Universitaet Muenchen, Garching (Germany); Department of Radiology, Technische Universitaet Muenchen, Munich (Germany)
2012-07-31
Modern x-ray techniques opened the possibility to retrieve phase information. Phase-contrast computed tomography (PCCT) has the potential to significantly improve soft tissue contrast. Radiation dose, however, continues to be an issue when moving from bench to bedside. Dose reduction in this work is achieved by sparsely acquiring PCCT data. To compensate for appearing aliasing artifacts we introduce a compressed sensing (CS) reconstruction framework. We present the feasibility of CS on PCCT with numerical as well as measured phantom data. The results proof that CS compensates for under-sampling artifacts and maintains the superior soft tissue contrast and detail visibility in the reconstructed images.
Compressed sensing for phase contrast CT
Gaass, Thomas; Potdevin, Guillaume; Noël, Peter B.; Tapfer, Arne; Willner, Marian; Herzen, Julia; Bech, Martin; Pfeiffer, Franz; Haase, Axel
2012-07-01
Modern x-ray techniques opened the possibility to retrieve phase information. Phase-contrast computed tomography (PCCT) has the potential to significantly improve soft tissue contrast. Radiation dose, however, continues to be an issue when moving from bench to bedside. Dose reduction in this work is achieved by sparsely acquiring PCCT data. To compensate for appearing aliasing artifacts we introduce a compressed sensing (CS) reconstruction framework. We present the feasibility of CS on PCCT with numerical as well as measured phantom data. The results proof that CS compensates for under-sampling artifacts and maintains the superior soft tissue contrast and detail visibility in the reconstructed images.
Compressive Sensing via Nonlocal Smoothed Rank Function.
Fan, Ya-Ru; Huang, Ting-Zhu; Liu, Jun; Zhao, Xi-Le
2016-01-01
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.
Compressive sensing with a spherical microphone array.
Fernandez-Grande, Efren; Xenaki, Angeliki
2016-02-01
A wave expansion method is proposed in this work, based on measurements with a spherical microphone array, and formulated in the framework provided by Compressive Sensing. The method promotes sparse solutions via ℓ1-norm minimization, so that the measured data are represented by few basis functions. This results in fine spatial resolution and accuracy. This publication covers the theoretical background of the method, including experimental results that illustrate some of the fundamental differences with the "conventional" least-squares approach. The proposed methodology is relevant for source localization, sound field reconstruction, and sound field analysis.
Information optimal compressive sensing: static measurement design.
Ashok, Amit; Huang, Liang-Chih; Neifeld, Mark A
2013-05-01
The compressive sensing paradigm exploits the inherent sparsity/compressibility of signals to reduce the number of measurements required for reliable reconstruction/recovery. In many applications additional prior information beyond signal sparsity, such as structure in sparsity, is available, and current efforts are mainly limited to exploiting that information exclusively in the signal reconstruction problem. In this work, we describe an information-theoretic framework that incorporates the additional prior information as well as appropriate measurement constraints in the design of compressive measurements. Using a Gaussian binomial mixture prior we design and analyze the performance of optimized projections relative to random projections under two specific design constraints and different operating measurement signal-to-noise ratio (SNR) regimes. We find that the information-optimized designs yield significant, in some cases nearly an order of magnitude, improvements in the reconstruction performance with respect to the random projections. These improvements are especially notable in the low measurement SNR regime where the energy-efficient design of optimized projections is most advantageous. In such cases, the optimized projection design departs significantly from random projections in terms of their incoherence with the representation basis. In fact, we find that the maximizing incoherence of projections with the representation basis is not necessarily optimal in the presence of additional prior information and finite measurement noise/error. We also apply the information-optimized projections to the compressive image formation problem for natural scenes, and the improved visual quality of reconstructed images with respect to random projections and other compressive measurement design affirms the overall effectiveness of the information-theoretic design framework.
Frequency extrapolation by nonconvex compressive sensing
Chartrand, Rick [Los Alamos National Laboratory; Sidky, Emil Y [UNIV OF CHICAGO; Pan, Xiaochaun [UNIV OF CHICAGO
2010-12-03
Tomographic imaging modalities sample subjects with a discrete, finite set of measurements, while the underlying object function is continuous. Because of this, inversion of the imaging model, even under ideal conditions, necessarily entails approximation. The error incurred by this approximation can be important when there is rapid variation in the object function or when the objects of interest are small. In this work, we investigate this issue with the Fourier transform (FT), which can be taken as the imaging model for magnetic resonance imaging (MRl) or some forms of wave imaging. Compressive sensing has been successful for inverting this data model when only a sparse set of samples are available. We apply the compressive sensing principle to a somewhat related problem of frequency extrapolation, where the object function is represented by a super-resolution grid with many more pixels than FT measurements. The image on the super-resolution grid is obtained through nonconvex minimization. The method fully utilizes the available FT samples, while controlling aliasing and ringing. The algorithm is demonstrated with continuous FT samples of the Shepp-Logan phantom with additional small, high-contrast objects.
Distributed Compressive Sensing: A Deep Learning Approach
Palangi, Hamid; Ward, Rabab; Deng, Li
2016-09-01
Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this condition. Instead we assume that these sparse vectors depend on each other but that this dependency is unknown. We capture this dependency by computing the conditional probability of each entry in each vector being non-zero, given the "residuals" of all previous vectors. To estimate these probabilities, we propose the use of the Long Short-Term Memory (LSTM)[1], a data driven model for sequence modelling that is deep in time. To calculate the model parameters, we minimize a cross entropy cost function. To reconstruct the sparse vectors at the decoder, we propose a greedy solver that uses the above model to estimate the conditional probabilities. By performing extensive experiments on two real world datasets, we show that the proposed method significantly outperforms the general MMV solver (the Simultaneous Orthogonal Matching Pursuit (SOMP)) and a number of the model-based Bayesian methods. The proposed method does not add any complexity to the general compressive sensing encoder. The trained model is used just at the decoder. As the proposed method is a data driven method, it is only applicable when training data is available. In many applications however, training data is indeed available, e.g. in recorded images and videos.
Phase diagram of matrix compressed sensing
Schülke, Christophe; Schniter, Philip; Zdeborová, Lenka
2016-12-01
In the problem of matrix compressed sensing, we aim to recover a low-rank matrix from a few noisy linear measurements. In this contribution, we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model where the matrix to be recovered is a product of random matrices. The results that we obtain using the replica method describe the state evolution of the Parametric Bilinear Generalized Approximate Message Passing (P-BiG-AMP) algorithm, recently introduced in J. T. Parker and P. Schniter [IEEE J. Select. Top. Signal Process. 10, 795 (2016), 10.1109/JSTSP.2016.2539123]. We show the existence of two different types of phase transition and their implications for the solvability of the problem, and we compare the results of our theoretical analysis to the numerical performance reached by P-BiG-AMP. Remarkably, the asymptotic replica equations for matrix compressed sensing are the same as those for a related but formally different problem of matrix factorization.
Compressive video sensing with side information.
Yuan, Xin; Sun, Yangyang; Pang, Shuo
2017-04-01
Our temporally compressive imaging system reconstructs a high-speed image sequence from a single, coded snapshot. The reconstruction quality, similar to that of other compressive sensing systems, often depends on the structure of the measurement, as well as the choice of regularization. In this paper, we report a compressive video system that also captures the side information to aid in the reconstruction of high-speed scenes. The integration of the side information not only improves the quality of reconstruction, but also reduces the dependence of the reconstruction on regularization. We have implemented a system prototype that splits the field of view of a single camera into two channels: one channel captures the coded, low-frame-rate measurement for high-speed video reconstruction, and the other channel captures a direct measurement without coding as the side information. A joint reconstruction model is developed to recover the high-speed videos from the two channels. By analyzing both the experimental and the simulation results, the reconstructions with side information have demonstrated superior performances in terms of both the peak signal-to-noise ratio and structural similarity.
Comprehensive Space-Object Characterization using Spectrally Compressive Polarimetric Sensing
2015-04-08
Space Object Characterization using Spectrally Compressive Polarimetric Sensing 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-11-1-0194 5c. PROGRAM...images. 15. SUBJECT TERMS Compressed spectral-polarimetric sensing , shape parameterization and reconstruction, Bayesian image analysis, statistical...Object Characterization using Spectrally Compressive Polarimetric Sensing Prof. S. Prasad, U. New Mexico, PI with contributions from the co-PIs, Prof
2014-11-10
AFRL-OSR-VA-TR-2014-0305 Frames in Compressive Sensing and Approximate Signal Recovery Pertaining to Physical Sensing Matrices Peter Casazza...in Compressive Sensing and Approximate Signal Recovery Pertaining to Physical Sensing Matrices. FA9550-11-1-0245 Casazza, Peter, Ph.D. The...of measurements). The method is based on a sparse signal reconstruction technique of null space tuning in the context of compressed sensing and
Compressed sensing recovery via nonconvex shrinkage penalties
Woodworth, Joseph; Chartrand, Rick
2016-07-01
The {{\\ell }}0 minimization of compressed sensing is often relaxed to {{\\ell }}1, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses. Recent work has derived a general class of shrinkages and associated nonconvex penalties that better approximate the original {{\\ell }}0 penalty and empirically can recover the original solution from fewer measurements. We specifically examine p-shrinkage and firm thresholding. In this work, we prove that given data and a measurement matrix from a broad class of matrices, one can choose parameters for these classes of shrinkages to guarantee exact recovery of the sparsest solution. We further prove convergence of the algorithm iterative p-shrinkage (IPS) for solving one such relaxed problem.
Robust facial expression recognition via compressive sensing.
Zhang, Shiqing; Zhao, Xiaoming; Lei, Bicheng
2012-01-01
Recently, compressive sensing (CS) has attracted increasing attention in the areas of signal processing, computer vision and pattern recognition. In this paper, a new method based on the CS theory is presented for robust facial expression recognition. The CS theory is used to construct a sparse representation classifier (SRC). The effectiveness and robustness of the SRC method is investigated on clean and occluded facial expression images. Three typical facial features, i.e., the raw pixels, Gabor wavelets representation and local binary patterns (LBP), are extracted to evaluate the performance of the SRC method. Compared with the nearest neighbor (NN), linear support vector machines (SVM) and the nearest subspace (NS), experimental results on the popular Cohn-Kanade facial expression database demonstrate that the SRC method obtains better performance and stronger robustness to corruption and occlusion on robust facial expression recognition tasks.
Optimized Projection Matrix for Compressive Sensing
Jianping Xu
2010-01-01
Full Text Available Compressive sensing (CS is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.
A Compressed Sensing Perspective of Hippocampal Function
Panagiotis ePetrantonakis
2014-08-01
Full Text Available Hippocampus is one of the most important information processing units in the brain. Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex. Here, we review evidence of the hypothesis that information flow and processing in the hippocampus complies with the principles of Compressed Sensing (CS. The CS theory comprises a mathematical framework that describes how and under which conditions, restricted sampling of information (data set can lead to condensed, yet concise, forms of the initial, subsampled information entity (i.e. of the original data set. In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes. This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.
Quantum Compressed Sensing Using 2-Designs
Liu, Yi-Kai; Kimmel, Shelby
We develop a method for quantum process tomography that combines the efficiency of compressed sensing with the robustness of randomized benchmarking. Our method is robust to state preparation and measurement errors, and it achieves a quadratic speedup over conventional tomography when the unknown process is a generic unitary evolution. Our method is based on PhaseLift, a convex programming technique for phase retrieval. We show that this method achieves approximate recovery of almost all signals, using measurements sampled from spherical or unitary 2-designs. This is the first positive result on PhaseLift using 2-designs. We also show that exact recovery of all signals is possible using measurements sampled from unitary 4-designs. Previous positive results for PhaseLift required spherical 4-designs, while PhaseLift was known to fail in certain cases when using spherical 2-designs.
Multichannel compressive sensing MRI using noiselet encoding.
Kamlesh Pawar
Full Text Available The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS. In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.
Multichannel compressive sensing MRI using noiselet encoding.
Pawar, Kamlesh; Egan, Gary; Zhang, Jingxin
2015-01-01
The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.
Compressed Sensing via Iterative Support Detection
Wang, Yilun
2009-01-01
We present a new compressive sensing reconstruction method "ISD". ISD addresses failed cases of L1-based construction due to insufficient measurements. ISD will learn from wrong solutions and come up with new minimization problems that return signals that are either correct or better. Specifically, from an incorrect signal ISD detects an index set I that includes components most likely to be true nonzeros, obtains a new signal x by solving min{sum_{i not in I} |x_i| : Ax = b}, and repeats such support detection and minimization using latest x and I from one another until convergence. We introduce an efficient implementation of ISD, called threshold-ISD, for recovering signals with fast decaying distributions of nonzeros from compressive measurements. Numerical experiments show that threshold-ISD has significant overall advantages over the classical L1 minimization approach, as well as two other state-of-the-art algorithms such as the iterative reweighted L1 minimization algorithm (IRL1) and the iterative rewe...
Detection Performance of Compressive Sensing Applied to Radar
Anitori, L.; Otten, M.P.G.; Hoogeboom, P.
2011-01-01
In this paper some results are presented on detection performance of radar using Compressive Sensing. Compressive sensing is a recently developed theory which allows reconstruction of sparse signals with a number of measurements much lower than implied by the Nyquist rate. In this work the behavior
Structure Assisted Compressed Sensing Reconstruction of Undersampled AFM Images
Oxvig, Christian Schou; Arildsen, Thomas; Larsen, Torben
2017-01-01
The use of compressed sensing in atomic force microscopy (AFM) can potentially speed-up image acquisition, lower probe-specimen interaction, or enable super resolution imaging. The idea in compressed sensing for AFM is to spatially undersample the specimen, i.e. only acquire a small fraction...
False Alarm Probability Estimation for Compressive Sensing Radar
Anitori, L.; Otten, M.P.G.; Hoogeboom, P.
2011-01-01
In this paper false alarm probability (FAP) estimation of a radar using Compressive Sensing (CS) in the frequency domain is investigated. Compressive Sensing is a recently proposed technique which allows reconstruction of sparse signal from sub-Nyquist rate measurements. The estimation of the FAP is
Research on compressive fusion for remote sensing images
Yang, Senlin; Wan, Guobin; Li, Yuanyuan; Zhao, Xiaoxia; Chong, Xin
2014-02-01
A compressive fusion of remote sensing images is presented based on the block compressed sensing (BCS) and non-subsampled contourlet transform (NSCT). Since the BCS requires small memory space and enables fast computation, firstly, the images with large amounts of data can be compressively sampled into block images with structured random matrix. Further, the compressive measurements are decomposed with NSCT and their coefficients are fused by a rule of linear weighting. And finally, the fused image is reconstructed by the gradient projection sparse reconstruction algorithm, together with consideration of blocking artifacts. The field test of remote sensing images fusion shows the validity of the proposed method.
Application of Compressive Sensing to Gravitational Microlensing Experiments
Korde-Patel, Asmita; Barry, Richard K.; Mohsenin, Tinoosh
2016-01-01
Compressive Sensing is an emerging technology for data compression and simultaneous data acquisition. This is an enabling technique for significant reduction in data bandwidth, and transmission power and hence, can greatly benefit spaceflight instruments. We apply this process to detect exoplanets via gravitational microlensing. We experiment with various impact parameters that describe microlensing curves to determine the effectiveness and uncertainty caused by Compressive Sensing. Finally, we describe implications for spaceflight missions.
Compressed Measurements Based Spectrum Sensing for Wideband Cognitive Radio Systems
Taha A. Khalaf
2015-01-01
Full Text Available Spectrum sensing is the most important component in the cognitive radio (CR technology. Spectrum sensing has considerable technical challenges, especially in wideband systems where higher sampling rates are required which increases the complexity and the power consumption of the hardware circuits. Compressive sensing (CS is successfully deployed to solve this problem. Although CS solves the higher sampling rate problem, it does not reduce complexity to a large extent. Spectrum sensing via CS technique is performed in three steps: sensing compressed measurements, reconstructing the Nyquist rate signal, and performing spectrum sensing on the reconstructed signal. Compressed detectors perform spectrum sensing from the compressed measurements skipping the reconstruction step which is the most complex step in CS. In this paper, we propose a novel compressed detector using energy detection technique on compressed measurements sensed by the discrete cosine transform (DCT matrix. The proposed algorithm not only reduces the computational complexity but also provides a better performance than the traditional energy detector and the traditional compressed detector in terms of the receiver operating characteristics. We also derive closed form expressions for the false alarm and detection probabilities. Numerical results show that the analytical expressions coincide with the exact probabilities obtained from simulations.
Is "Compressed Sensing" compressive? Can it beat the Nyquist Sampling Approach?
Yaroslavsky, L
2015-01-01
Measurement redundancy required for sampling and restoration of signals/images using "Compressed sensing (sampling)" techniques is compared with that of their more traditional alternatives. It is shown that "Compressed sensing" is not more compressive than the conventional sampling and that it is inferior in this respect to other available methods of sampling with reduced redundancy such as DPCM coding or random sparse sampling and restoration of image band-limited approximations. It is also shown that assertions that "Compressed sensing" can beat the Nyquist sampling approach are rooted in misinterpretation of the sampling theory.
Estimating Unknown Sparsity in Compressed Sensing
Lopes, Miles E
2012-01-01
Within the framework of compressed sensing, many theoretical guarantees for signal reconstruction require that the number of linear measurements $n$ exceed the sparsity ||x||_0 of the unknown signal x\\in\\R^p. However, if the sparsity ||x||_0 is unknown, the choice of $n$ remains problematic. This paper considers the problem of estimating the unknown degree of sparsity of $x$ with only a small number of linear measurements. Although we show that estimation of ||x||_0 is generally intractable in this framework, we consider an alternative measure of sparsity s(x):=\\frac{\\|x\\|_1^2}{\\|x\\|_2^2}, which is a sharp lower bound on ||x||_0, and is more amenable to estimation. When $x$ is a non-negative vector, we propose a computationally efficient estimator \\hat{s}(x), and use non-asymptotic methods to bound the relative error of \\hat{s}(x) in terms of a finite number of measurements. Remarkably, the quality of estimation is \\emph{dimension-free}, which ensures that \\hat{s}(x) is well-suited to the high-dimensional reg...
Compressed Sensing, Pseudodictionary-Based, Superresolution Reconstruction
Chun-mei Li
2016-01-01
Full Text Available The spatial resolution of digital images is the critical factor that affects photogrammetry precision. Single-frame, superresolution, image reconstruction is a typical underdetermined, inverse problem. To solve this type of problem, a compressive, sensing, pseudodictionary-based, superresolution reconstruction method is proposed in this study. The proposed method achieves pseudodictionary learning with an available low-resolution image and uses the K-SVD algorithm, which is based on the sparse characteristics of the digital image. Then, the sparse representation coefficient of the low-resolution image is obtained by solving the norm of l0 minimization problem, and the sparse coefficient and high-resolution pseudodictionary are used to reconstruct image tiles with high resolution. Finally, single-frame-image superresolution reconstruction is achieved. The proposed method is applied to photogrammetric images, and the experimental results indicate that the proposed method effectively increase image resolution, increase image information content, and achieve superresolution reconstruction. The reconstructed results are better than those obtained from traditional interpolation methods in aspect of visual effects and quantitative indicators.
Inverse lithography source optimization via compressive sensing.
Song, Zhiyang; Ma, Xu; Gao, Jie; Wang, Jie; Li, Yanqiu; Arce, Gonzalo R
2014-06-16
Source optimization (SO) has emerged as a key technique for improving lithographic imaging over a range of process variations. Current SO approaches are pixel-based, where the source pattern is designed by solving a quadratic optimization problem using gradient-based algorithms or solving a linear programming problem. Most of these methods, however, are either computational intensive or result in a process window (PW) that may be further extended. This paper applies the rich theory of compressive sensing (CS) to develop an efficient and robust SO method. In order to accelerate the SO design, the source optimization is formulated as an underdetermined linear problem, where the number of equations can be much less than the source variables. Assuming the source pattern is a sparse pattern on a certain basis, the SO problem is transformed into a l1-norm image reconstruction problem based on CS theory. The linearized Bregman algorithm is applied to synthesize the sparse optimal source pattern on a representation basis, which effectively improves the source manufacturability. It is shown that the proposed linear SO formulation is more effective for improving the contrast of the aerial image than the traditional quadratic formulation. The proposed SO method shows that sparse-regularization in inverse lithography can indeed extend the PW of lithography systems. A set of simulations and analysis demonstrate the superiority of the proposed SO method over the traditional approaches.
Bacterial community reconstruction using compressed sensing.
Amir, Amnon; Zuk, Or
2011-11-01
Bacteria are the unseen majority on our planet, with millions of species and comprising most of the living protoplasm. We propose a novel approach for reconstruction of the composition of an unknown mixture of bacteria using a single Sanger-sequencing reaction of the mixture. Our method is based on compressive sensing theory, which deals with reconstruction of a sparse signal using a small number of measurements. Utilizing the fact that in many cases each bacterial community is comprised of a small subset of all known bacterial species, we show the feasibility of this approach for determining the composition of a bacterial mixture. Using simulations, we show that sequencing a few hundred base-pairs of the 16S rRNA gene sequence may provide enough information for reconstruction of mixtures containing tens of species, out of tens of thousands, even in the presence of realistic measurement noise. Finally, we show initial promising results when applying our method for the reconstruction of a toy experimental mixture with five species. Our approach may have a potential for a simple and efficient way for identifying bacterial species compositions in biological samples. All supplementary data and the MATLAB code are available at www.broadinstitute.org/?orzuk/publications/BCS/.
Energy Preserved Sampling for Compressed Sensing MRI
Yudong Zhang
2014-01-01
Full Text Available The sampling patterns, cost functions, and reconstruction algorithms play important roles in optimizing compressed sensing magnetic resonance imaging (CS-MRI. Simple random sampling patterns did not take into account the energy distribution in k-space and resulted in suboptimal reconstruction of MR images. Therefore, a variety of variable density (VD based samplings patterns had been developed. To further improve it, we propose a novel energy preserving sampling (ePRESS method. Besides, we improve the cost function by introducing phase correction and region of support matrix, and we propose iterative thresholding algorithm (ITA to solve the improved cost function. We evaluate the proposed ePRESS sampling method, improved cost function, and ITA reconstruction algorithm by 2D digital phantom and 2D in vivo MR brains of healthy volunteers. These assessments demonstrate that the proposed ePRESS method performs better than VD, POWER, and BKO; the improved cost function can achieve better reconstruction quality than conventional cost function; and the ITA is faster than SISTA and is competitive with FISTA in terms of computation time.
Visually weighted reconstruction of compressive sensing MRI.
Oh, Heeseok; Lee, Sanghoon
2014-04-01
Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ℓ1 norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.
Multimode waveguide speckle patterns for compressive sensing.
Valley, George C; Sefler, George A; Justin Shaw, T
2016-06-01
Compressive sensing (CS) of sparse gigahertz-band RF signals using microwave photonics may achieve better performances with smaller size, weight, and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a sub-Gaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with a performance similar to that of the multimode fiber. The CS simulations show that all measured and calculated speckle MMs exhibit a robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse gigahertz-band RF signals using CS.
Informationally complete measurements from compressed sensing methodology
Kalev, Amir; Riofrio, Carlos; Kosut, Robert; Deutsch, Ivan
2015-03-01
Compressed sensing (CS) is a technique to faithfully estimate an unknown signal from relatively few data points when the measurement samples satisfy a restricted isometry property (RIP). Recently this technique has been ported to quantum information science to perform tomography with a substantially reduced number of measurement settings. In this work we show that the constraint that a physical density matrix is positive semidefinite provides a rigorous connection between the RIP and the informational completeness (IC) of a POVM used for state tomography. This enables us to construct IC measurements that are robust to noise using tools provided by the CS methodology. The exact recovery no longer hinges on a particular convex optimization program; solving any optimization, constrained on the cone of positive matrices, effectively results in a CS estimation of the state. From a practical point of view, we can therefore employ fast algorithms developed to handle large dimensional matrices for efficient tomography of quantum states of a large dimensional Hilbert space. Supported by the National Science Foundation.
Energy-efficient sensing in wireless sensor networks using compressed sensing.
Razzaque, Mohammad Abdur; Dobson, Simon
2014-02-12
Sensing of the application environment is the main purpose of a wireless sensor network. Most existing energy management strategies and compression techniques assume that the sensing operation consumes significantly less energy than radio transmission and reception. This assumption does not hold in a number of practical applications. Sensing energy consumption in these applications may be comparable to, or even greater than, that of the radio. In this work, we support this claim by a quantitative analysis of the main operational energy costs of popular sensors, radios and sensor motes. In light of the importance of sensing level energy costs, especially for power hungry sensors, we consider compressed sensing and distributed compressed sensing as potential approaches to provide energy efficient sensing in wireless sensor networks. Numerical experiments investigating the effectiveness of compressed sensing and distributed compressed sensing using real datasets show their potential for efficient utilization of sensing and overall energy costs in wireless sensor networks. It is shown that, for some applications, compressed sensing and distributed compressed sensing can provide greater energy efficiency than transform coding and model-based adaptive sensing in wireless sensor networks.
Can compressed sensing beat the Nyquist sampling rate?
Yaroslavsky, L
2015-01-01
Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that, in a realistic scenario for signals that are believed to be sparse, one can achieve a substantially larger saving than compressing sensing can. It is also shown that frequent assertions in the literature that "Compressed sensing" can beat the Nyquist sampling approach are misleading substitution of terms and are rooted in misinterpretation of the sampling theory.
Shale nanopore reconstruction with compressive sensing
Guo, Long; Xiao, Lizhi
2017-03-01
With increasing global demand for energy resources, shale gas has been paid considerable attention in recent years. Nanopore geometry is the basis for all microscopic rock physics and petrophysical numerical experiments for shale. At present, nano digital cores can be acquired via thin section reconstruction, nanometer-scale x-ray computed tomography (nano-CT), and focused ion beam and scanning electron microscopy (FIB-SEM). FIB-SEM detects nanoscale pores in the xy-plane with a resolution of up to 0.8 nm voxel‑1, and it is usually provides higher resolution than nano-CT. The main workload associated with FIB-SEM is the need to recut the sample many times and scan every section, with these then being overlaid to create a three-dimensional (3D) pore model. Each cutting distance can be ascertained, but this cannot be controlled precisely because of the fundamental limits of focused ion beams. Many interpolation methods can be used to fit the anisotropy resolution. However, these methods can also alter the geometry of the pores. Nanopores that are close to the limiting resolution are particularly susceptible to stretching. Linear interpolation is likely to lengthen the pores in the low-resolution direction. The subsequent calculation of sensitive physical attributes will be affected by geometric alterations. Through foundational work in the compressive sensing (CS) method, we present a reconstruction workflow for maintaining the pore shape using prior knowledge and reliable information. The images are reassembled with equal distance, so the nanoscale structures can have a resolution of unity in three dimensions.
Joint Sparsity and Frequency Estimation for Spectral Compressive Sensing
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2014-01-01
Parameter estimation from compressively sensed signals has recently received some attention. We here also consider this problem in the context of frequency sparse signals which are encountered in many application. Existing methods perform the estimation using finite dictionaries or incorporate...
Signal Recovery in Compressive Sensing via Multiple Sparsifying Bases
Wijewardhana, U. L.; Belyaev, Evgeny; Codreanu, M.
2017-01-01
Compressive sensing theory asserts that, under certain conditions, a high dimensional but compressible signal can be recovered from a small number of random linear projections by utilizing computationally efficient algorithms. The a priori knowledge of the basis in which the signal of interest is...... estimates of a 2-D signal (image) from compressive measurements utilizing multiple sparsifying bases as well as the fact that the images usually have a sparse gradient....
Structured sublinear compressive sensing via dense belief propagation
Dai, Wei; Pham, Hoa Vin
2011-01-01
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with Orthogonal Matching Pursuit (OMP) methods. For more elaborate greedy reconstruction schemes, we propose a new family of dense list decoding belief propagation algorithms, as well as reinforced- and multiple-basis belief propagation algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity-performance tradeoffs for very sparse signal vectors.
Phase Imaging: A Compressive Sensing Approach
Schneider, Sebastian; Stevens, Andrew; Browning, Nigel D.; Pohl, Darius; Nielsch, Kornelius; Rellinghaus, Bernd
2017-07-01
Since Wolfgang Pauli posed the question in 1933, whether the probability densities |Ψ(r)|² (real-space image) and |Ψ(q)|² (reciprocal space image) uniquely determine the wave function Ψ(r) [1], the so called Pauli Problem sparked numerous methods in all fields of microscopy [2, 3]. Reconstructing the complete wave function Ψ(r) = a(r)e-iφ(r) with the amplitude a(r) and the phase φ(r) from the recorded intensity enables the possibility to directly study the electric and magnetic properties of the sample through the phase. In transmission electron microscopy (TEM), electron holography is by far the most established method for phase reconstruction [4]. Requiring a high stability of the microscope, next to the installation of a biprism in the TEM, holography cannot be applied to any microscope straightforwardly. Recently, a phase retrieval approach was proposed using conventional TEM electron diffractive imaging (EDI). Using the SAD aperture as reciprocal-space constraint, a localized sample structure can be reconstructed from its diffraction pattern and a real-space image using the hybrid input-output algorithm [5]. We present an alternative approach using compressive phase-retrieval [6]. Our approach does not require a real-space image. Instead, random complimentary pairs of checkerboard masks are cut into a 200 nm Pt foil covering a conventional TEM aperture (cf. Figure 1). Used as SAD aperture, subsequently diffraction patterns are recorded from the same sample area. Hereby every mask blocks different parts of gold particles on a carbon support (cf. Figure 2). The compressive sensing problem has the following formulation. First, we note that the complex-valued reciprocal-space wave-function is the Fourier transform of the (also complex-valued) real-space wave-function, Ψ(q) = F[Ψ(r)], and subsequently the diffraction pattern image is given by |Ψ(q)|2 = |F[Ψ(r)]|2. We want to find Ψ(r) given a few differently coded diffraction pattern measurements yn
Compression and Encryption of Search Survey Gamma Spectra using Compressive Sensing
Heifetz, Alexander
2014-01-01
We have investigated the application of Compressive Sensing (CS) computational method to simultaneous compression and encryption of gamma spectra measured with NaI(Tl) detector during wide area search survey applications. Our numerical experiments have demonstrated secure encryption and nearly lossless recovery of gamma spectra coded and decoded with CS routines.
Overview of compressive sensing techniques applied in holography [Invited].
Rivenson, Yair; Stern, Adrian; Javidi, Bahram
2013-01-01
In recent years compressive sensing (CS) has been successfully introduced in digital holography (DH). Depending on the ability to sparsely represent an object, the CS paradigm provides an accurate object reconstruction framework from a relatively small number of encoded signal samples. DH has proven to be an efficient and physically realizable sensing modality that can exploit the benefits of CS. In this paper, we provide an overview of the theoretical guidelines for application of CS in DH and demonstrate the benefits of compressive digital holographic sensing.
Spread spectrum compressed sensing MRI using chirp radio frequency pulses
Qu, Xiaobo; Zhuang, Xiaoxing; Yan, Zhiyu; Guo, Di; Chen, Zhong
2013-01-01
Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). Recently, a spread spectrum compressed sensing MRI method modulates an image with a quadratic phase. It performs better than the conventional compressed sensing MRI with variable density sampling, since the coherence between the sensing and sparsity bases are reduced. However, spread spectrum in that method is implemented via a shim coil which limits its modulation intensity and is not convenient to operate. In this letter, we propose to apply chirp (linear frequency-swept) radio frequency pulses to easily control the spread spectrum. To accelerate the image reconstruction, an alternating direction algorithm is modified by exploiting the complex orthogonality of the quadratic phase encoding. Reconstruction on the acquired data demonstrates that more image features are preserved using the proposed approach than those of conventional CS-MRI.
Compressive sensing by learning a Gaussian mixture model from measurements.
Yang, Jianbo; Liao, Xuejun; Yuan, Xin; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2015-01-01
Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.
Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems
Blumensath, Thomas
2012-01-01
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions similar to those required in the linear setting, the Iterative Hard Thresholding algorithm can be used to accurately recover sparse or structured signals from few non-linear observations. Similar ideas can also be developed in a more general non-linear optimisation framework. In the second part of this paper we therefore present related result that show how this can be done under sparsity and union of subspaces constraints, wh...
Compressed sensing with side information on the feasible region
Rostami, Mohammad
2013-01-01
This book discusses compressive sensing in the presence of side information. Compressive sensing is an emerging technique for efficiently acquiring and reconstructing a signal. Interesting instances of Compressive Sensing (CS) can occur when, apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In these cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of samples required for accurate reconstruction. In this book we assume availability of side information about the feasible region. The main applications investigated are image deblurring for optical imaging, 3D surface reconstruction, and reconstructing spatiotemporally correlated sources. The author shows that the side information can be used to improve the quality of the reconstruction compared to the classic...
Imaging industry expectations for compressed sensing in MRI
King, Kevin F.; Kanwischer, Adriana; Peters, Rob
2015-09-01
Compressed sensing requires compressible data, incoherent acquisition and a nonlinear reconstruction algorithm to force creation of a compressible image consistent with the acquired data. MRI images are compressible using various transforms (commonly total variation or wavelets). Incoherent acquisition of MRI data by appropriate selection of pseudo-random or non-Cartesian locations in k-space is straightforward. Increasingly, commercial scanners are sold with enough computing power to enable iterative reconstruction in reasonable times. Therefore integration of compressed sensing into commercial MRI products and clinical practice is beginning. MRI frequently requires the tradeoff of spatial resolution, temporal resolution and volume of spatial coverage to obtain reasonable scan times. Compressed sensing improves scan efficiency and reduces the need for this tradeoff. Benefits to the user will include shorter scans, greater patient comfort, better image quality, more contrast types per patient slot, the enabling of previously impractical applications, and higher throughput. Challenges to vendors include deciding which applications to prioritize, guaranteeing diagnostic image quality, maintaining acceptable usability and workflow, and acquisition and reconstruction algorithm details. Application choice depends on which customer needs the vendor wants to address. The changing healthcare environment is putting cost and productivity pressure on healthcare providers. The improved scan efficiency of compressed sensing can help alleviate some of this pressure. Image quality is strongly influenced by image compressibility and acceleration factor, which must be appropriately limited. Usability and workflow concerns include reconstruction time and user interface friendliness and response. Reconstruction times are limited to about one minute for acceptable workflow. The user interface should be designed to optimize workflow and minimize additional customer training. Algorithm
Ring artifacts correction in compressed sensing tomographic reconstruction
Paleo, Pierre
2015-01-01
We present a novel approach to handle ring artifacts correction in compressed sensing tomographic reconstruction. The correction is part of the reconstruction process, which differs from classical sinogram pre-processing and image post-processing techniques. The principle of compressed sensing tomographic reconstruction is presented. Then, we show that the ring artifacts correction can be integrated in the reconstruction problem formalism. We provide numerical results for both simulated and real data. This technique is included in the PyHST2 code which is used at the European Synchrotron Radiation Facility for tomographic reconstruction.
The Application of Compressive Sensing on Spectra De-noising
Mingxia Xiao
2013-10-01
Full Text Available Through the analyzing of limitations on wavelet threshold filter de-noising, this paper applies wavelet filter based on compressed sensing to reduce the signal noise of spectral signals, and compares the two methods through experiments. The results of experiments shown that the wavelet filter based on compressed sensing can effectively reduce the signal noise of spectral signal. The de-noising effect of the method is better than that of wavelet filter. The method provides a new approach for reducing the signal noise of spectral signals.
Compressed wideband spectrum sensing based on discrete cosine transform.
Wang, Yulin; Zhang, Gengxin
2014-01-01
Discrete cosine transform (DCT) is a special type of transform which is widely used for compression of speech and image. However, its use for spectrum sensing has not yet received widespread attention. This paper aims to alleviate the sampling requirements of wideband spectrum sensing by utilizing the compressive sampling (CS) principle and exploiting the unique sparsity structure in the DCT domain. Compared with discrete Fourier transform (DFT), wideband communication signal has much sparser representation and easier implementation in DCT domain. Simulation result shows that the proposed DCT-CSS scheme outperforms the conventional DFT-CSS scheme in terms of MSE of reconstruction signal, detection probability, and computational complexity.
Compressed Wideband Spectrum Sensing Based on Discrete Cosine Transform
Yulin Wang
2014-01-01
Full Text Available Discrete cosine transform (DCT is a special type of transform which is widely used for compression of speech and image. However, its use for spectrum sensing has not yet received widespread attention. This paper aims to alleviate the sampling requirements of wideband spectrum sensing by utilizing the compressive sampling (CS principle and exploiting the unique sparsity structure in the DCT domain. Compared with discrete Fourier transform (DFT, wideband communication signal has much sparser representation and easier implementation in DCT domain. Simulation result shows that the proposed DCT-CSS scheme outperforms the conventional DFT-CSS scheme in terms of MSE of reconstruction signal, detection probability, and computational complexity.
Optical frequency comb interference profilometry using compressive sensing.
Pham, Quang Duc; Hayasaki, Yoshio
2013-08-12
We describe a new optical system using an ultra-stable mode-locked frequency comb femtosecond laser and compressive sensing to measure an object's surface profile. The ultra-stable frequency comb laser was used to precisely measure an object with a large depth, over a wide dynamic range. The compressive sensing technique was able to obtain the spatial information of the object with two single-pixel fast photo-receivers, with no mechanical scanning and fewer measurements than the number of sampling points. An optical experiment was performed to verify the advantages of the proposed method.
Robust compressive sensing of sparse signals: a review
Carrillo, Rafael E.; Ramirez, Ana B.; Arce, Gonzalo R.; Barner, Kenneth E.; Sadler, Brian M.
2016-12-01
Compressive sensing generally relies on the ℓ 2 norm for data fidelity, whereas in many applications, robust estimators are needed. Among the scenarios in which robust performance is required, applications where the sampling process is performed in the presence of impulsive noise, i.e., measurements are corrupted by outliers, are of particular importance. This article overviews robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used ℓ 2 norm by M-estimators as data fidelity functions. The derived methods outperform existing compressed sensing techniques in impulsive environments, while achieving good performance in light-tailed environments, thus offering a robust framework for CS.
Diffuse optical tomography based on time-resolved compressive sensing
Farina, A.; Betcke, M.; Di Sieno, L.; Bassi, A.; Ducros, N.; Pifferi, A.; Valentini, G.; Arridge, S.; D'Andrea, C.
2017-02-01
Diffuse Optical Tomography (DOT) can be described as a highly multidimensional problem generating a huge data set with long acquisition/computational times. Biological tissue behaves as a low pass filter in the spatial frequency domain, hence compressive sensing approaches, based on both patterned illumination and detection, are useful to reduce the data set while preserving the information content. In this work, a multiple-view time-domain compressed sensing DOT system is presented and experimentally validated on non-planar tissue-mimicking phantoms containing absorbing inclusions.
Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization
Markovich, Thomas; Sanders, Jacob N; Aspuru-Guzik, Alan
2015-01-01
Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in order to discover when and how each method can be used most profitably. We find that filter diagonalization provides the best results for Lorentzian signals, while compressed sensing and super-resolution perform better for arbitrary signals.
Compressed Sensing for Thoracic MRI with Partial Random Circulant Matrices
Hideaki Haneishi
2012-03-01
Full Text Available The use of Circulant matrix as the sensing matrix in compressed sensing (CS scheme has recently been proposed to overcome the limitation of random or partial Fourier matrices. Aside from reducing computational complexity, the use of circulant matrix for MR image offers the feasibility in hardware implementations. This paper presents the simulation of compressed sensing for thoracic MR imaging with circulant matrix as the sensing matrix. The comparisons of reconstruction of three different type MR images using circulant matrix are investigated in term of number of samples, number of iteration and signal to noise ratio (SNR. The simulation results showed that Circulant Matrix works efficiently for encoding the MR image of respiratory organ, especially for smooth and sparse image in spatial domain.
Yu, Hengyong; Wang, Ge
2009-07-01
The authors would like to add some missing references. On page 2799, lines 15 and 16 from the bottom should read 'Specifically, the algorithm can be summarized in the following pseudo-code (Candes and Romberg 2005, Candes et al 2006, Sidky et al 2006, Chen et al 2008, Sidky and Pan 2008)'. References Candes E J and Romberg J 2005 Signal recovery from random projections Computational Imaging III; Proc. SPIE 5764 76-86 Candes E J, Romberg J and Tao T 2006 Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information IEEE Trans. Inf. Theory 52 489-509 Chen G H, Tang J and Leng S 2008 Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets Med. Phys. 35 660-3 Sidky E Y, Kao C M and Pan X C 2006 Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT J. X-ray Sci. Technol. 14 119-39 Sidky E Y and Pan X C 2008 Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization Phys. Med. Biol. 53 4777-807
When 'exact recovery' is exact recovery in compressed sensing simulation
Sturm, Bob L.
2012-01-01
In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...... for a given distribution of \\(\\vx\\)? We show that, in a best case scenario, \\(\\epsilon^2\\) sets a maximum allowed missed detection rate in a majority sense....
Compressive sensing scalp EEG signals: implementations and practical performance.
Abdulghani, Amir M; Casson, Alexander J; Rodriguez-Villegas, Esther
2012-11-01
Highly miniaturised, wearable computing and communication systems allow unobtrusive, convenient and long term monitoring of a range of physiological parameters. For long term operation from the physically smallest batteries, the average power consumption of a wearable device must be very low. It is well known that the overall power consumption of these devices can be reduced by the inclusion of low power consumption, real-time compression of the raw physiological data in the wearable device itself. Compressive sensing is a new paradigm for providing data compression: it has shown significant promise in fields such as MRI; and is potentially suitable for use in wearable computing systems as the compression process required in the wearable device has a low computational complexity. However, the practical performance very much depends on the characteristics of the signal being sensed. As such the utility of the technique cannot be extrapolated from one application to another. Long term electroencephalography (EEG) is a fundamental tool for the investigation of neurological disorders and is increasingly used in many non-medical applications, such as brain-computer interfaces. This article investigates in detail the practical performance of different implementations of the compressive sensing theory when applied to scalp EEG signals.
Compressive Sensing Radar: Simulation and Experiments for Target Detection
Anitori, L.; Rossum, W.L. van; Otten, M.P.G.; Maleki, A.; Baraniuk, R.
2013-01-01
In this paper the performance of a combined Constant False Alarm Rate (CFAR) Compressive Sensing (CS) radar detector is investigated Using the properties of the Complex Approximate Message Passing (CAMP) algorithm, it is demonstratedthat the behavior of the CFAR processor can be separated from that
Compressive sensing for high resolution profiles with enhanced Doppler performance
Anitori, L.; Hoogeboom, P.; Chevalier, F. Le; Otten, M.P.G.
2012-01-01
In this paper we demonstrate how Compressive Sensing (CS) can be used in pulse-Doppler radars to improve the Doppler performance while preserving range resolution. We investigate here two types of stepped frequency waveforms, the coherent frequency bursts and successive frequency ramps, which can be
Photoacoustic image reconstruction based on Bayesian compressive sensing algorithm
Mingjian Sun; Naizhang Feng; Yi Shen; Jiangang Li; Liyong Ma; Zhenghua Wu
2011-01-01
The photoacoustic tomography (PAT) method, based on compressive sensing (CS) theory, requires that,for the CS reconstruction, the desired image should have a sparse representation in a known transform domain. However, the sparsity of photoacoustic signals is destroyed because noises always exist. Therefore,the original sparse signal cannot be effectively recovered using the general reconstruction algorithm. In this study, Bayesian compressive sensing (BCS) is employed to obtain highly sparse representations of photoacoustic images based on a set of noisy CS measurements. Results of simulation demonstrate that the BCS-reconstructed image can achieve superior performance than other state-of-the-art CS-reconstruction algorithms.%@@ The photoacoustic tomography (PAT) method, based on compressive sensing (CS) theory, requires that,for the CS reconstruction, the desired image should have a sparse representation in a known transform domain.However, the sparsity of photoacoustic signals is destroyed because noises always exist.Therefore,the original sparse signal cannot be effectively recovered using the general reconstruction algorithm.In this study, Bayesian compressive sensing (BCS) is employed to obtain highly sparse representations of photoacoustic inages based on a set of noisy CS measurements.Results of simulation demonstrate that the BCS-reconstructed image can achieve superior performance than other state-of-the-art CS-reconstruction algorithms.
OPTIMAL WAVELET FILTER DESIGN FOR REMOTE SENSING IMAGE COMPRESSION
Yang Guoan; Zheng Nanning; Guo Shugang
2007-01-01
A new approach for designing the Biorthogonal Wavelet Filter Bank (BWFB) for the purpose of image compression is presented in this letter. The approach is decomposed into two steps.First, an optimal filter bank is designed in theoretical sense based on Vaidyanathan's coding gain criterion in SubBand Coding (SBC) system. Then the above filter bank is optimized based on the criterion of Peak Signal-to-Noise Ratio (PSNR) in JPEG2000 image compression system, resulting in a BWFB in practical application sense. With the approach, a series of BWFB for a specific class of applications related to image compression, such as remote sensing images, can be fast designed. Here,new 5/3 BWFB and 9/7 BWFB are presented based on the above approach for the remote sensing image compression applications. Experiments show that the two filter banks are equally performed with respect to CDF 9/7 and LT 5/3 filter in JPEG2000 standard; at the same time, the coefficients and the lifting parameters of the lifting scheme are all rational, which bring the computational advantage, and the ease for VLSI implementation.
Design and analysis of compressed sensing radar detectors
Anitori, L.; Maleki, A.; Otten, M.P.G.; Baraniuk, R.G.; Hoogeboom, P.
2013-01-01
We consider the problem of target detection from a set of Compressed Sensing (CS) radar measurements corrupted by additive white Gaussian noise. We propose two novel architectures and compare their performance by means of Receiver Operating Characteristic (ROC) curves. Using asymptotic arguments and
Low power real-time data acquisition using compressive sensing
Powers, Linda S.; Zhang, Yiming; Chen, Kemeng; Pan, Huiqing; Wu, Wo-Tak; Hall, Peter W.; Fairbanks, Jerrie V.; Nasibulin, Radik; Roveda, Janet M.
2017-05-01
New possibilities exist for the development of novel hardware/software platforms havin g fast data acquisition capability with low power requirements. One application is a high speed Adaptive Design for Information (ADI) system that combines the advantages of feature-based data compression, low power nanometer CMOS technology, and stream computing [1]. We have developed a compressive sensing (CS) algorithm which linearly reduces the data at the analog front end, an approach which uses analog designs and computations instead of smaller feature size transistors for higher speed and lower power. A level-crossing sampling approach replaces Nyquist sampling. With an in-memory design, the new compressive sensing based instrumentation performs digitization only when there is enough variation in the input and when the random selection matrix chooses this input.
Compressive sensing spectrometry based on liquid crystal devices.
August, Yitzhak; Stern, Adrian
2013-12-01
We present a new type of compressive spectroscopy technique employing a liquid crystal (LC) phase retarder. A tunable LC cell is used in a manner compliant with the compressive sensing (CS) framework to significantly reduce the spectral scanning effort. The presented optical spectrometer consists of a single LC phase retarder combined with a single photo detector, where the LC phase retarder is used to modulate the input spectrum and the photodiode is used to measure the transmitted spectral signal. Sequences of measurements are taken, where each measurement is done with a different state of the retarder. Then, the set of photodiode measurements is used as input data to a CS solver algorithm. We demonstrate numerally compressive spectral sensing with approximately ten times fewer measurements than with an equivalent conventional spectrometer.
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions
Li, Xiaodong
2011-01-01
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \\times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tractable \\ell1 minimimization even if a positive fraction of the measurements are arbitrarily corrupted, provided the number of nonzero entries in x is O(m/(log(n/m) + 1)). 2) In the very general sensing model introduced in "A probabilistic and RIPless theory of compressed sensing" by Candes and Plan, and assuming a positive fraction of corrupted measurements, exact recovery still holds if the signal now has O(m/(log^2 n)) nonzero entries. 3) Finally, we prove that one can recover an n \\times n low-rank matrix from m corrupted sampled entries by tractable optimization provided the rank is on the order of O(m/(n log^2 n)); again, this holds when there is a positive fraction of corrupted samples.
3D passive integral imaging using compressive sensing.
Cho, Myungjin; Mahalanobis, Abhijit; Javidi, Bahram
2012-11-19
Passive 3D sensing using integral imaging techniques has been well studied in the literature. It has been shown that a scene can be reconstructed at various depths using several 2D elemental images. This provides the ability to reconstruct objects in the presence of occlusions, and passively estimate their 3D profile. However, high resolution 2D elemental images are required for high quality 3D reconstruction. Compressive Sensing (CS) provides a way to dramatically reduce the amount of data that needs to be collected to form the elemental images, which in turn can reduce the storage and bandwidth requirements. In this paper, we explore the effects of CS in acquisition of the elemental images, and ultimately on passive 3D scene reconstruction and object recognition. Our experiments show that the performance of passive 3D sensing systems remains robust even when elemental images are recovered from very few compressive measurements.
Chen, Tinghuan; Zhang, Meng; Wu, Jianhui; Yuen, Chau; Tong, You
2016-10-01
Because of simple encryption and compression procedure in single step, compressed sensing (CS) is utilized to encrypt and compress an image. Difference of sparsity levels among blocks of the sparsely transformed image degrades compression performance. In this paper, motivated by this difference of sparsity levels, we propose an encryption and compression approach combining Kronecker CS (KCS) with elementary cellular automata (ECA). In the first stage of encryption, ECA is adopted to scramble the sparsely transformed image in order to uniformize sparsity levels. A simple approximate evaluation method is introduced to test the sparsity uniformity. Due to low computational complexity and storage, in the second stage of encryption, KCS is adopted to encrypt and compress the scrambled and sparsely transformed image, where the measurement matrix with a small size is constructed from the piece-wise linear chaotic map. Theoretical analysis and experimental results show that our proposed scrambling method based on ECA has great performance in terms of scrambling and uniformity of sparsity levels. And the proposed encryption and compression method can achieve better secrecy, compression performance and flexibility.
A DISTRIBUTED COMPRESSED SENSING APPROACH FOR SPEECH SIGNAL DENOISING
Ji Yunyun; Yang Zhen
2011-01-01
Compressed sensing,a new area of signal processing rising in recent years,seeks to minimize the number of samples that is necessary to be taken from a signal for precise reconstruction.The precondition of compressed sensing theory is the sparsity of signals.In this paper,two methods to estimate the sparsity level of the signal are formulated.And then an approach to estimate the sparsity level directly from the noisy signal is presented.Moreover,a scheme based on distributed compressed sensing for speech signal denoising is described in this work which exploits multiple measurements of the noisy speech signal to construct the block-sparse data and then reconstruct the original speech signal using block-sparse model-based Compressive Sampling Matching Pursuit (CoSaMP) algorithm.Several simulation results demonstrate the accuracy of the estimated sparsity level and that this denoising system for noisy speech signals can achieve favorable performance especially when speech signals suffer severe noise.
Cooperative Spectrum Sensing and Localization in Cognitive Radio Systems Using Compressed Sensing
Wael Guibène
2013-01-01
Full Text Available We propose to fuse two main enabling features in cognitive radio systems (CRS: spectrum sensing and location awareness in a single compressed sensing based formalism. In this way, we exploit sparse characteristics of primary units to be detected, both in terms of spectrum used and location occupied. The compressed sensing approach also allows to overcome hardware limitations, in terms of the incapacity to acquire measurements and signals at the Nyquist rate when the spectrum to be scanned is large. Simulation results for realistic network topologies and different compressed sensing reconstruction algorithms testify to the performance and the feasibility of the proposed technique to enable in a single formalism the two main features of cognitive sensor networks.
CMOS low data rate imaging method based on compressed sensing
Xiao, Long-long; Liu, Kun; Han, Da-peng
2012-07-01
Complementary metal-oxide semiconductor (CMOS) technology enables the integration of image sensing and image compression processing, making improvements on overall system performance possible. We present a CMOS low data rate imaging approach by implementing compressed sensing (CS). On the basis of the CS framework, the image sensor projects the image onto a separable two-dimensional (2D) basis set and measures the corresponding coefficients obtained. First, the electrical current output from the pixels in a column are combined, with weights specified by voltage, in accordance with Kirchhoff's law. The second computation is performed in an analog vector-matrix multiplier (VMM). Each element of the VMM considers the total value of each column as the input and multiplies it by a unique coefficient. Both weights and coefficients are reprogrammable through analog floating-gate (FG) transistors. The image can be recovered from a percentage of these measurements using an optimization algorithm. The percentage, which can be altered flexibly by programming on the hardware circuit, determines the image compression ratio. These novel designs facilitate image compression during the image-capture phase before storage, and have the potential to reduce power consumption. Experimental results demonstrate that the proposed method achieves a large image compression ratio and ensures imaging quality.
Compressive MUSIC: A Missing Link Between Compressive Sensing and Array Signal Processing
Kim, Jong Min; Ye, Jong Chul
2010-01-01
Multiple measurement vector (MMV) problem addresses identification of unknown input vectors that share common sparse support sets, and has many practical applications. Even though MMV problems had been traditionally addressed within the context of sensory array signal processing, recent research trend is to apply compressive sensing (CS) theory due to its capability to estimate sparse support even with insufficient number of snapshots, in which cases classical array signal processing approaches fail. However, CS approaches guarantees the accurate recovery of support in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The main contribution of the present article is, therefore, a unified approach that unveils a {missing link} between compressive sensing and array signal processing approaches for the multiple measurement vector problem. The new algorithm, which we call {\\em compressive MUSIC}, identifies the parts of su...
High-resolution three-dimensional imaging with compress sensing
Wang, Jingyi; Ke, Jun
2016-10-01
LIDAR three-dimensional imaging technology have been used in many fields, such as military detection. However, LIDAR require extremely fast data acquisition speed. This makes the manufacture of detector array for LIDAR system is very difficult. To solve this problem, we consider using compress sensing which can greatly decrease the data acquisition and relax the requirement of a detection device. To use the compressive sensing idea, a spatial light modulator will be used to modulate the pulsed light source. Then a photodetector is used to receive the reflected light. A convex optimization problem is solved to reconstruct the 2D depth map of the object. To improve the resolution in transversal direction, we use multiframe image restoration technology. For each 2D piecewise-planar scene, we move the SLM half-pixel each time. Then the position where the modulated light illuminates will changed accordingly. We repeat moving the SLM to four different directions. Then we can get four low-resolution depth maps with different details of the same plane scene. If we use all of the measurements obtained by the subpixel movements, we can reconstruct a high-resolution depth map of the sense. A linear minimum-mean-square error algorithm is used for the reconstruction. By combining compress sensing and multiframe image restoration technology, we reduce the burden on data analyze and improve the efficiency of detection. More importantly, we obtain high-resolution depth maps of a 3D scene.
Compressive sensing in a photonic link with optical integration
Chen, Ying; Yu, Xianbin; Chi, Hao
2014-01-01
In this Letter, we present a novel structure to realize photonics-assisted compressive sensing (CS) with optical integration. In the system, a spectrally sparse signal modulates a multiwavelength continuous-wave light and then is mixed with a random sequence in optical domain. The optical signal......, which is equivalent to the function of integration required in CS. A proof-of-concept experiment with four wavelengths, corresponding to a compression factor of 4, is demonstrated. More simulation results are also given to show the potential of the technique....
Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing
Zhou, Nanrun; Pan, Shumin; Cheng, Shan; Zhou, Zhihong
2016-08-01
Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.
2015-03-26
Recent Advances in Compressed Sensing : Discrete Uncertainty Principles and Fast Hyperspectral Imaging THESIS MARCH 2015 Megan E. Lewis, Second...IN COMPRESSED SENSING : DISCRETE UNCERTAINTY PRINCIPLES AND FAST HYPERSPECTRAL IMAGING THESIS Presented to the Faculty Department of Mathematics and...MARCH 2015 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENC–MS-15-M-002 RECENT ADVANCES IN COMPRESSED SENSING
Cognitive Radios Exploiting Gray Spaces via Compressed Sensing
Wieruch, Dennis; Jung, Peter; Wirth, Thomas; Dekorsy, Armin; Haustein, Thomas
2016-07-01
We suggest an interweave cognitive radio system with a gray space detector, which is properly identifying a small fraction of unused resources within an active band of a primary user system like 3GPP LTE. Therefore, the gray space detector can cope with frequency fading holes and distinguish them from inactive resources. Different approaches of the gray space detector are investigated, the conventional reduced-rank least squares method as well as the compressed sensing-based orthogonal matching pursuit and basis pursuit denoising algorithm. In addition, the gray space detector is compared with the classical energy detector. Simulation results present the receiver operating characteristic at several SNRs and the detection performance over further aspects like base station system load for practical false alarm rates. The results show, that especially for practical false alarm rates the compressed sensing algorithm are more suitable than the classical energy detector and reduced-rank least squares approach.
Sampling theory, a renaissance compressive sensing and other developments
2015-01-01
Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
Compressed Sensing with Linear Correlation Between Signal and Measurement Noise
Arildsen, Thomas; Larsen, Torben
2014-01-01
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed...... sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard...... reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low...
Blind Source Separation with Compressively Sensed Linear Mixtures
Kleinsteuber, Martin
2011-01-01
This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical Compressive Sensing (CS) theory with a linear mixing model. It allows the mixtures to be sampled independently of each other. If samples are acquired in the time domain, this means that the sensors need not be synchronized. Since Blind Source Separation (BSS) from a linear mixture is only possible up to permutation and scaling, factoring out these ambiguities leads to a minimization problem on the so-called oblique manifold. We develop a geometric conjugate subgradient method that scales to large systems for solving the problem. Numerical results demonstrate the promising performance of the proposed algorithm compared to several state of the art methods.
On ECG reconstruction using weighted-compressive sensing.
Zonoobi, Dornoosh; Kassim, Ashraf A
2014-06-01
The potential of the new weighted-compressive sensing approach for efficient reconstruction of electrocardiograph (ECG) signals is investigated. This is motivated by the observation that ECG signals are hugely sparse in the frequency domain and the sparsity changes slowly over time. The underlying idea of this approach is to extract an estimated probability model for the signal of interest, and then use this model to guide the reconstruction process. The authors show that the weighted-compressive sensing approach is able to achieve reconstruction performance comparable with the current state-of-the-art discrete wavelet transform-based method, but with substantially less computational cost to enable it to be considered for use in the next generation of miniaturised wearable ECG monitoring devices.
Statistical mechanics analysis of thresholding 1-bit compressed sensing
Xu, Yingying
2016-01-01
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering the signal by imposing an additional constraint on the L2-norm of the signal. Recently, an alternative strategy that captures scale information by introducing a threshold parameter to the quantization process was advanced. In this paper, we analyze the typical behavior of the thresholding 1-bit compressed sensing utilizing the replica method of statistical mechanics, so as to gain an insight for properly setting the threshold value. Our result shows that, fixing the threshold at a constant value yields better performance than varying it randomly when the constant is optimally tuned, statistically. Unfortunately, the optimal threshold value depends on the statistical properties of the target signal, which may not be known in advance. In order to handle this inconvenience, we ...
Accelerated MR imaging using compressive sensing with no free parameters.
Khare, Kedar; Hardy, Christopher J; King, Kevin F; Turski, Patrick A; Marinelli, Luca
2012-11-01
We describe and evaluate a robust method for compressive sensing MRI reconstruction using an iterative soft thresholding framework that is data-driven, so that no tuning of free parameters is required. The approach described here combines a Nesterov type optimal gradient scheme for iterative update along with standard wavelet-based adaptive denoising methods, resulting in a leaner implementation compared with the nonlinear conjugate gradient method. Tests with T₂ weighted brain data and vascular 3D phase contrast data show that the image quality of reconstructions is comparable with those from an empirically tuned nonlinear conjugate gradient approach. Statistical analysis of image quality scores for multiple datasets indicates that the iterative soft thresholding approach as presented here may improve the robustness of the reconstruction and the image quality, when compared with nonlinear conjugate gradient that requires manual tuning for each dataset. A data-driven approach as illustrated in this article should improve future clinical applicability of compressive sensing image reconstruction.
Acceleration of multi-dimensional propagator measurements with compressed sensing.
Paulsen, Jeffrey L; Cho, HyungJoon; Cho, Gyunggoo; Song, Yi-Qiao
2011-12-01
NMR can probe the microstructures of anisotropic materials such as liquid crystals, stretched polymers and biological tissues through measurement of the diffusion propagator, where internal structures are indicated by restricted diffusion. Multi-dimensional measurements can probe the microscopic anisotropy, but full sampling can then quickly become prohibitively time consuming. However, for incompletely sampled data, compressed sensing is an effective reconstruction technique to enable accelerated acquisition. We demonstrate that with a compressed sensing scheme, one can greatly reduce the sampling and the experimental time with minimal effect on the reconstruction of the diffusion propagator with an example of anisotropic diffusion. We compare full sampling down to 64× sub-sampling for the 2D propagator measurement and reduce the acquisition time for the 3D experiment by a factor of 32 from ∼80 days to ∼2.5 days. Copyright Â© 2011 Elsevier Inc. All rights reserved.
Learning physical descriptors for materials science by compressed sensing
Ghiringhelli, Luca M.; Vybiral, Jan; Ahmetcik, Emre; Ouyang, Runhai; Levchenko, Sergey V.; Draxl, Claudia; Scheffler, Matthias
2017-02-01
The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in these data that is not directly visible by standard tools and exploitation of the scientific information requires new and dedicated methodology based on approaches from statistical learning, compressed sensing, and other recent methods from applied mathematics, computer science, statistics, signal processing, and information science. In this paper, we explain and demonstrate a compressed-sensing based methodology for feature selection, specifically for discovering physical descriptors, i.e., physical parameters that describe the material and its properties of interest, and associated equations that explicitly and quantitatively describe those relevant properties. As showcase application and proof of concept, we describe how to build a physical model for the quantitative prediction of the crystal structure of binary compound semiconductors.
Prior image constrained compressed sensing: a quantitative performance evaluation
Thériault Lauzier, Pascal; Tang, Jie; Chen, Guang-Hong
2012-03-01
The appeal of compressed sensing (CS) in the context of medical imaging is undeniable. In MRI, it could enable shorter acquisition times while in CT, it has the potential to reduce the ionizing radiation dose imparted to patients. However, images reconstructed using a CS-based approach often show an unusual texture and a potential loss in spatial resolution. The prior image constrained compressed sensing (PICCS) algorithm has been shown to enable accurate image reconstruction at lower levels of sampling. This study systematically evaluates an implementation of PICCS applied to myocardial perfusion imaging with respect to two parameters of its objective function. The prior image parameter α was shown here to yield an optimal image quality in the range 0.4 to 0.5. A quantitative evaluation in terms of temporal resolution, spatial resolution, noise level, noise texture, and reconstruction accuracy was performed.
Compressed Sensing Based Fingerprint Identification for Wireless Transmitters
Caidan Zhao
2014-01-01
Full Text Available Most of the existing fingerprint identification techniques are unable to distinguish different wireless transmitters, whose emitted signals are highly attenuated, long-distance propagating, and of strong similarity to their transient waveforms. Therefore, this paper proposes a new method to identify different wireless transmitters based on compressed sensing. A data acquisition system is designed to capture the wireless transmitter signals. Complex analytical wavelet transform is used to obtain the envelope of the transient signal, and the corresponding features are extracted by using the compressed sensing theory. Feature selection utilizing minimum redundancy maximum relevance (mRMR is employed to obtain the optimal feature subsets for identification. The results show that the proposed method is more efficient for the identification of wireless transmitters with similar transient waveforms.
Fast Adaptive Wavelet for Remote Sensing Image Compression
Bo Li; Run-Hai Jiao; Yuan-Cheng Li
2007-01-01
Remote sensing images are hard to achieve high compression ratio because of their rich texture. By analyzing the influence of wavelet properties on image compression, this paper proposes wavelet construction rules and builds a new biorthogonal wavelet construction model with parameters. The model parameters are optimized by using genetic algorithm and adopting energy compaction as the optimization object function. In addition, in order to resolve the computation complexity problem of online construction, according to the image classification rule proposed in this paper we construct wavelets for different classes of images and implement the fast adaptive wavelet selection algorithm (FAWS). Experimental results show wavelet bases of FAWS gain better compression performance than Daubechies9/7.
Feasibility Study of Compressive Sensing Underwater Imaging Lidar
2014-03-28
patterns generated using this scheme can significantly reduce the cost and complexity of the antenna design in such imaging systems. Another...currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1, REPORT DATE (’DD- MW -yYVyj 03/28/2014 2. REPORT TYPE Final...Feasibility study of Compressive Sensing Underwater Imaging Lidar 5a. CONTRACT NUMBER 5b. GRANT NUMBER N00014-12-1-0921 5c. PROGRAM ELEMENT NUMBER 6
Compressed Sensing for Time-Frequency Gravitational Wave Data Analysis
Addesso, Paolo; Marano, Stefano; Matta, Vincenzo; Principe, Maria; Pinto, Innocenzo M
2016-01-01
The potential of compressed sensing for obtaining sparse time-frequency representations for gravitational wave data analysis is illustrated by comparison with existing methods, as regards i) shedding light on the fine structure of noise transients (glitches) in preparation of their classification, and ii) boosting the performance of waveform consistency tests in the detection of unmodeled transient gravitational wave signals using a network of detectors affected by unmodeled noise transient
Sparse Vector Distributions and Recovery from Compressed Sensing
Sturm, Bob L.
It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I...... distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal....
Compressive sensing holography based on optical heterodyne detection
Hu, Youjun; Zhou, Dingfu; Yuan, Sheng; Wei, Yayun; Wang, Mengting; Zhou, Xin
2016-12-01
In this paper, compressive sensing holography based on optical heterodyne detection is presented, which can photograph the hologram of an object. The complex hologram is composed of a sine-hologram and a cosine-hologram. A single pixel photoelectric conversion element is used to detect the time-varying optical field which contains the amplitude and phase information of the transmitted light, and a simulation result is demonstrated further by recording the Fresnel hologram of a complex amplitude object.
Study on adaptive compressed sensing & reconstruction of quantized speech signals
Yunyun, Ji; Zhen, Yang
2012-12-01
Compressed sensing (CS) is a rising focus in recent years for its simultaneous sampling and compression of sparse signals. Speech signals can be considered approximately sparse or compressible in some domains for natural characteristics. Thus, it has great prospect to apply compressed sensing to speech signals. This paper is involved in three aspects. Firstly, the sparsity and sparsifying matrix for speech signals are analyzed. Simultaneously, a kind of adaptive sparsifying matrix based on the long-term prediction of voiced speech signals is constructed. Secondly, a CS matrix called two-block diagonal (TBD) matrix is constructed for speech signals based on the existing block diagonal matrix theory to find out that its performance is empirically superior to that of the dense Gaussian random matrix when the sparsifying matrix is the DCT basis. Finally, we consider the quantization effect on the projections. Two corollaries about the impact of the adaptive quantization and nonadaptive quantization on reconstruction performance with two different matrices, the TBD matrix and the dense Gaussian random matrix, are derived. We find that the adaptive quantization and the TBD matrix are two effective ways to mitigate the quantization effect on reconstruction of speech signals in the framework of CS.
Optimizing measurements for feature-specific compressive sensing.
Mahalanobis, Abhijit; Neifeld, Mark
2014-09-10
While the theory of compressive sensing has been very well investigated in the literature, comparatively little attention has been given to the issues that arise when compressive measurements are made in hardware. For instance, compressive measurements are always corrupted by detector noise. Further, the number of photons available is the same whether a conventional image is sensed or multiple coded measurements are made in the same interval of time. Thus it is essential that the effects of noise and the constraint on the number of photons must be taken into account in the analysis, design, and implementation of a compressive imager. In this paper, we present a methodology for designing a set of measurement kernels (or masks) that satisfy the photon constraint and are optimum for making measurements that minimize the reconstruction error in the presence of noise. Our approach finds the masks one at a time, by determining the vector that yields the best possible measurement for reducing the reconstruction error. The subspace represented by the optimized mask is removed from the signal space, and the process is repeated to find the next best measurement. Results of simulations are presented that show that the optimum masks always outperform reconstructions based on traditional feature measurements (such as principle components), and are also better than the conventional images in high noise conditions.
Early Detection of Rogue Waves Using Compressive Sensing
Bayindir, Cihan
2016-01-01
We discuss the possible usage of the compressive sampling for the early detection of rogue waves in a chaotic sea state. One of the promising techniques for the early detection of the oceanic rogue waves is to measure the triangular Fourier spectra which begin to appear at the early stages of their development. For the early detection of the rogue waves it is possible to treat such a spectrum as a sparse signal since we would mainly be interested in the high amplitude triangular region located at the central wavenumber. Therefore compressive sampling can be a very efficient tool for the rogue wave early warning systems. Compressed measurements can be acquired by remote sensing techniques such as coherent SAR which measure the ocean surface fluctuation or by insitu techniques such as spectra measuring tools mounted on a ship hull or bottom mounted pressure gauges. By employing a numerical approach we show that triangular Fourier spectra can be sensed by compressed measurements at the early stages of the develo...
Quantum tomography protocols with positivity are compressed sensing protocols
Kalev, Amir; Kosut, Robert L.; Deutsch, Ivan H.
2015-12-01
Characterising complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is, however, notoriously inefficient. Recently, the classical signal reconstruction technique known as ‘compressed sensing’ has been ported to quantum information science to overcome this challenge: accurate tomography can be achieved with substantially fewer measurement settings, thereby greatly enhancing the efficiency of quantum tomography. Here we show that compressed sensing tomography of quantum systems is essentially guaranteed by a special property of quantum mechanics itself—that the mathematical objects that describe the system in quantum mechanics are matrices with non-negative eigenvalues. This result has an impact on the way quantum tomography is understood and implemented. In particular, it implies that the information obtained about a quantum system through compressed sensing methods exhibits a new sense of ‘informational completeness.’ This has important consequences on the efficiency of the data taking for quantum tomography, and enables us to construct informationally complete measurements that are robust to noise and modelling errors. Moreover, our result shows that one can expand the numerical tool-box used in quantum tomography and employ highly efficient algorithms developed to handle large dimensional matrices on a large dimensional Hilbert space. Although we mainly present our results in the context of quantum tomography, they apply to the general case of positive semidefinite matrix recovery.
Residual Distributed Compressive Video Sensing Based on Double Side Information
CHEN Jian; SU Kai-Xiong; WANG Wei-Xing; LAN Cheng-Dong
2014-01-01
Compressed sensing (CS) is a novel technology to acquire and reconstruct sparse signals below the Nyquist rate. It has great potential in image and video acquisition and processing. To effectively improve the sparsity of signal being measured and reconstructing efficiency, an encoding and decoding model of residual distributed compressive video sensing based on double side information (RDCVS-DSI) is proposed in this paper. Exploiting the characteristics of image itself in the frequency domain and the correlation between successive frames, the model regards the video frame in low quality as the first side information in the process of coding, and generates the second side information for the non-key frames using motion estimation and compensation technology at its decoding end. Performance analysis and simulation experiments show that the RDCVS-DSI model can rebuild the video sequence with high fidelity in the consumption of quite low complexity. About 1∼5 dB gain in the average peak signal-to-noise ratio of the reconstructed frames is observed, and the speed is close to the least complex DCVS, when compared with prior works on compressive video sensing.
Statistical mechanics approach to 1-bit compressed sensing
Xu, Yingying; Kabashima, Yoshiyuki
2013-02-01
Compressed sensing is a framework that makes it possible to recover an N-dimensional sparse vector x∈RN from its linear transformation y∈RM of lower dimensionality M entry of y to recover x was recently proposed. This is often termed 1-bit compressed sensing. Here, we analyze the typical performance of an l1-norm-based signal recovery scheme for 1-bit compressed sensing using statistical mechanics methods. We show that the signal recovery performance predicted by the replica method under the replica symmetric ansatz, which turns out to be locally unstable for modes breaking the replica symmetry, is in good consistency with experimental results of an approximate recovery algorithm developed earlier. This suggests that the l1-based recovery problem typically has many local optima of a similar recovery accuracy, which can be achieved by the approximate algorithm. We also develop another approximate recovery algorithm inspired by the cavity method. Numerical experiments show that when the density of nonzero entries in the original signal is relatively large the new algorithm offers better performance than the abovementioned scheme and does so with a lower computational cost.
Hybrid tenso-vectorial compressive sensing for hyperspectral imaging
Li, Qun; Bernal, Edgar A.
2016-05-01
Hyperspectral imaging has a wide range of applications relying on remote material identification, including astronomy, mineralogy, and agriculture; however, due to the large volume of data involved, the complexity and cost of hyperspectral imagers can be prohibitive. The exploitation of redundancies along the spatial and spectral dimensions of a hyperspectral image of a scene has created new paradigms that overcome the limitations of traditional imaging systems. While compressive sensing (CS) approaches have been proposed and simulated with success on already acquired hyperspectral imagery, most of the existing work relies on the capability to simultaneously measure the spatial and spectral dimensions of the hyperspectral cube. Most real-life devices, however, are limited to sampling one or two dimensions at a time, which renders a significant portion of the existing work unfeasible. We propose a new variant of the recently proposed serial hybrid vectorial and tensorial compressive sensing (HCS-S) algorithm that, like its predecessor, is compatible with real-life devices both in terms of the acquisition and reconstruction requirements. The newly introduced approach is parallelizable, and we abbreviate it as HCS-P. Together, HCS-S and HCS-P comprise a generalized framework for hybrid tenso-vectorial compressive sensing, or HCS for short. We perform a detailed analysis that demonstrates the uniqueness of the signal reconstructed by both the original HCS-S and the proposed HCS-P algorithms. Last, we analyze the behavior of the HCS reconstruction algorithms in the presence of measurement noise, both theoretically and experimentally.
A CLASS OF DETERMINISTIC CONSTRUCTION OF BINARY COMPRESSED SENSING MATRICES
Li Dandan; Liu Xinji; Xia Shutao; Jiang Yong
2012-01-01
Compressed Sensing (CS) is an emerging technology in the field of signal processing,which can recover a sparse signal by taking very few samples and solving a linear programming problem.In this paper,we study the application of Low-Density Parity-Check (LDPC) Codes in CS.Firstly,we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property (RIP).Then,by employing the LDPC codes based on Berlekamp-Justesen (B-J) codes,we construct two classes of binary structured matrices and show that these matrices satisfy RIP.Thus,the proposed matrices could be used as sensing matrices for CS.Finally,simulation results show that the performance of the Droposed matrices can be comparable with the widely used random sensing matrices.
Texture-based medical image retrieval in compressed domain using compressive sensing.
Yadav, Kuldeep; Srivastava, Avi; Mittal, Ankush; Ansari, M A
2014-01-01
Content-based image retrieval has gained considerable attention in today's scenario as a useful tool in many applications; texture is one of them. In this paper, we focus on texture-based image retrieval in compressed domain using compressive sensing with the help of DC coefficients. Medical imaging is one of the fields which have been affected most, as there had been huge size of image database and getting out the concerned image had been a daunting task. Considering this, in this paper we propose a new model of image retrieval process using compressive sampling, since it allows accurate recovery of image from far fewer samples of unknowns and it does not require a close relation of matching between sampling pattern and characteristic image structure with increase acquisition speed and enhanced image quality.
Survey for Image Representation Using Block Compressive Sensing For Compression Applications
Ankita Hundet
2014-04-01
Full Text Available Compressing sensing theory have been favourable in evolving data compression techniques, though it was put forward with objective to achieve dimension reduced sampling for saving data sampling cost. In this paper two sampling methods are explored for block CS (BCS with discrete cosine transform (DCT based image representation for compression applications - (a coefficient random permutation (b adaptive sampling. CRP method has the potency to balance the sparsity of sampled vectors in DCT field of image, and then in improving the CS sampling efficiency. To attain AS we design an adaptive measurement matrix used in CS based on the energy distribution characteristics of image in DCT domain, which has a good impact in magnifying the CS performance. It has been revealed in our experimental results that our proposed methods are efficacious in reducing the dimension of the BCS-based image representation and/or improving the recovered image quality. The planned BCS based image representation scheme could be an efficient alternative for applications of encrypted image compression and/or robust image compression.
An Energy Efficient Compressed Sensing Framework for the Compression of Electroencephalogram Signals
Simon Fauvel
2014-01-01
Full Text Available The use of wireless body sensor networks is gaining popularity in monitoring and communicating information about a person’s health. In such applications, the amount of data transmitted by the sensor node should be minimized. This is because the energy available in these battery powered sensors is limited. In this paper, we study the wireless transmission of electroencephalogram (EEG signals. We propose the use of a compressed sensing (CS framework to efficiently compress these signals at the sensor node. Our framework exploits both the temporal correlation within EEG signals and the spatial correlations amongst the EEG channels. We show that our framework is up to eight times more energy efficient than the typical wavelet compression method in terms of compression and encoding computations and wireless transmission. We also show that for a fixed compression ratio, our method achieves a better reconstruction quality than the CS-based state-of-the art method. We finally demonstrate that our method is robust to measurement noise and to packet loss and that it is applicable to a wide range of EEG signal types.
Modeling 3D faces from samplings via compressive sensing
Sun, Qi; Tang, Yanlong; Hu, Ping
2013-07-01
3D data is easier to acquire for family entertainment purpose today because of the mass-production, cheapness and portability of domestic RGBD sensors, e.g., Microsoft Kinect. However, the accuracy of facial modeling is affected by the roughness and instability of the raw input data from such sensors. To overcome this problem, we introduce compressive sensing (CS) method to build a novel 3D super-resolution scheme to reconstruct high-resolution facial models from rough samples captured by Kinect. Unlike the simple frame fusion super-resolution method, this approach aims to acquire compressed samples for storage before a high-resolution image is produced. In this scheme, depth frames are firstly captured and then each of them is measured into compressed samples using sparse coding. Next, the samples are fused to produce an optimal one and finally a high-resolution image is recovered from the fused sample. This framework is able to recover 3D facial model of a given user from compressed simples and this can reducing storage space as well as measurement cost in future devices e.g., single-pixel depth cameras. Hence, this work can potentially be applied into future applications, such as access control system using face recognition, and smart phones with depth cameras, which need high resolution and little measure time.
Compressive sensing in a photonic link with optical integration.
Chen, Ying; Yu, Xianbin; Chi, Hao; Jin, Xiaofeng; Zhang, Xianmin; Zheng, Shilie; Galili, Michael
2014-04-15
In this Letter, we present a novel structure to realize photonics-assisted compressive sensing (CS) with optical integration. In the system, a spectrally sparse signal modulates a multiwavelength continuous-wave light and then is mixed with a random sequence in optical domain. The optical signal passes through a length of dispersive fiber, the dispersion amount of which is set to ensure that the group delay between the adjacent wavelength channels is equal to the bit duration of the applied random sequence. As a result, the detected signal is a delay-and-sum version of the randomly mixed signal, which is equivalent to the function of integration required in CS. A proof-of-concept experiment with four wavelengths, corresponding to a compression factor of 4, is demonstrated. More simulation results are also given to show the potential of the technique.
Compressed Sensing for Denoising in Adaptive System Identification
Hosseini, Seyed Hossein
2012-01-01
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter approach the compressed version of the sparse system instead of the original system. To this end, we use random filter structure at the transmitter to form the measurement matrix according to the CS framework. The original sparse system can be reconstructed by the conventional recovery algorithms. As a result, the denoising property of CS can be deployed in the proposed method at the recovery stage. The experiments indicate significant performance improvement of proposed method compared to the conventional LMS method which directly identifies the sparse system. Furthermore, at low levels of sparsity, our method outperforms a specialized identification algorithm that promotes sparsity.
K-cluster-valued compressive sensing for imaging
Xu Mai
2011-01-01
Full Text Available Abstract The success of compressive sensing (CS implies that an image can be compressed directly into acquisition with the measurement number over the whole image less than pixel number of the image. In this paper, we extend the existing CS by including the prior knowledge of K-cluster values available for the pixels or wavelet coefficients of an image. In order to model such prior knowledge, we propose in this paper K-cluster-valued CS approach for imaging, by incorporating the K-means algorithm in CoSaMP recovery algorithm. One significant advantage of the proposed approach, rather than the conventional CS, is the capability of reducing measurement numbers required for the accurate image reconstruction. Finally, the performance of conventional CS and K-cluster-valued CS is evaluated using some natural images and background subtraction images.
A distributed compressive sensing technique for data gathering in Wireless Sensor Networks
Masoum, Alireza; Meratnia, Nirvana; Havinga, Paul J.M.
2013-01-01
Compressive sensing is a new technique utilized for energy efficient data gathering in wireless sensor networks. It is characterized by its simple encoding and complex decoding. The strength of compressive sensing is its ability to reconstruct sparse or compressible signals from small number of meas
MAXAD distortion minimization for wavelet compression of remote sensing data
Alecu, Alin; Munteanu, Adrian; Schelkens, Peter; Cornelis, Jan P.; Dewitte, Steven
2001-12-01
In the context of compression of high resolution multi-spectral satellite image data consisting of radiances and top-of-the-atmosphere fluxes, it is vital that image calibration characteristics (luminance, radiance) must be preserved within certain limits in lossy image compression. Though existing compression schemes (SPIHT, JPEG2000, SQP) give good results as far as minimization of the global PSNR error is concerned, they fail to guarantee a maximum local error. With respect to this, we introduce a new image compression scheme, which guarantees a MAXAD distortion, defined as the maximum absolute difference between original pixel values and reconstructed pixel values. In terms of defining the Lagrangian optimization problem, this reflects in minimization of the rate given the MAXAD distortion. Our approach thus uses the l-infinite distortion measure, which is applied to the lifting scheme implementation of the 9-7 floating point Cohen-Daubechies-Feauveau (CDF) filter. Scalar quantizers, optimal in the D-R sense, are derived for every subband, by solving a global optimization problem that guarantees a user-defined MAXAD. The optimization problem has been defined and solved for the case of the 9-7 filter, and we show that our approach is valid and may be applied to any finite wavelet filters synthesized via lifting. The experimental assessment of our codec shows that our technique provides excellent results in applications such as those for remote sensing, in which reconstruction of image calibration characteristics within a tolerable local error (MAXAD) is perceived as being of crucial importance compared to obtaining an acceptable global error (PSNR), as is the case of existing quantizer design techniques.
Initial results for compressive sensing in electronic support receiver systems
Du Plessis, WP
2011-04-01
Full Text Available of 80 Gb/s which is 25% more than the optimistic assumption of 64 Gb/s for the fastest Serial RapidIO line. This means that data will take 25% longer to read from memory than it took to write into memory, so the above example will only be sampling 44... of compressive sensing are considered in Section V showing that real-time operation is possible. Finally, a brief conclusion and suggestions for future research are provided in Section VI. II. DATA RATES OF MODERN ES SYSTEMS AND THEIR EFFECT ON SYSTEM...
Multifrequency Bayesian compressive sensing methods for microwave imaging.
Poli, Lorenzo; Oliveri, Giacomo; Ding, Ping Ping; Moriyama, Toshifumi; Massa, Andrea
2014-11-01
The Bayesian retrieval of sparse scatterers under multifrequency transverse magnetic illuminations is addressed. Two innovative imaging strategies are formulated to process the spectral content of microwave scattering data according to either a frequency-hopping multistep scheme or a multifrequency one-shot scheme. To solve the associated inverse problems, customized implementations of single-task and multitask Bayesian compressive sensing are introduced. A set of representative numerical results is discussed to assess the effectiveness and the robustness against the noise of the proposed techniques also in comparison with some state-of-the-art deterministic strategies.
Scrambling-based speech encryption via compressed sensing
Zeng, Li; Zhang, Xiongwei; Chen, Liang; Fan, Zhangjun; Wang, Yonggang
2012-12-01
Conventional speech scramblers have three disadvantages, including heavy communication overhead, signal features underexploitation, and low attack resistance. In this study, we propose a scrambling-based speech encryption scheme via compressed sensing (CS). Distinguished from conventional scramblers, the above problems are solved in a unified framework by utilizing the advantages of CS. The presented encryption idea is general and easily applies to speech communication systems. Compared with the state-of-the-art methods, the proposed scheme provides lower residual intelligibility and greater cryptanalytic efforts. Meanwhile, it ensures desirable channel usage and notable resistibility to hostile attack. Extensive experimental results also confirm the effectiveness of the proposed scheme.
OTHR Spectrum Reconstruction of Maneuvering Target with Compressive Sensing
Yinghui Quan
2014-01-01
Full Text Available High-frequency (HF over-the-horizon radar (OTHR works in a very complicated electromagnetic environment. It usually suffers performance degradation caused by transient interference. In this paper, we study the transient interference excision and full spectrum reconstruction of maneuvering targets. The segmental subspace projection (SP approach is applied to suppress the clutter and locate the transient interference. After interference excision, the spectrum is reconstructed from incomplete measurements via compressive sensing (CS by using a redundant Fourier-chirp dictionary. An improved orthogonal matching pursuit (IOMP algorithm is developed to solve the sparse decomposition optimization. Experimental results demonstrate the effectiveness of the proposed methods.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing.
Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-04-15
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wang, Wen-Xu; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-01-01
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
On Phase Transition of Compressed Sensing in the Complex Domain
Yang, Zai; Xie, Lihua
2011-01-01
The phase transition is a performance measure of the sparsity-undersampling tradeoff in compressed sensing (CS). This letter reports, for the first time, the existence of an exact phase transition for the $\\ell_1$ minimization approach to the complex valued CS problem. This discovery is not only a complementary result to the known phase transition of the real valued CS but also shows considerable superiority of the phase transition of complex valued CS over that of the real valued CS. The results are obtained by extending the recently developed ONE-L1 algorithms to complex valued CS and applying their optimal and iterative solutions to empirically evaluate the phase transition.
Highly compressible fluorescent particles for pressure sensing in liquids
Cellini, F.; Peterson, S. D.; Porfiri, M.
2017-05-01
Pressure sensing in liquids is important for engineering applications ranging from industrial processing to naval architecture. Here, we propose a pressure sensor based on highly compressible polydimethylsiloxane foam particles embedding fluorescent Nile Red molecules. The particles display pressure sensitivities as low as 0.0018 kPa-1, which are on the same order of magnitude of sensitivities reported in commercial pressure-sensitive paints for air flows. We envision the application of the proposed sensor in particle image velocimetry toward an improved understanding of flow kinetics in liquids.
Acquisition of STEM Images by Adaptive Compressive Sensing
Xie, Weiyi; Feng, Qianli; Srinivasan, Ramprakash; Stevens, Andrew; Browning, Nigel D.
2017-07-01
Compressive Sensing (CS) allows a signal to be sparsely measured first and accurately recovered later in software [1]. In scanning transmission electron microscopy (STEM), it is possible to compress an image spatially by reducing the number of measured pixels, which decreases electron dose and increases sensing speed [2,3,4]. The two requirements for CS to work are: (1) sparsity of basis coefficients and (2) incoherence of the sensing system and the representation system. However, when pixels are missing from the image, it is difficult to have an incoherent sensing matrix. Nevertheless, dictionary learning techniques such as Beta-Process Factor Analysis (BPFA) [5] are able to simultaneously discover a basis and the sparse coefficients in the case of missing pixels. On top of CS, we would like to apply active learning [6,7] to further reduce the proportion of pixels being measured, while maintaining image reconstruction quality. Suppose we initially sample 10% of random pixels. We wish to select the next 1% of pixels that are most useful in recovering the image. Now, we have 11% of pixels, and we want to decide the next 1% of “most informative” pixels. Active learning methods are online and sequential in nature. Our goal is to adaptively discover the best sensing mask during acquisition using feedback about the structures in the image. In the end, we hope to recover a high quality reconstruction with a dose reduction relative to the non-adaptive (random) sensing scheme. In doing this, we try three metrics applied to the partial reconstructions for selecting the new set of pixels: (1) variance, (2) Kullback-Leibler (KL) divergence using a Radial Basis Function (RBF) kernel, and (3) entropy. Figs. 1 and 2 display the comparison of Peak Signal-to-Noise (PSNR) using these three different active learning methods at different percentages of sampled pixels. At 20% level, all the three active learning methods underperform the original CS without active learning. However
Statistical mechanics analysis of thresholding 1-bit compressed sensing
Xu, Yingying; Kabashima, Yoshiyuki
2016-08-01
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering the signal by imposing an additional constraint on the l 2-norm of the signal. Recently, an alternative strategy that captures scale information by introducing a threshold parameter to the quantization process was advanced. In this paper, we analyze the typical behavior of thresholding 1-bit compressed sensing utilizing the replica method of statistical mechanics, so as to gain an insight for properly setting the threshold value. Our result shows that fixing the threshold at a constant value yields better performance than varying it randomly when the constant is optimally tuned, statistically. Unfortunately, the optimal threshold value depends on the statistical properties of the target signal, which may not be known in advance. In order to handle this inconvenience, we develop a heuristic that adaptively tunes the threshold parameter based on the frequency of positive (or negative) values in the binary outputs. Numerical experiments show that the heuristic exhibits satisfactory performance while incurring low computational cost.
A novel image fusion approach based on compressive sensing
Yin, Hongpeng; Liu, Zhaodong; Fang, Bin; Li, Yanxia
2015-11-01
Image fusion can integrate complementary and relevant information of source images captured by multiple sensors into a unitary synthetic image. The compressive sensing-based (CS) fusion approach can greatly reduce the processing speed and guarantee the quality of the fused image by integrating fewer non-zero coefficients. However, there are two main limitations in the conventional CS-based fusion approach. Firstly, directly fusing sensing measurements may bring greater uncertain results with high reconstruction error. Secondly, using single fusion rule may result in the problems of blocking artifacts and poor fidelity. In this paper, a novel image fusion approach based on CS is proposed to solve those problems. The non-subsampled contourlet transform (NSCT) method is utilized to decompose the source images. The dual-layer Pulse Coupled Neural Network (PCNN) model is used to integrate low-pass subbands; while an edge-retention based fusion rule is proposed to fuse high-pass subbands. The sparse coefficients are fused before being measured by Gaussian matrix. The fused image is accurately reconstructed by Compressive Sampling Matched Pursuit algorithm (CoSaMP). Experimental results demonstrate that the fused image contains abundant detailed contents and preserves the saliency structure. These also indicate that our proposed method achieves better visual quality than the current state-of-the-art methods.
Measurement Matrix Design for Compressive Sensing Based MIMO Radar
Yu, Y; Poor, H V
2011-01-01
In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced...
Hierarchical Compressed Sensing for Cluster Based Wireless Sensor Networks
Vishal Krishna Singh
2016-02-01
Full Text Available Data transmission consumes significant amount of energy in large scale wireless sensor networks (WSNs. In such an environment, reducing the in-network communication and distributing the load evenly over the network can reduce the overall energy consumption and maximize the network lifetime significantly. In this work, the aforementioned problem of network lifetime and uneven energy consumption in large scale wireless sensor networks is addressed. This work proposes a hierarchical compressed sensing (HCS scheme to reduce the in-network communication during the data gathering process. Co-related sensor readings are collected via a hierarchical clustering scheme. A compressed sensing (CS based data processing scheme is devised to transmit the data from the source to the sink. The proposed HCS is able to identify the optimal position for the application of CS to achieve reduced and similar number of transmissions on all the nodes in the network. An activity map is generated to validate the reduced and uniformly distributed communication load of the WSN. Based on the number of transmissions per data gathering round, the bit-hop metric model is used to analyse the overall energy consumption. Simulation results validate the efficiency of the proposed method over the existing CS based approaches.
Compressed-sensing application - Pre-stack kirchhoff migration
Aldawood, Ali
2013-01-01
Least-squares migration is a linearized form of waveform inversion that aims to enhance the spatial resolution of the subsurface reflectivity distribution and reduce the migration artifacts due to limited recording aperture, coarse sampling of sources and receivers, and low subsurface illumination. Least-squares migration, however, due to the nature of its minimization process, tends to produce smoothed and dispersed versions of the reflectivity of the subsurface. Assuming that the subsurface reflectivity distribution is sparse, we propose the addition of a non-quadratic L1-norm penalty term on the model space in the objective function. This aims to preserve the sparse nature of the subsurface reflectivity series and enhance resolution. We further use a compressed-sensing algorithm to solve the linear system, which utilizes the sparsity assumption to produce highly resolved migrated images. Thus, the Kirchhoff migration implementation is formulated as a Basis Pursuit denoise (BPDN) problem to obtain the sparse reflectivity model. Applications on synthetic data show that reflectivity models obtained using this compressed-sensing algorithm are highly accurate with optimal resolution.
Modelling compression sensing in ionic polymer metal composites
Volpini, Valentina; Bardella, Lorenzo; Rodella, Andrea; Cha, Youngsu; Porfiri, Maurizio
2017-03-01
Ionic polymer metal composites (IPMCs) consist of an ionomeric membrane, including mobile counterions, sandwiched between two thin noble metal electrodes. IPMCs find application as sensors and actuators, where an imposed mechanical loading generates a voltage across the electrodes, and, vice versa, an imposed electric field causes deformation. Here, we present a predictive modelling approach to elucidate the dynamic sensing response of IPMCs subject to a time-varying through-the-thickness compression (‘compression sensing’). The model relies on the continuum theory recently developed by Porfiri and co-workers, which couples finite deformations to the modified Poisson–Nernst–Planck (PNP) system governing the IPMC electrochemistry. For the ‘compression sensing’ problem we establish a perturbative closed-form solution along with a finite element (FE) solution. The systematic comparison between these two solutions is a central contribution of this study, offering insight on accuracy and mathematical complexity. The method of matched asymptotic expansions is employed to find the analytical solution. To this end, we uncouple the force balance from the modified PNP system and separately linearise the PNP equations in the ionomer bulk and in the boundary layers at the ionomer–electrode interfaces. Comparison with FE results for the fully coupled nonlinear system demonstrates the accuracy of the analytical solution to describe IPMC sensing for moderate deformation levels. We finally demonstrate the potential of the modelling scheme to accurately reproduce experimental results from the literature. The proposed model is expected to aid in the design of IPMC sensors, contribute to an improved understanding of IPMC electrochemomechanical response, and offer insight into the role of nonlinear phenomena across mechanics and electrochemistry.
Experimental Study of Super-Resolution Using a Compressive Sensing Architecture
2015-03-01
Experimental study of super-resolution using a compressive sensing architecture J. Christopher Flakea,c, Gary Eulissa, John B. Greerb, Stephanie...laboratory imaging system was constructed following an architecture that has become familiar from the theory of compressive sensing . The system uses...choices in system design will become increasingly more important. We present a compressive sensing image system designed for super-resolution: the
An Efficient Distributed Compressed Sensing Algorithm for Decentralized Sensor Network.
Liu, Jing; Huang, Kaiyu; Zhang, Guoxian
2017-04-20
We consider the joint sparsity Model 1 (JSM-1) in a decentralized scenario, where a number of sensors are connected through a network and there is no fusion center. A novel algorithm, named distributed compact sensing matrix pursuit (DCSMP), is proposed to exploit the computational and communication capabilities of the sensor nodes. In contrast to the conventional distributed compressed sensing algorithms adopting a random sensing matrix, the proposed algorithm focuses on the deterministic sensing matrices built directly on the real acquisition systems. The proposed DCSMP algorithm can be divided into two independent parts, the common and innovation support set estimation processes. The goal of the common support set estimation process is to obtain an estimated common support set by fusing the candidate support set information from an individual node and its neighboring nodes. In the following innovation support set estimation process, the measurement vector is projected into a subspace that is perpendicular to the subspace spanned by the columns indexed by the estimated common support set, to remove the impact of the estimated common support set. We can then search the innovation support set using an orthogonal matching pursuit (OMP) algorithm based on the projected measurement vector and projected sensing matrix. In the proposed DCSMP algorithm, the process of estimating the common component/support set is decoupled with that of estimating the innovation component/support set. Thus, the inaccurately estimated common support set will have no impact on estimating the innovation support set. It is proven that under the condition the estimated common support set contains the true common support set, the proposed algorithm can find the true innovation set correctly. Moreover, since the innovation support set estimation process is independent of the common support set estimation process, there is no requirement for the cardinality of both sets; thus, the proposed DCSMP
Zhou, Nanrun; Zhang, Aidi; Zheng, Fen; Gong, Lihua
2014-10-01
The existing ways to encrypt images based on compressive sensing usually treat the whole measurement matrix as the key, which renders the key too large to distribute and memorize or store. To solve this problem, a new image compression-encryption hybrid algorithm is proposed to realize compression and encryption simultaneously, where the key is easily distributed, stored or memorized. The input image is divided into 4 blocks to compress and encrypt, then the pixels of the two adjacent blocks are exchanged randomly by random matrices. The measurement matrices in compressive sensing are constructed by utilizing the circulant matrices and controlling the original row vectors of the circulant matrices with logistic map. And the random matrices used in random pixel exchanging are bound with the measurement matrices. Simulation results verify the effectiveness, security of the proposed algorithm and the acceptable compression performance.
Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation
Liu, Yipeng
2010-01-01
Too high sampling rate is the bottleneck to wideband spectrum sensing for cognitive radio (CR). As the survey shows that the sensed signal has a sparse representation in frequency domain in the mass, compressed sensing (CS) can be used to transfer the sampling burden to the digital signal processor. An analog to information converter (AIC) can randomly sample the received signal with sub-Nyquist rate to obtained the random measurements. Considering that the static frequency spectrum allocation of primary radios means the bounds between different primary radios is known in advance, here we incorporate information of the spectrum boundaries between different primary user as a priori information to obtain a mixed l2/l1 norm denoising operator (MNDO). In the MNDO, the estimated power spectrum density (PSD) vector is divided into block sections with bounds corresponding different allocated primary radios. Different from previous standard l1-norm constraint on the whole PSD vector, a sum of the l2 norm of each sect...
Vibha Tiwari
2015-12-01
Full Text Available Compressive sensing theory enables faithful reconstruction of signals, sparse in domain $ \\Psi $, at sampling rate lesser than Nyquist criterion, while using sampling or sensing matrix $ \\Phi $ which satisfies restricted isometric property. The role played by sensing matrix $ \\Phi $ and sparsity matrix $ \\Psi $ is vital in faithful reconstruction. If the sensing matrix is dense then it takes large storage space and leads to high computational cost. In this paper, effort is made to design sparse sensing matrix with least incurred computational cost while maintaining quality of reconstructed image. The design approach followed is based on sparse block circulant matrix (SBCM with few modifications. The other used sparse sensing matrix consists of 15 ones in each column. The medical images used are acquired from US, MRI and CT modalities. The image quality measurement parameters are used to compare the performance of reconstructed medical images using various sensing matrices. It is observed that, since Gram matrix of dictionary matrix ($ \\Phi \\Psi \\mathrm{} $ is closed to identity matrix in case of proposed modified SBCM, therefore, it helps to reconstruct the medical images of very good quality.
Compressive sensing for feedback reduction in MIMO broadcast channels
Eltayeb, Mohammed E.
2014-09-01
In multi-antenna broadcast networks, the base stations (BSs) rely on the channel state information (CSI) of the users to perform user scheduling and downlink transmission. However, in networks with large number of users, obtaining CSI from all users is arduous, if not impossible, in practice. This paper proposes channel feedback reduction techniques based on the theory of compressive sensing (CS), which permits the BS to obtain CSI with acceptable recovery guarantees under substantially reduced feedback overhead. Additionally, assuming noisy CS measurements at the BS, inexpensive ways for improving post-CS detection are explored. The proposed techniques are shown to reduce the feedback overhead, improve CS detection at the BS, and achieve a sum-rate close to that obtained by noiseless dedicated feedback channels.
Radial Velocity Data Analysis with Compressed Sensing Techniques
Hara, Nathan C.; Boué, G.; Laskar, J.; Correia, A. C. M.
2016-09-01
We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.
Compressive sensing via nonlocal low-rank regularization.
Dong, Weisheng; Shi, Guangming; Li, Xin; Ma, Yi; Huang, Feng
2014-08-01
Sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements. Recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing (CS) studies. In this paper, we propose a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its application into CS of both photographic and MRI images. We also propose the use of a nonconvex log det ( X) as a smooth surrogate function for the rank instead of the convex nuclear norm and justify the benefit of such a strategy using extensive experiments. To further improve the computational efficiency of the proposed algorithm, we have developed a fast implementation using the alternative direction multiplier method technique. Experimental results have shown that the proposed NLR-CS algorithm can significantly outperform existing state-of-the-art CS techniques for image recovery.
Simultaneous measurement of complementary observables with compressive sensing.
Howland, Gregory A; Schneeloch, James; Lum, Daniel J; Howell, John C
2014-06-27
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the entropic formulation of the uncertainty principle. Traditionally, uncertainly relations correspond to resolution limits; increasing a detector's position sensitivity decreases its momentum sensitivity and vice versa. However, this is not required in general; for example, position information can instead be extracted at the cost of noise in momentum. Using random, partial projections in position followed by strong measurements in momentum, we efficiently determine the transverse-position and transverse-momentum distributions of an unknown optical field with a single set of measurements. The momentum distribution is directly imaged, while the position distribution is recovered using compressive sensing. At no point do we violate uncertainty relations; rather, we economize the use of information we obtain.
Volumetric (3D) compressive sensing spectral domain optical coherence tomography.
Xu, Daguang; Huang, Yong; Kang, Jin U
2014-11-01
In this work, we proposed a novel three-dimensional compressive sensing (CS) approach for spectral domain optical coherence tomography (SD OCT) volumetric image acquisition and reconstruction. Instead of taking a spectral volume whose size is the same as that of the volumetric image, our method uses a sub set of the original spectral volume that is under-sampled in all three dimensions, which reduces the amount of spectral measurements to less than 20% of that required by the Shan-non/Nyquist theory. The 3D image is recovered from the under-sampled spectral data dimension-by-dimension using the proposed three-step CS reconstruction strategy. Experimental results show that our method can significantly reduce the sampling rate required for a volumetric SD OCT image while preserving the image quality.
Recovering network topologies via Taylor expansion and compressive sensing
Li, Guangjun; Liu, Juan, E-mail: xqwu@whu.edu.cn, E-mail: liujuanjp@163.com [Computer School, Wuhan University, Hubei 430072 (China); Wu, Xiaoqun, E-mail: xqwu@whu.edu.cn, E-mail: liujuanjp@163.com; Lu, Jun-an [School of Mathematics and Statistics, Wuhan University, Hubei 430072 (China); Guo, Chi [Global Navigation Satellite System Research Center, Wuhan University, Hubei 430072 (China)
2015-04-15
Gaining knowledge of the intrinsic topology of a complex dynamical network is the precondition to understand its evolutionary mechanisms and to control its dynamical and functional behaviors. In this article, a general framework is developed to recover topologies of complex networks with completely unknown node dynamics based on Taylor expansion and compressive sensing. Numerical simulations illustrate the feasibility and effectiveness of the proposed method. Moreover, this method is found to have good robustness to weak stochastic perturbations. Finally, the impact of two major factors on the topology identification performance is evaluated. This method provides a natural and direct point to reconstruct network topologies from measurable data, which is likely to have potential applicability in a wide range of fields.
Resolving intravoxel fiber architecture using nonconvex regularized blind compressed sensing
Chu, C. Y.; Huang, J. P.; Sun, C. Y.; Liu, W. Y.; Zhu, Y. M.
2015-03-01
In diffusion magnetic resonance imaging, accurate and reliable estimation of intravoxel fiber architectures is a major prerequisite for tractography algorithms or any other derived statistical analysis. Several methods have been proposed that estimate intravoxel fiber architectures using low angular resolution acquisitions owing to their shorter acquisition time and relatively low b-values. But these methods are highly sensitive to noise. In this work, we propose a nonconvex regularized blind compressed sensing approach to estimate intravoxel fiber architectures in low angular resolution acquisitions. The method models diffusion-weighted (DW) signals as a sparse linear combination of unfixed reconstruction basis functions and introduces a nonconvex regularizer to enhance the noise immunity. We present a general solving framework to simultaneously estimate the sparse coefficients and the reconstruction basis. Experiments on synthetic, phantom, and real human brain DW images demonstrate the superiority of the proposed approach.
Design and realization of random measurement scheme for compressed sensing
XIE Cheng-jun; XU Lin
2012-01-01
Design and realization of random measurement scheme for compressed sensing (CS) are presented in this paper,and lower limits of the measurement number are achieved when the precise reconstruction is realized.Four kinds of random measurement matrices are designed according to the constraint conditions of random measurement.The performance is tested employing the algorithm of stagewise orthogonal matching pursuit (StOMP).Results of the experiment show that lower limits of the measurement number are much better than the results described in Refs.[ 13-15].When the ratios of measurement to sparsity are 3.8 and 4.0,the mean relative errors of the reconstructed signals are 8.57 × 10-13 and 2.43 × 10-14,respectively,which confirms that the random measurement scheme of this paper is very effective.
Compressive sensing as a paradigm for building physics models
Nelson, Lance J.; Hart, Gus L. W.; Zhou, Fei; Ozoliņš, Vidvuds
2013-01-01
The widely accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be limited because the intuition for identifying the key variables often does not exist or is difficult to develop. Machine learning algorithms (genetic programming, neural networks, Bayesian methods, etc.) attempt to eliminate the a priori need for such intuition but often do so with increased computational burden and human time. A recently developed technique in the field of signal processing, compressive sensing (CS), provides a simple, general, and efficient way of finding the key descriptive variables. CS is a powerful paradigm for model building; we show that its models are more physical and predict more accurately than current state-of-the-art approaches and can be constructed at a fraction of the computational cost and user effort.
Compressed Sensing ISAR Reconstruction Considering Highly Maneuvering Motion
Ahmed Shaharyar Khwaja
2017-03-01
Full Text Available In this report, we propose compressed sensing inverse synthetic aperture radar (ISAR imaging in the presence of highly maneuvering motion using a modified orthogonal matching pursuit (OMP reconstruction algorithm. Unlike existing methods where motion is limited to first- or second-order phase terms, we take into account realistic motion of a maneuvering target that can involve a third-order phase term corresponding to the rate of rotational acceleration. In addition, unlike existing fixed dictionary-based methods, which require designing a large dictionary that needs to take into account all of the possible motion parameters, we propose a modified OMP reconstruction method that requires a dictionary only based on the first-order phase term and estimates the secondand third-order phase terms using an optimization algorithm. Simulation examples and comparison with existing methods show the viability of our approach for imaging moving targets consisting of higher order motion.
A Compressed Sensing Approach to 3D Weak Lensing
Leonard, Adrienne; Starck, Jean-Luc
2011-01-01
(Abridged) Weak gravitational lensing is an ideal probe of the dark universe. In recent years, several linear methods have been developed to reconstruct the density distribution in the Universe in three dimensions, making use of photometric redshift information to determine the radial distribution of lensed sources. In this paper, we aim to address three key issues seen in these methods; namely, the bias in the redshifts of detected objects, the line of sight smearing seen in reconstructions, and the damping of the amplitude of the reconstruction relative to the underlying density. We consider the problem under the framework of compressed sensing (CS). Under the assumption that the data are sparse in an appropriate dictionary, we construct a robust estimator and employ state-of-the-art convex optimisation methods to reconstruct the density contrast. For simplicity in implementation, and as a proof of concept of our method, we reduce the problem to one-dimension, considering the reconstruction along each line ...
Sparse Vector Distributions and Recovery from Compressed Sensing
Sturm, Bob L.
It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I...... empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector...... distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal....
Single image non-uniformity correction using compressive sensing
Jian, Xian-zhong; Lu, Rui-zhi; Guo, Qiang; Wang, Gui-pu
2016-05-01
A non-uniformity correction (NUC) method for an infrared focal plane array imaging system was proposed. The algorithm, based on compressive sensing (CS) of single image, overcame the disadvantages of "ghost artifacts" and bulk calculating costs in traditional NUC algorithms. A point-sampling matrix was designed to validate the measurements of CS on the time domain. The measurements were corrected using the midway infrared equalization algorithm, and the missing pixels were solved with the regularized orthogonal matching pursuit algorithm. Experimental results showed that the proposed method can reconstruct the entire image with only 25% pixels. A small difference was found between the correction results using 100% pixels and the reconstruction results using 40% pixels. Evaluation of the proposed method on the basis of the root-mean-square error, peak signal-to-noise ratio, and roughness index (ρ) proved the method to be robust and highly applicable.
Compressive Sensing for Feedback Reduction in Wireless Multiuser Networks
Elkhalil, Khalil
2015-05-01
User/relay selection is a simple technique that achieves spatial diversity in multiuser networks. However, for user/relay selection algorithms to make a selection decision, channel state information (CSI) from all cooperating users/relays is usually required at a central node. This requirement poses two important challenges. Firstly, CSI acquisition generates a great deal of feedback overhead (air-time) that could result in significant transmission delays. Secondly, the fed-back channel information is usually corrupted by additive noise. This could lead to transmission outages if the central node selects the set of cooperating relays based on inaccurate feedback information. Motivated by the aforementioned challenges, we propose a limited feedback user/relay selection scheme that is based on the theory of compressed sensing. Firstly, we introduce a limited feedback relay selection algorithm for a multicast relay network. The proposed algorithm exploits the theory of compressive sensing to first obtain the identity of the “strong” relays with limited feedback air-time. Following that, the CSI of the selected relays is estimated using minimum mean square error estimation without any additional feedback. To minimize the effect of noise on the fed-back CSI, we introduce a back-off strategy that optimally backs-off on the noisy received CSI. In the second part of the thesis, we propose a feedback reduction scheme for full-duplex relay-aided multiuser networks. The proposed scheme permits the base station (BS) to obtain channel state information (CSI) from a subset of strong users under substantially reduced feedback overhead. More specifically, we cast the problem of user identification and CSI estimation as a block sparse signal recovery problem in compressive sensing (CS). Using existing CS block recovery algorithms, we first obtain the identity of the strong users and then estimate their CSI using the best linear unbiased estimator (BLUE). Moreover, we derive the
Compressed sensing sparse reconstruction for coherent field imaging
Bei, Cao; Xiu-Juan, Luo; Yu, Zhang; Hui, Liu; Ming-Lai, Chen
2016-04-01
Return signal processing and reconstruction plays a pivotal role in coherent field imaging, having a significant influence on the quality of the reconstructed image. To reduce the required samples and accelerate the sampling process, we propose a genuine sparse reconstruction scheme based on compressed sensing theory. By analyzing the sparsity of the received signal in the Fourier spectrum domain, we accomplish an effective random projection and then reconstruct the return signal from as little as 10% of traditional samples, finally acquiring the target image precisely. The results of the numerical simulations and practical experiments verify the correctness of the proposed method, providing an efficient processing approach for imaging fast-moving targets in the future. Project supported by the National Natural Science Foundation of China (Grant No. 61505248) and the Fund from Chinese Academy of Sciences, the Light of “Western” Talent Cultivation Plan “Dr. Western Fund Project” (Grant No. Y429621213).
Uncovering transportation networks from traffic flux by compressed sensing
Tang, Si-Qi; Shen, Zhesi; Wang, Wen-Xu; Di, Zengru
2015-08-01
Transportation and communication networks are ubiquitous in nature and society. Uncovering the underlying topology as well as link weights, is fundamental to understanding traffic dynamics and designing effective control strategies to facilitate transmission efficiency. We develop a general method for reconstructing transportation networks from detectable traffic flux data using the aid of a compressed sensing algorithm. Our approach enables full reconstruction of network topology and link weights for both directed and undirected networks from relatively small amounts of data compared to the network size. The limited data requirement and certain resistance to noise allows our method to achieve real-time network reconstruction. We substantiate the effectiveness of our method through systematic numerical tests with respect to several different network structures and transmission strategies. We expect our approach to be widely applicable in a variety of transportation and communication systems.
Radial Velocity Data Analysis with Compressed Sensing Techniques
Hara, Nathan C; Laskar, Jacques; Correia, Alexandre C M
2016-01-01
We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.
Recoverability analysis for modified compressive sensing with partially known support.
Jun Zhang
Full Text Available The recently proposed modified-compressive sensing (modified-CS, which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on the reliability of the known support. An important problem, which must be studied further, is the recoverability of modified-CS when the known support contains a number of errors. In this letter, we analyze the recoverability of modified-CS in a stochastic framework. A sufficient and necessary condition is established for exact recovery of a sparse signal. Utilizing this condition, the recovery probability that reflects the recoverability of modified-CS can be computed explicitly for a sparse signal with [Formula: see text] nonzero entries. Simulation experiments have been carried out to validate our theoretical results.
Robust signal recovery algorithm for structured perturbation compressive sensing
Youhua Wang; Jianqiu Zhang
2016-01-01
It is understood that the sparse signal recovery with a standard compressive sensing (CS) strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application. In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm (SPSRA) is then pro-posed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analyticaly given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.
Compressed Sensing Inspired Image Reconstruction from Overlapped Projections
Lin Yang
2010-01-01
Full Text Available The key idea discussed in this paper is to reconstruct an image from overlapped projections so that the data acquisition process can be shortened while the image quality remains essentially uncompromised. To perform image reconstruction from overlapped projections, the conventional reconstruction approach (e.g., filtered backprojection (FBP algorithms cannot be directly used because of two problems. First, overlapped projections represent an imaging system in terms of summed exponentials, which cannot be transformed into a linear form. Second, the overlapped measurement carries less information than the traditional line integrals. To meet these challenges, we propose a compressive sensing-(CS- based iterative algorithm for reconstruction from overlapped data. This algorithm starts with a good initial guess, relies on adaptive linearization, and minimizes the total variation (TV. Then, we demonstrated the feasibility of this algorithm in numerical tests.
Fast Second Degree Total Variation Method for Image Compressive Sensing.
Liu, Pengfei; Xiao, Liang; Zhang, Jun
2015-01-01
This paper presents a computationally efficient algorithm for image compressive sensing reconstruction using a second degree total variation (HDTV2) regularization. Firstly, a preferably equivalent formulation of the HDTV2 functional is derived, which can be formulated as a weighted L1-L2 mixed norm of second degree image derivatives under the spectral decomposition framework. Secondly, using the equivalent formulation of HDTV2, we introduce an efficient forward-backward splitting (FBS) scheme to solve the HDTV2-based image reconstruction model. Furthermore, from the averaged non-expansive operator point of view, we make a detailed analysis on the convergence of the proposed FBS algorithm. Experiments on medical images demonstrate that the proposed method outperforms several fast algorithms of the TV and HDTV2 reconstruction models in terms of peak signal to noise ratio (PSNR), structural similarity index (SSIM) and convergence speed.
Radial velocity data analysis with compressed sensing techniques
Hara, Nathan C.; Boué, G.; Laskar, J.; Correia, A. C. M.
2017-01-01
We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian process framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick Observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.
Simultaneous Measurement of Complementary Observables with Compressive Sensing
Howland, Gregory A; Lum, Daniel J; Howell, John C
2016-01-01
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the entropic formulation of the uncertainty principle. Traditionally, uncertainty relations correspond to resolution limits; increasing a detector's position sensitivity decreases its momentum sensitivity and vice-versa. However, this is not required in general; for example, position information can instead be extracted at the cost of noise in momentum. Using random, partial projections in position followed by strong measurements in momentum, we efficiently determine the transverse-position and transverse-momentum distributions of an unknown optical field with a single set of measurements. The momentum distribution is directly imaged, while the position distribution is recovered using compressive sensing. At no point do we violate uncertainty relations; rather, we economize the use o...
Adaptive-Rate Compressive Sensing Using Side Information.
Warnell, Garrett; Bhattacharya, Sourabh; Chellappa, Rama; Başar, Tamer
2015-11-01
We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. The first method uses extra cross-validation measurements, and the second one exploits extra low-resolution measurements. Unlike the majority of current CS techniques, we do not assume that we know an upper bound on the number of significant coefficients that comprises the images in the video sequence. Instead, we use the side information to predict the number of significant coefficients in the signal at the next time instant. We develop our techniques in the specific context of background subtraction using a spatially multiplexing CS camera such as the single-pixel camera. For each image in the video sequence, the proposed techniques specify a fixed number of CS measurements to acquire and adjust this quantity from image to image. We experimentally validate the proposed methods on real surveillance video sequences.
Recovering network topologies via Taylor expansion and compressive sensing.
Li, Guangjun; Wu, Xiaoqun; Liu, Juan; Lu, Jun-an; Guo, Chi
2015-04-01
Gaining knowledge of the intrinsic topology of a complex dynamical network is the precondition to understand its evolutionary mechanisms and to control its dynamical and functional behaviors. In this article, a general framework is developed to recover topologies of complex networks with completely unknown node dynamics based on Taylor expansion and compressive sensing. Numerical simulations illustrate the feasibility and effectiveness of the proposed method. Moreover, this method is found to have good robustness to weak stochastic perturbations. Finally, the impact of two major factors on the topology identification performance is evaluated. This method provides a natural and direct point to reconstruct network topologies from measurable data, which is likely to have potential applicability in a wide range of fields.
Compressive sensing spectroscopy with a single pixel camera.
Starling, David J; Storer, Ian; Howland, Gregory A
2016-07-01
Spectrometry requires high spectral resolution and high photometric precision while also balancing cost and complexity. We address these requirements by employing a compressive-sensing camera capable of improving signal acquisition speed and sensitivity in limited signal scenarios. In particular, we implement a fast single pixel spectrophotometer with no moving parts and measure absorption and emission spectra comparable with commercial products. Our method utilizes Hadamard matrices to sample the spectra and then minimizes the total variation of the signal. The experimental setup includes standard optics and a grating, a low-cost digital micromirror device, and an intensity detector. The resulting spectrometer produces a 512 pixel spectrum with low mean-squared error and up to a 90% reduction in data acquisition time when compared with a standard spectrophotometer.
SAR Imaging of Moving Targets via Compressive Sensing
Wang, Jun; Zhang, Hao; Wang, Xiqin
2011-01-01
An algorithm based on compressive sensing (CS) is proposed for synthetic aperture radar (SAR) imaging of moving targets. The received SAR echo is decomposed into the sum of basis sub-signals, which are generated by discretizing the target spatial domain and velocity domain and synthesizing the SAR received data for every discretized spatial position and velocity candidate. In this way, the SAR imaging problem is converted into sub-signal selection problem. In the case that moving targets are sparsely distributed in the observed scene, their reflectivities, positions and velocities can be obtained by using the CS technique. It is shown that, compared with traditional algorithms, the target image obtained by the proposed algorithm has higher resolution and lower side-lobe while the required number of measurements can be an order of magnitude less than that by sampling at Nyquist sampling rate. Moreover, multiple targets with different speeds can be imaged simultaneously, so the proposed algorithm has higher eff...
Causal MRI reconstruction via Kalman prediction and compressed sensing correction.
Majumdar, Angshul
2017-02-04
This technical note addresses the problem of causal online reconstruction of dynamic MRI, i.e. given the reconstructed frames till the previous time instant, we reconstruct the frame at the current instant. Our work follows a prediction-correction framework. Given the previous frames, the current frame is predicted based on a Kalman estimate. The difference between the estimate and the current frame is then corrected based on the k-space samples of the current frame; this reconstruction assumes that the difference is sparse. The method is compared against prior Kalman filtering based techniques and Compressed Sensing based techniques. Experimental results show that the proposed method is more accurate than these and considerably faster.
The MUSIC Algorithm for Sparse Objects: A Compressed Sensing Analysis
Fannjiang, Albert C
2010-01-01
The MUSIC algorithm, with its extension for imaging sparse {\\em extended} objects, is analyzed by compressed sensing (CS) techniques. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant (RIC) are employed to establish sufficient conditions for the exact localization by MUSIC with or without the presence of noise. In the noiseless case, the sufficient condition gives an upper bound on the numbers of random sampling and incident directions necessary for exact localization. In the noisy case, the sufficient condition assumes additionally an upper bound for the noise-to-object ratio (NOR) in terms of the RIC. Rigorous comparison of performance between MUSIC and the CS minimization principle, Lasso, is given. In general, the MUSIC algorithm guarantees to recover, with high probability, $s$ scatterers with $n=\\cO(s^2)$ random sampling and incident directions and sufficiently high frequency. For the favorable imaging geometry where the scatterers are distributed on...
Unified framework and algorithm for quantized compressed sensing
Yang, Zai; Zhang, Cishen
2012-01-01
Compressed sensing (CS) studies the recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior. This paper is focused on the CS problem with quantized measurements. There have been research results dealing with different scenarios including a single/multiple bits per measurement, noiseless/noisy environment, and an unsaturated/saturated quantizer. While the existing methods are only for one or more specific cases, this paper presents a framework to unify all the above mentioned scenarios of the quantized CS problem. Under the unified framework, a variational Bayesian inference based algorithm is proposed which is applicable to the signal recovery of different application cases. Numerical simulations are carried out to illustrate the improved signal recovery accuracy of the unified algorithm in comparison with state-of-the-art methods for both multiple and single bit CS problems.
Compressed sensing in MRI – mathematical preliminaries and basic examples
Błaszczyk Łukasz
2016-03-01
Full Text Available In magnetic resonance imaging (MRI, k-space sampling, due to physical restrictions, is very time-consuming. It cannot be much improved using classical Nyquist-based sampling theory. Recent developments utilize the fact that MR images are sparse in some representations (i.e. wavelet coefficients. This new theory, created by Candès and Romberg, called compressed sensing (CS, shows that images with sparse representations can be recovered from randomly undersampled k-space data, by using nonlinear reconstruction algorithms (i.e. l1-norm minimization. Throughout this paper, mathematical preliminaries of CS are outlined, in the form introduced by Candès. We describe the main conditions for measurement matrices and recovery algorithms and present a basic example, showing that while the method really works (reducing the time of MR examination, there are some major problems that need to be taken into consideration.
Multi-Sparse Signal Recovery for Compressive Sensing
Liu, Yipeng; Matic, Vladimir; De Vos, Maarten; Van Huffel, Sabine
2012-01-01
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains. To further improve the signal reconstruction performance, we can exploit this multi-sparsity to generate a new convex programming model. The latter is formulated with multiple sparsity constraints in multiple domains and the linear measurement fitting constraint. It improves signal recovery performance by additional a priori information. Since some EMG signals exhibit sparsity both in time and frequency domains, we take them as example in numerical experiments. Results show that the newly proposed method achieves better performance for multi-sparse signals.
Underwater Acoustic Matched Field Imaging Based on Compressed Sensing
Huichen Yan
2015-10-01
Full Text Available Matched field processing (MFP is an effective method for underwater target imaging and localizing, but its performance is not guaranteed due to the nonuniqueness and instability problems caused by the underdetermined essence of MFP. By exploiting the sparsity of the targets in an imaging area, this paper proposes a compressive sensing MFP (CS-MFP model from wave propagation theory by using randomly deployed sensors. In addition, the model’s recovery performance is investigated by exploring the lower bounds of the coherence parameter of the CS dictionary. Furthermore, this paper analyzes the robustness of CS-MFP with respect to the displacement of the sensors. Subsequently, a coherence-excluding coherence optimized orthogonal matching pursuit (CCOOMP algorithm is proposed to overcome the high coherent dictionary problem in special cases. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed CS-MFP method.
Experimental Investigations on Airborne Gravimetry Based on Compressed Sensing
Yapeng Yang
2014-03-01
Full Text Available Gravity surveys are an important research topic in geophysics and geodynamics. This paper investigates a method for high accuracy large scale gravity anomaly data reconstruction. Based on the airborne gravimetry technology, a flight test was carried out in China with the strap-down airborne gravimeter (SGA-WZ developed by the Laboratory of Inertial Technology of the National University of Defense Technology. Taking into account the sparsity of airborne gravimetry by the discrete Fourier transform (DFT, this paper proposes a method for gravity anomaly data reconstruction using the theory of compressed sensing (CS. The gravity anomaly data reconstruction is an ill-posed inverse problem, which can be transformed into a sparse optimization problem. This paper uses the zero-norm as the objective function and presents a greedy algorithm called Orthogonal Matching Pursuit (OMP to solve the corresponding minimization problem. The test results have revealed that the compressed sampling rate is approximately 14%, the standard deviation of the reconstruction error by OMP is 0.03 mGal and the signal-to-noise ratio (SNR is 56.48 dB. In contrast, the standard deviation of the reconstruction error by the existing nearest-interpolation method (NIPM is 0.15 mGal and the SNR is 42.29 dB. These results have shown that the OMP algorithm can reconstruct the gravity anomaly data with higher accuracy and fewer measurements.
Experimental investigations on airborne gravimetry based on compressed sensing.
Yang, Yapeng; Wu, Meiping; Wang, Jinling; Zhang, Kaidong; Cao, Juliang; Cai, Shaokun
2014-03-18
Gravity surveys are an important research topic in geophysics and geodynamics. This paper investigates a method for high accuracy large scale gravity anomaly data reconstruction. Based on the airborne gravimetry technology, a flight test was carried out in China with the strap-down airborne gravimeter (SGA-WZ) developed by the Laboratory of Inertial Technology of the National University of Defense Technology. Taking into account the sparsity of airborne gravimetry by the discrete Fourier transform (DFT), this paper proposes a method for gravity anomaly data reconstruction using the theory of compressed sensing (CS). The gravity anomaly data reconstruction is an ill-posed inverse problem, which can be transformed into a sparse optimization problem. This paper uses the zero-norm as the objective function and presents a greedy algorithm called Orthogonal Matching Pursuit (OMP) to solve the corresponding minimization problem. The test results have revealed that the compressed sampling rate is approximately 14%, the standard deviation of the reconstruction error by OMP is 0.03 mGal and the signal-to-noise ratio (SNR) is 56.48 dB. In contrast, the standard deviation of the reconstruction error by the existing nearest-interpolation method (NIPM) is 0.15 mGal and the SNR is 42.29 dB. These results have shown that the OMP algorithm can reconstruct the gravity anomaly data with higher accuracy and fewer measurements.
Resolution enhancement for ISAR imaging via improved statistical compressive sensing
Zhang, Lei; Wang, Hongxian; Qiao, Zhi-jun
2016-12-01
Developing compressed sensing (CS) theory reveals that optimal reconstruction of an unknown signal can be achieved from very limited observations by utilizing signal sparsity. For inverse synthetic aperture radar (ISAR), the image of an interesting target is generally constructed by limited strong scattering centers, representing strong spatial sparsity. Such prior sparsity intrinsically paves a way to improved ISAR imaging performance. In this paper, we develop a super-resolution algorithm for forming ISAR images from limited observations. When the amplitude of the target scattered field follows an identical Laplace probability distribution, the approach converts super-resolution imaging into sparsity-driven optimization in the Bayesian statistics sense. We show that improved performance is achievable by taking advantage of the meaningful spatial structure of the scattered field. Further, we use the nonidentical Laplace distribution with small scale on strong signal components and large scale on noise to discriminate strong scattering centers from noise. A maximum likelihood estimator combined with a bandwidth extrapolation technique is also developed to estimate the scale parameters. Real measured data processing indicates the proposal can reconstruct the high-resolution image though only limited pulses even with low SNR, which shows advantages over current super-resolution imaging methods.
Compressed Sensing Techniques Applied to Ultrasonic Imaging of Cargo Containers
Álvarez López, Yuri; Martínez Lorenzo, José Ángel
2017-01-01
One of the key issues in the fight against the smuggling of goods has been the development of scanners for cargo inspection. X-ray-based radiographic system scanners are the most developed sensing modality. However, they are costly and use bulky sources that emit hazardous, ionizing radiation. Aiming to improve the probability of threat detection, an ultrasonic-based technique, capable of detecting the footprint of metallic containers or compartments concealed within the metallic structure of the inspected cargo, has been proposed. The system consists of an array of acoustic transceivers that is attached to the metallic structure-under-inspection, creating a guided acoustic Lamb wave. Reflections due to discontinuities are detected in the images, provided by an imaging algorithm. Taking into consideration that the majority of those images are sparse, this contribution analyzes the application of Compressed Sensing (CS) techniques in order to reduce the amount of measurements needed, thus achieving faster scanning, without compromising the detection capabilities of the system. A parametric study of the image quality, as a function of the samples needed in spatial and frequency domains, is presented, as well as the dependence on the sampling pattern. For this purpose, realistic cargo inspection scenarios have been simulated. PMID:28098841
Vibration-based monitoring and diagnostics using compressive sensing
Ganesan, Vaahini; Das, Tuhin; Rahnavard, Nazanin; Kauffman, Jeffrey L.
2017-04-01
Vibration data from mechanical systems carry important information that is useful for characterization and diagnosis. Standard approaches rely on continually streaming data at a fixed sampling frequency. For applications involving continuous monitoring, such as Structural Health Monitoring (SHM), such approaches result in high volume data and rely on sensors being powered for prolonged durations. Furthermore, for spatial resolution, structures are instrumented with a large array of sensors. This paper shows that both volume of data and number of sensors can be reduced significantly by applying Compressive Sensing (CS) in vibration monitoring applications. The reduction is achieved by using random sampling and capitalizing on the sparsity of vibration signals in the frequency domain. Preliminary experimental results validating CS-based frequency recovery are also provided. By exploiting the sparsity of mode shapes, CS can also enable efficient spatial reconstruction using fewer spatially distributed sensors. CS can thereby reduce the cost and power requirement of sensing as well as streamline data storage and processing in monitoring applications. In well-instrumented structures, CS can enable continued monitoring in case of sensor or computational failures.
Compressed Sensing Techniques Applied to Ultrasonic Imaging of Cargo Containers.
López, Yuri Álvarez; Lorenzo, José Ángel Martínez
2017-01-15
One of the key issues in the fight against the smuggling of goods has been the development of scanners for cargo inspection. X-ray-based radiographic system scanners are the most developed sensing modality. However, they are costly and use bulky sources that emit hazardous, ionizing radiation. Aiming to improve the probability of threat detection, an ultrasonic-based technique, capable of detecting the footprint of metallic containers or compartments concealed within the metallic structure of the inspected cargo, has been proposed. The system consists of an array of acoustic transceivers that is attached to the metallic structure-under-inspection, creating a guided acoustic Lamb wave. Reflections due to discontinuities are detected in the images, provided by an imaging algorithm. Taking into consideration that the majority of those images are sparse, this contribution analyzes the application of Compressed Sensing (CS) techniques in order to reduce the amount of measurements needed, thus achieving faster scanning, without compromising the detection capabilities of the system. A parametric study of the image quality, as a function of the samples needed in spatial and frequency domains, is presented, as well as the dependence on the sampling pattern. For this purpose, realistic cargo inspection scenarios have been simulated.
Compressed Sensing Techniques Applied to Ultrasonic Imaging of Cargo Containers
Yuri Álvarez López
2017-01-01
Full Text Available One of the key issues in the fight against the smuggling of goods has been the development of scanners for cargo inspection. X-ray-based radiographic system scanners are the most developed sensing modality. However, they are costly and use bulky sources that emit hazardous, ionizing radiation. Aiming to improve the probability of threat detection, an ultrasonic-based technique, capable of detecting the footprint of metallic containers or compartments concealed within the metallic structure of the inspected cargo, has been proposed. The system consists of an array of acoustic transceivers that is attached to the metallic structure-under-inspection, creating a guided acoustic Lamb wave. Reflections due to discontinuities are detected in the images, provided by an imaging algorithm. Taking into consideration that the majority of those images are sparse, this contribution analyzes the application of Compressed Sensing (CS techniques in order to reduce the amount of measurements needed, thus achieving faster scanning, without compromising the detection capabilities of the system. A parametric study of the image quality, as a function of the samples needed in spatial and frequency domains, is presented, as well as the dependence on the sampling pattern. For this purpose, realistic cargo inspection scenarios have been simulated.
Signal agnostic compressive sensing for Body Area Networks: comparison of signal reconstructions.
Casson, Alexander J; Rodriguez-Villegas, Esther
2012-01-01
Compressive sensing is a lossy compression technique that is potentially very suitable for use in power constrained sensor nodes and Body Area Networks as the compression process has a low computational complexity. This paper investigates the reconstruction performance of compressive sensing when applied to EEG, ECG, EOG and EMG signals; establishing the performance of a signal agnostic compressive sensing strategy that could be used in a Body Area Network monitoring all of these. The results demonstrate that the EEG, ECG and EOG can all be reconstructed satisfactorily, although large inter- and intra- subject variations are present. EMG signals are not well reconstructed. Compressive sensing may therefore also find use as a novel method for the identification of EMG artefacts in other electro-physiological signals.
Compressed Sensing Methods in Radio Receivers Exposed to Noise and Interference
Pierzchlewski, Jacek
, there is a problem of interference, which makes digitization of radio receivers even more dicult. High-order low-pass lters are needed to remove interfering signals and secure a high-quality reception. In the mid-2000s a new method of signal acquisition, called compressed sensing, emerged. Compressed sensing...... is a mathematical tool which allows for sub-Nyquist signal sampling. In this thesis the author opens a new possibility of relaxing requirements for analog signal ltering in a direct conversion receiver by applying compressed sensing. In the proposed solution,high-order low-pass lters which separate...... the downconverted baseband signal and interference, may be replaced by low-order lters. Additional digital signal processing is a price to pay for this feature. Hence, the signal processing is moved from the analog to the digital domain. Filtering compressed sensing, which is a new application of compressed sensing...
Two-Dimensional DOA Estimation in Compressed Sensing with Compressive-Reduced Dimension-lp-MUSIC
Weijian Si
2015-01-01
Full Text Available This paper presents a novel two-dimensional (2D direction of arrival (DOA estimation method in compressed sensing (CS to remove the estimation failure problem and achieve superior performance. The proposed method separates the steering vector into two parts to construct two corresponding noise subspaces by introducing electric angles. Then, electric angles are estimated based on the constructed noise subspaces. In order to estimate the azimuth and elevation angles in terms of estimates of electric angles, arc-tangent operations are exploited. The arc-tangent is a one-to-one function and allows the value of the argument to be larger than unity so that the proposed method never fails. The proposed method can avoid pair matching to reduce the computational complexity and extend the number of snapshots to improve performance. Simulation results show that the proposed method can avoid estimation failure occurrence and has superior performance as compared to existing methods.
Feizi, Soheil
2011-01-01
We propose a joint source-channel-network coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint source-channel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomness of the network allows a mapping to lower dimensional spaces. Our approach relies on using analog random linear network coding. The receiver uses compressive sensing decoders to reconstruct sources. Our key insight is the fact that, compressive sensing and analog network coding both preserve the source characteristics required for compressive sensing decoding.
COxSwAIN: Compressive Sensing for Advanced Imaging and Navigation
Kurwitz, Richard; Pulley, Marina; LaFerney, Nathan; Munoz, Carlos
2015-01-01
The COxSwAIN project focuses on building an image and video compression scheme that can be implemented in a small or low-power satellite. To do this, we used Compressive Sensing, where the compression is performed by matrix multiplications on the satellite and reconstructed on the ground. Our paper explains our methodology and demonstrates the results of the scheme, being able to achieve high quality image compression that is robust to noise and corruption.
Recent results of medium wave infrared compressive sensing.
Mahalanobis, A; Shilling, R; Murphy, R; Muise, R
2014-12-01
The application of compressive sensing (CS) for imaging has been extensively investigated and the underlying mathematical principles are well understood. The theory of CS is motivated by the sparse nature of real-world signals and images, and provides a framework in which high-resolution information can be recovered from low-resolution measurements. This, in turn, enables hardware concepts that require much fewer detectors than a conventional sensor. For infrared imagers there is a significant potential impact on the cost and footprint of the sensor. When smaller focal plane arrays (FPAs) to obtain large images are allowed, large formats FPAs are unnecessary. From a hardware standpoint, this benefit is independent of the actual level of compression and effective data rate reduction, which depend on the choice of codes and information recovery algorithm. Toward this end, we used a CS testbed for mid-wave infrared (MWIR) to experimentally show that information at high spatial resolution can be successfully recovered from measurements made with a small FPA. We describe the highly parallel and scalable CS architecture of the testbed, and its implementation using a reflective spatial light modulator and a focal plane array with variable pixel sizes. We also discuss the impact of real-world devices and the effect of sensor calibration that must be addressed in practice. Finally, we present preliminary results of image reconstruction, which demonstrate the testbed operation. These results experimentally confirm that high-resolution spatial information (for tasks such as imaging and target detection) can be successfully recovered from low-resolution measurements. We also discuss the potential system-level benefits of CS for infrared imaging, and some of the challenges that must be addressed in future infrared CS imagers designs.
2014-01-01
MATLAB simulation software used for the PhD thesis "Acquisition of Multi-Band Signals via Compressed Sensing......MATLAB simulation software used for the PhD thesis "Acquisition of Multi-Band Signals via Compressed Sensing...
A Computational model for compressed sensing RNAi cellular screening
2012-01-01
Background RNA interference (RNAi) becomes an increasingly important and effective genetic tool to study the function of target genes by suppressing specific genes of interest. This system approach helps identify signaling pathways and cellular phase types by tracking intensity and/or morphological changes of cells. The traditional RNAi screening scheme, in which one siRNA is designed to knockdown one specific mRNA target, needs a large library of siRNAs and turns out to be time-consuming and expensive. Results In this paper, we propose a conceptual model, called compressed sensing RNAi (csRNAi), which employs a unique combination of group of small interfering RNAs (siRNAs) to knockdown a much larger size of genes. This strategy is based on the fact that one gene can be partially bound with several small interfering RNAs (siRNAs) and conversely, one siRNA can bind to a few genes with distinct binding affinity. This model constructs a multi-to-multi correspondence between siRNAs and their targets, with siRNAs much fewer than mRNA targets, compared with the conventional scheme. Mathematically this problem involves an underdetermined system of equations (linear or nonlinear), which is ill-posed in general. However, the recently developed compressed sensing (CS) theory can solve this problem. We present a mathematical model to describe the csRNAi system based on both CS theory and biological concerns. To build this model, we first search nucleotide motifs in a target gene set. Then we propose a machine learning based method to find the effective siRNAs with novel features, such as image features and speech features to describe an siRNA sequence. Numerical simulations show that we can reduce the siRNA library to one third of that in the conventional scheme. In addition, the features to describe siRNAs outperform the existing ones substantially. Conclusions This csRNAi system is very promising in saving both time and cost for large-scale RNAi screening experiments which
Accelerated radial Fourier-velocity encoding using compressed sensing
Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)
2014-10-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Adaptive compressed sensing recovery utilizing the property of signal's autocorrelations.
Fu, Changjun; Ji, Xiangyang; Dai, Qionghai
2012-05-01
Perfect compressed sensing (CS) recovery can be achieved when a certain basis space is found to sparsely represent the original signal. However, due to the diversity of the signals, there does not exist a universal predetermined basis space that can sparsely represent all kinds of signals, which results in an unsatisfying performance. To improve the accuracy of recovered signal, this paper proposes an adaptive basis CS reconstruction algorithm by minimizing the rank of an accumulated matrix (MRAM), whose eigenvectors approximate the optimal basis sparsely representing the original signal. The accumulated matrix is constructed to efficiently exploit the second-order statistical property of the signal's autocorrelations. Based on the theory of matrix completion, MRAM reconstructs the original signal from its random projections under the observation that the constructed accumulated matrix is of low rank for most natural signals such as periodic signals and those coming from an autoregressive stationary process. Experimental results show that the proposed MRAM efficiently improves the reconstruction quality compared with the existing algorithms.
Block Compressed Sensing of Images Using Adaptive Granular Reconstruction
Ran Li
2016-01-01
Full Text Available In the framework of block Compressed Sensing (CS, the reconstruction algorithm based on the Smoothed Projected Landweber (SPL iteration can achieve the better rate-distortion performance with a low computational complexity, especially for using the Principle Components Analysis (PCA to perform the adaptive hard-thresholding shrinkage. However, during learning the PCA matrix, it affects the reconstruction performance of Landweber iteration to neglect the stationary local structural characteristic of image. To solve the above problem, this paper firstly uses the Granular Computing (GrC to decompose an image into several granules depending on the structural features of patches. Then, we perform the PCA to learn the sparse representation basis corresponding to each granule. Finally, the hard-thresholding shrinkage is employed to remove the noises in patches. The patches in granule have the stationary local structural characteristic, so that our method can effectively improve the performance of hard-thresholding shrinkage. Experimental results indicate that the reconstructed image by the proposed algorithm has better objective quality when compared with several traditional ones. The edge and texture details in the reconstructed image are better preserved, which guarantees the better visual quality. Besides, our method has still a low computational complexity of reconstruction.
Genetic optical design for a compressive sensing task
Horisaki, Ryoichi; Niihara, Takahiro; Tanida, Jun
2016-07-01
We present a sophisticated optical design method for reducing the number of photodetectors for a specific sensing task. The chosen design parameter is the point spread function, and the selected task is object recognition. The point spread function is optimized iteratively with a genetic algorithm for object recognition based on a neural network. In the experimental demonstration, binary classification of face and non-face datasets was performed with a single measurement using two photodetectors. A spatial light modulator operating in the amplitude modulation mode was provided in the imaging optics and was used to modulate the point spread function. In each generation of the genetic algorithm, the classification accuracy with a pattern displayed on the spatial light modulator was fed-back to the next generation to find better patterns. The proposed method increased the accuracy by about 30 % compared with a conventional imaging system in which the point spread function was the delta function. This approach is practically useful for compressing the cost, size, and observation time of optical sensors in specific applications, and robust for imperfections in optical elements.
Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling
Barranca, Victor J.; Kovačič, Gregor; Zhou, Douglas; Cai, David
2016-08-01
Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.
The possibilities of compressed-sensing-based Kirchhoff prestack migration
Aldawood, Ali
2014-05-08
An approximate subsurface reflectivity distribution of the earth is usually obtained through the migration process. However, conventional migration algorithms, including those based on the least-squares approach, yield structure descriptions that are slightly smeared and of low resolution caused by the common migration artifacts due to limited aperture, coarse sampling, band-limited source, and low subsurface illumination. To alleviate this problem, we use the fact that minimizing the L1-norm of a signal promotes its sparsity. Thus, we formulated the Kirchhoff migration problem as a compressed-sensing (CS) basis pursuit denoise problem to solve for highly focused migrated images compared with those obtained by standard and least-squares migration algorithms. The results of various subsurface reflectivity models revealed that solutions computed using the CS based migration provide a more accurate subsurface reflectivity location and amplitude. We applied the CS algorithm to image synthetic data from a fault model using dense and sparse acquisition geometries. Our results suggest that the proposed approach may still provide highly resolved images with a relatively small number of measurements. We also evaluated the robustness of the basis pursuit denoise algorithm in the presence of Gaussian random observational noise and in the case of imaging the recorded data with inaccurate migration velocities.
Compressed Sensing Based Encryption Approach for Tax Forms Data
Adrian Brezulianu
2015-11-01
Full Text Available In this work we investigate the possibility to use the measurement matrices from compressed sensing as secret key to encrypt / decrypt signals. Practical results and a comparison between BP (basis pursuit and OMP (orthogonal matching pursuit decryption algorithms are presented. To test our method, we used 10 text messages (10 different tax forms and we generated 10 random matrices and for distortion validate we used the PRD (the percentage root-mean-square difference, its normalized version (PRDN measures and NMSE (normalized mean square error. From the practical results we found that the time for BP algorithm is much higher than for OMP algorithm and the errors are smaller and should be noted that the OMP does not guarantee the convergence of the algorithm. We found that it is more advantageous, for tax forms (or other templates that show no interest for encryption to encrypt only the recorded data. The time required for decoding is significantly lower than the decryption for the entire form
Genetic optical design for a compressive sensing task
Horisaki, Ryoichi; Niihara, Takahiro; Tanida, Jun
2016-10-01
We present a sophisticated optical design method for reducing the number of photodetectors for a specific sensing task. The chosen design parameter is the point spread function, and the selected task is object recognition. The point spread function is optimized iteratively with a genetic algorithm for object recognition based on a neural network. In the experimental demonstration, binary classification of face and non-face datasets was performed with a single measurement using two photodetectors. A spatial light modulator operating in the amplitude modulation mode was provided in the imaging optics and was used to modulate the point spread function. In each generation of the genetic algorithm, the classification accuracy with a pattern displayed on the spatial light modulator was fed-back to the next generation to find better patterns. The proposed method increased the accuracy by about 30 % compared with a conventional imaging system in which the point spread function was the delta function. This approach is practically useful for compressing the cost, size, and observation time of optical sensors in specific applications, and robust for imperfections in optical elements.
Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising
Osher, Stanley; Dong, Bin; Yin, Wotao
2011-01-01
We propose and analyze an extremely fast, efficient, and simple method for solving the problem:min{parallel to u parallel to(1) : Au = f, u is an element of R-n}.This method was first described in [J. Darbon and S. Osher, preprint, 2007], with more details in [W. Yin, S. Osher, D. Goldfarb and J. Darbon, SIAM J. Imaging Sciences, 1(1), 143-168, 2008] and rigorous theory given in [J. Cai, S. Osher and Z. Shen, Math. Comp., to appear, 2008, see also UCLA CAM Report 08-06] and [J. Cai, S. Osher and Z. Shen, UCLA CAM Report, 08-52, 2008]. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, et. al. [E. Candes, J. Romberg and T. Tao, 52(2), 489-509, 2006] and Donoho, [D. L. Donoho, IEEE Trans. Inform. Theory, 52, 1289-1306, 2006]. See [W. Yin, S. Osher, D. Goldfarb and J. Darbon, SIAM J. Imaging Sciences 1(1), 143-168, 2008] and [J. Cai, S. Osher and Z. Shen, Math. Comp., to appear, 2008, see also UCLA CAM Report, 08-06] and [J. Cai, S. Osher a...
Implementation of compressive sensing for preclinical cine-MRI
Tan, Elliot; Yang, Ming; Ma, Lixin; Zheng, Yahong Rosa
2014-03-01
This paper presents a practical implementation of Compressive Sensing (CS) for a preclinical MRI machine to acquire randomly undersampled k-space data in cardiac function imaging applications. First, random undersampling masks were generated based on Gaussian, Cauchy, wrapped Cauchy and von Mises probability distribution functions by the inverse transform method. The best masks for undersampling ratios of 0.3, 0.4 and 0.5 were chosen for animal experimentation, and were programmed into a Bruker Avance III BioSpec 7.0T MRI system through method programming in ParaVision. Three undersampled mouse heart datasets were obtained using a fast low angle shot (FLASH) sequence, along with a control undersampled phantom dataset. ECG and respiratory gating was used to obtain high quality images. After CS reconstructions were applied to all acquired data, resulting images were quantitatively analyzed using the performance metrics of reconstruction error and Structural Similarity Index (SSIM). The comparative analysis indicated that CS reconstructed images from MRI machine undersampled data were indeed comparable to CS reconstructed images from retrospective undersampled data, and that CS techniques are practical in a preclinical setting. The implementation achieved 2 to 4 times acceleration for image acquisition and satisfactory quality of image reconstruction.
Filter for speckle noise reduction based on compressive sensing
Leportier, Thibault; Park, Min-Chul
2016-12-01
In holographic reconstruction, speckle noise is a serious factor that may degrade the image quality greatly. Several methods have been proposed, so far, to filter speckle from hologram reconstruction. The first approach is based on averaging several speckle patterns. The second solution is to apply a filter on the reconstructed image. In the first case, several holograms should be acquired, while compromise between speckle reduction and edge preservation is usually a challenge in the case of digital filtering. We propose a method to filter speckle noise based on compressive sensing (CS). CS is a method that has been demonstrated recently to reconstruct images with a sampling inferior to the Nyquist rate. By applying several times the CS algorithm on the hologram reconstruction with different initial downsampling, several versions of the same images can be reconstructed with slightly different speckle patterns. Then, speckle noise can be greatly decreased while preserving sharpness of the image. We demonstrate the effectiveness of our proposed method with simulations as well as with holograms acquired by phase-shifting method.
Compressive Sensing Based Design of Sparse Tripole Arrays.
Hawes, Matthew; Liu, Wei; Mihaylova, Lyudmila
2015-12-10
This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS). However, unlike for isotropic array elements (single antenna), we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles), which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA) of equivalent length.
Compressive-Sensing-Based Structure Identification for Multilayer Networks.
Mei, Guofeng; Wu, Xiaoqun; Wang, Yingfei; Hu, Mi; Lu, Jun-An; Chen, Guanrong
2017-02-13
The coexistence of multiple types of interactions within social, technological, and biological networks has motivated the study of the multilayer nature of real-world networks. Meanwhile, identifying network structures from dynamical observations is an essential issue pervading over the current research on complex networks. This paper addresses the problem of structure identification for multilayer networks, which is an important topic but involves a challenging inverse problem. To clearly reveal the formalism, the simplest two-layer network model is considered and a new approach to identifying the structure of one layer is proposed. Specifically, if the interested layer is sparsely connected and the node behaviors of the other layer are observable at a few time points, then a theoretical framework is established based on compressive sensing and regularization. Some numerical examples illustrate the effectiveness of the identification scheme, its requirement of a relatively small number of observations, as well as its robustness against small noise. It is noteworthy that the framework can be straightforwardly extended to multilayer networks, thus applicable to a variety of real-world complex systems.
Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing
Ri-Qi Su
2014-07-01
Full Text Available We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.
Compressive sensing for direct millimeter-wave holographic imaging.
Qiao, Lingbo; Wang, Yingxin; Shen, Zongjun; Zhao, Ziran; Chen, Zhiqiang
2015-04-10
Direct millimeter-wave (MMW) holographic imaging, which provides both the amplitude and phase information by using the heterodyne mixing technique, is considered a powerful tool for personnel security surveillance. However, MWW imaging systems usually suffer from the problem of high cost or relatively long data acquisition periods for array or single-pixel systems. In this paper, compressive sensing (CS), which aims at sparse sampling, is extended to direct MMW holographic imaging for reducing the number of antenna units or the data acquisition time. First, following the scalar diffraction theory, an exact derivation of the direct MMW holographic reconstruction is presented. Then, CS reconstruction strategies for complex-valued MMW images are introduced based on the derived reconstruction formula. To pursue the applicability for near-field MMW imaging and more complicated imaging targets, three sparsity bases, including total variance, wavelet, and curvelet, are evaluated for the CS reconstruction of MMW images. We also discuss different sampling patterns for single-pixel, linear array and two-dimensional array MMW imaging systems. Both simulations and experiments demonstrate the feasibility of recovering MMW images from measurements at 1/2 or even 1/4 of the Nyquist rate.
Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling.
Barranca, Victor J; Kovačič, Gregor; Zhou, Douglas; Cai, David
2016-08-24
Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.
The fast algorithm of spark in compressive sensing
Xie, Meihua; Yan, Fengxia
2017-01-01
Compressed Sensing (CS) is an advanced theory on signal sampling and reconstruction. In CS theory, the reconstruction condition of signal is an important theory problem, and spark is a good index to study this problem. But the computation of spark is NP hard. In this paper, we study the problem of computing spark. For some special matrixes, for example, the Gaussian random matrix and 0-1 random matrix, we obtain some conclusions. Furthermore, for Gaussian random matrix with fewer rows than columns, we prove that its spark equals to the number of its rows plus one with probability 1. For general matrix, two methods are given to compute its spark. One is the method of directly searching and the other is the method of dual-tree searching. By simulating 24 Gaussian random matrixes and 18 0-1 random matrixes, we tested the computation time of these two methods. Numerical results showed that the dual-tree searching method had higher efficiency than directly searching, especially for those matrixes which has as much as rows and columns.
Interferometric radio transient reconstruction in compressed sensing framework
Jiang, M; Starck, J -L; Corbel, S; Tasse, C
2015-01-01
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier samples of the sky. However, these imagers assumes a steady sky and the complexity of the problem increases when transients radio sources are also present in the data. Hopefully, in the context of transient imaging, the spatial and temporal information are separable which enable extension of an imager fit for a steady sky. We introduce independent spatial and temporal wavelet dictionaries to sparsely represent the transient in both spatial domain and temporal domain. These dictionaries intervenes in a new reconstruction method developed in the Compressed Sensing (CS) framework and using a primal-dual splitting algorithm. According to the preliminary tests in different noise regimes, this new "Time-agile" (or 2D-1D) method seems to be efficient in detecting and reconstructing the...
Passive Source Localization Using Compressively Sensed Towed Array
N. Suresh Kumar
2013-12-01
Full Text Available The objective of this work is to estimate the sparse angular power spectrum using a towed acoustic pressure sensor (APS array. In a passive towed array sonar, any reduction in the analog sensor signal conditioning receiver hardware housed inside the array tube, significantly improves the signal integrity and hence the localization performance. In this paper, a novel sparse acoustic pressure sensor (SAPS array architecture is proposed to estimate the direction of arrival (DOA of multiple acoustic sources. Bearing localization is effectively achieved by customizing the Capons spatial filter algorithm to suit the SAPS array architecture. Apart from the Monte Carlo simulations, the acoustic performance of the SAPS array with compressively sensed minimum variance distortionless response (CS-MVDR filter is demonstrated using a real passive towed array data. The proposed sparse towed array architecture promises a significant reduction in the analog signal acquisition receiver hardware, transmission data rate, number of snapshots and software complexity.Defence Science Journal, 2013, 63(6, pp.630-635, DOI:http://dx.doi.org/10.14429/dsj.63.5765
Opportunistic Relay Selection in Multicast Relay Networks using Compressive Sensing
Elkhalil, Khalil
2014-12-01
Relay selection is a simple technique that achieves spatial diversity in cooperative relay networks. However, for relay selection algorithms to make a selection decision, channel state information (CSI) from all cooperating relays is usually required at a central node. This requirement poses two important challenges. Firstly, CSI acquisition generates a great deal of feedback overhead (air-time) that could result in significant transmission delays. Secondly, the fed back channel information is usually corrupted by additive noise. This could lead to transmission outages if the central node selects the set of cooperating relays based on inaccurate feedback information. In this paper, we introduce a limited feedback relay selection algorithm for a multicast relay network. The proposed algorithm exploits the theory of compressive sensing to first obtain the identity of the “strong” relays with limited feedback. Following that, the CSI of the selected relays is estimated using linear minimum mean square error estimation. To minimize the effect of noise on the fed back CSI, we introduce a back-off strategy that optimally backs-off on the noisy estimated CSI. For a fixed group size, we provide closed form expressions for the scaling law of the maximum equivalent SNR for both Decode and Forward (DF) and Amplify and Forward (AF) cases. Numerical results show that the proposed algorithm drastically reduces the feedback air-time and achieves a rate close to that obtained by selection algorithms with dedicated error-free feedback channels.
Compressed Sensing Electron Tomography for Determining Biological Structure
Guay, Matthew D.; Czaja, Wojciech; Aronova, Maria A.; Leapman, Richard D.
2016-06-01
There has been growing interest in applying compressed sensing (CS) theory and practice to reconstruct 3D volumes at the nanoscale from electron tomography datasets of inorganic materials, based on known sparsity in the structure of interest. Here we explore the application of CS for visualizing the 3D structure of biological specimens from tomographic tilt series acquired in the scanning transmission electron microscope (STEM). CS-ET reconstructions match or outperform commonly used alternative methods in full and undersampled tomogram recovery, but with less significant performance gains than observed for the imaging of inorganic materials. We propose that this disparity stems from the increased structural complexity of biological systems, as supported by theoretical CS sampling considerations and numerical results in simulated phantom datasets. A detailed analysis of the efficacy of CS-ET for undersampled recovery is therefore complicated by the structure of the object being imaged. The numerical nonlinear decoding process of CS shares strong connections with popular regularized least-squares methods, and the use of such numerical recovery techniques for mitigating artifacts and denoising in reconstructions of fully sampled datasets remains advantageous. This article provides a link to the software that has been developed for CS-ET reconstruction of electron tomographic data sets.
Compressive Sensing Based Design of Sparse Tripole Arrays
Matthew Hawes
2015-12-01
Full Text Available This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS. However, unlike for isotropic array elements (single antenna, we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles, which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l 1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA of equivalent length.
Compressed sensing methods for DNA microarrays, RNA interference, and metagenomics.
Rao, Aditya; P, Deepthi; Renumadhavi, C H; Chandra, M Girish; Srinivasan, Rajgopal
2015-02-01
Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.
Peak Reduction and Clipping Mitigation by Compressive Sensing
Al-Safadi, Ebrahim B
2011-01-01
This work establishes the design, analysis, and fine-tuning of a Peak-to-Average-Power-Ratio (PAPR) reducing system, based on compressed sensing at the receiver of a peak-reducing sparse clipper applied to an OFDM signal at the transmitter. By exploiting the sparsity of the OFDM signal in the time domain relative to a pre-defined clipping threshold, the method depends on partially observing the frequency content of extremely simple sparse clippers to recover the locations, magnitudes, and phases of the clipped coefficients of the peak-reduced signal. We claim that in the absence of optimization algorithms at the transmitter that confine the frequency support of clippers to a predefined set of reserved-tones, no other tone-reservation method can reliably recover the original OFDM signal with such low complexity. Afterwards we focus on designing different clipping signals that can embed a priori information regarding the support and phase of the peak-reducing signal to the receiver, followed by modified compres...
Single-snapshot DOA estimation by using Compressed Sensing
Fortunati, Stefano; Grasso, Raffaele; Gini, Fulvio; Greco, Maria S.; LePage, Kevin
2014-12-01
This paper deals with the problem of estimating the directions of arrival (DOA) of multiple source signals from a single observation vector of an array data. In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classical ℓ 1 minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smooth ℓ 0 minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phase Estimation, IAA-APES algorithms, are analyzed, and their statistical properties are investigated and compared with the classical Fourier beamformer (FB) in different simulated scenarios. We show that unlike the classical FB, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g., Capon and MUSIC) even in the single snapshot case. Particular attention is devoted to the super-resolution property. Theoretical arguments and simulation analysis provide evidence that a CS-based beamformer can achieve resolution beyond the classical Rayleigh limit. Finally, the theoretical findings are validated by processing a real sonar dataset.
A high-resolution SWIR camera via compressed sensing
McMackin, Lenore; Herman, Matthew A.; Chatterjee, Bill; Weldon, Matt
2012-06-01
Images from a novel shortwave infrared (SWIR, 900 nm to 1.7 μm) camera system are presented. Custom electronics and software are combined with a digital micromirror device (DMD) and a single-element sensor; the latter are commercial off-the-shelf devices, which together create a lower-cost imaging system than is otherwise available in this wavelength regime. A compressive sensing (CS) encoding schema is applied to the DMD to modulate the light that has entered the camera. This modulated light is directed to a single-element sensor and an ensemble of measurements is collected. With the data ensemble and knowledge of the CS encoding, images are computationally reconstructed. The hardware and software combination makes it possible to create images with the resolution of the DMD while employing a substantially lower-cost sensor subsystem than would otherwise be required by the use of traditional focal plane arrays (FPAs). In addition to the basic camera architecture, we also discuss a technique that uses the adaptive functionality of the DMD to search and identify regions of interest. We demonstrate adaptive CS in solar exclusion experiments where bright pixels, which would otherwise reduce dynamic range in the images, are automatically removed.
Deconvolution of serum cortisol levels by using compressed sensing.
Rose T Faghih
Full Text Available The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH from the hypothalamus, adrenocorticotropin hormone (ACTH from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i compressed sensing for recovering the amplitude and timing of the secretory events, and (ii generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R (2 above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii potentially designing optimal approaches for treating hormonal disorders.
Deconvolution of serum cortisol levels by using compressed sensing.
Faghih, Rose T; Dahleh, Munther A; Adler, Gail K; Klerman, Elizabeth B; Brown, Emery N
2014-01-01
The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R (2) above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.
Rapid MR spectroscopic imaging of lactate using compressed sensing
Vidya Shankar, Rohini; Agarwal, Shubhangi; Geethanath, Sairam; Kodibagkar, Vikram D.
2015-03-01
Imaging lactate metabolism in vivo may improve cancer targeting and therapeutics due to its key role in the development, maintenance, and metastasis of cancer. The long acquisition times associated with magnetic resonance spectroscopic imaging (MRSI), which is a useful technique for assessing metabolic concentrations, are a deterrent to its routine clinical use. The objective of this study was to combine spectral editing and prospective compressed sensing (CS) acquisitions to enable precise and high-speed imaging of the lactate resonance. A MRSI pulse sequence with two key modifications was developed: (1) spectral editing components for selective detection of lactate, and (2) a variable density sampling mask for pseudo-random under-sampling of the k-space `on the fly'. The developed sequence was tested on phantoms and in vivo in rodent models of cancer. Datasets corresponding to the 1X (fully-sampled), 2X, 3X, 4X, 5X, and 10X accelerations were acquired. The under-sampled datasets were reconstructed using a custom-built algorithm in MatlabTM, and the fidelity of the CS reconstructions was assessed in terms of the peak amplitudes, SNR, and total acquisition time. The accelerated reconstructions demonstrate a reduction in the scan time by up to 90% in vitro and up to 80% in vivo, with negligible loss of information when compared with the fully-sampled dataset. The proposed unique combination of spectral editing and CS facilitated rapid mapping of the spatial distribution of lactate at high temporal resolution. This technique could potentially be translated to the clinic for the routine assessment of lactate changes in solid tumors.
Accelerated high-resolution photoacoustic tomography via compressed sensing
Arridge, Simon; Beard, Paul; Betcke, Marta; Cox, Ben; Huynh, Nam; Lucka, Felix; Ogunlade, Olumide; Zhang, Edward
2016-12-01
Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue (4D PAT). A particular example is the planar Fabry-Pérot (FP) photoacoustic scanner, which yields high-resolution 3D images but takes several minutes to sequentially map the incident photoacoustic field on the 2D sensor plane, point-by-point. However, as the spatio-temporal complexity of many absorbing tissue structures is rather low, the data recorded in such a conventional, regularly sampled fashion is often highly redundant. We demonstrate that combining model-based, variational image reconstruction methods using spatial sparsity constraints with the development of novel PAT acquisition systems capable of sub-sampling the acoustic wave field can dramatically increase the acquisition speed while maintaining a good spatial resolution: first, we describe and model two general spatial sub-sampling schemes. Then, we discuss how to implement them using the FP interferometer and demonstrate the potential of these novel compressed sensing PAT devices through simulated data from a realistic numerical phantom and through measured data from a dynamic experimental phantom as well as from in vivo experiments. Our results show that images with good spatial resolution and contrast can be obtained from highly sub-sampled PAT data if variational image reconstruction techniques that describe the tissues structures with suitable sparsity-constraints are used. In particular, we examine the use of total variation (TV) regularization enhanced by Bregman iterations. These novel reconstruction strategies offer new opportunities to dramatically increase the acquisition speed of photoacoustic scanners that employ point-by-point sequential scanning as well as reducing the channel count of parallelized schemes that use detector arrays.
On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
Compressed sensing (CS) has in recent years become a very popular way of sampling sparse signals. This sparsity is measured with respect to some known dictionary consisting of a finite number of atoms. Most models for real world signals, however, are parametrised by continuous parameters......-Rao lower bound (CRLB) which is frequently used for benchmarking the estimation accuracy of unbiased estimators. For the popular sensing matrices such as the Gaussian sensing matrix, our analysis shows that compressed sensing on average degrades the estimation accuracy by at least the down-sample factor....
Blind Compressed Sensing Parameter Estimation of Non-cooperative Frequency Hopping Signal
Chen Ying
2016-10-01
Full Text Available To overcome the disadvantages of a non-cooperative frequency hopping communication system, such as a high sampling rate and inadequate prior information, parameter estimation based on Blind Compressed Sensing (BCS is proposed. The signal is precisely reconstructed by the alternating iteration of sparse coding and basis updating, and the hopping frequencies are directly estimated based on the results. Compared with conventional compressive sensing, blind compressed sensing does not require prior information of the frequency hopping signals; hence, it offers an effective solution to the inadequate prior information problem. In the proposed method, the signal is first modeled and then reconstructed by Orthonormal Block Diagonal Blind Compressed Sensing (OBD-BCS, and the hopping frequencies and hop period are finally estimated. The simulation results suggest that the proposed method can reconstruct and estimate the parameters of noncooperative frequency hopping signals with a low signal-to-noise ratio.
Compressive Sensing Based Bio-Inspired Shape Feature Detection CMOS Imager
Duong, Tuan A. (Inventor)
2015-01-01
A CMOS imager integrated circuit using compressive sensing and bio-inspired detection is presented which integrates novel functions and algorithms within a novel hardware architecture enabling efficient on-chip implementation.
2016-02-01
with equal probability. The scheme was proposed [2] for image processing using single pixel camera, where the field of view was masked by a grid...distribution unlimited. 3.0 SUMMARY AND FUTURE WORK Compressed sensing technology has generated interest in image and signal processing . It is of great...Reconstruction Algorithm, Master Thesis , Feb, 2009. [5] S. R. Becker, “Practical Compressed Sensing: Modern Data Acquistion and Signal Processing
Zhou Jianming; Liu Fan; Lu Qiuyuan
2014-01-01
In mobile Internet of Tings, based on cross-layer design and resource-aware scheduling, the combination of light weight coding and compressed sensing is used to improve the real-time performance of acquisition of system resource and reliability of resource management in this paper. Compressed sensing scheme based on the adaptive frame format definition of lightweight coding is able to set up the parameters such as sample signal, signal and hops. The nonlinear relationship matrixes between res...
Zhou Jianming; Liu Fan; Lu Qiuyuan
2014-01-01
In mobile Internet of Tings, based on cross-layer design and resource-aware scheduling, the combination of light weight coding and compressed sensing is used to improve the real-time performance of acquisition of system resource and reliability of resource management in this paper. Compressed sensing scheme based on the adaptive frame format definition of lightweight coding is able to set up the parameters such as sample signal, signal and hops. The nonlinear relationship matrixes between res...
Wang, Qingzhu; Chen, Xiaoming; Wei, Mengying; Miao, Zhuang
2016-11-04
The existing techniques for simultaneous encryption and compression of images refer lossy compression. Their reconstruction performances did not meet the accuracy of medical images because most of them have not been applicable to three-dimensional (3D) medical image volumes intrinsically represented by tensors. We propose a tensor-based algorithm using tensor compressive sensing (TCS) to address these issues. Alternating least squares is further used to optimize the TCS with measurement matrices encrypted by discrete 3D Lorenz. The proposed method preserves the intrinsic structure of tensor-based 3D images and achieves a better balance of compression ratio, decryption accuracy, and security. Furthermore, the characteristic of the tensor product can be used as additional keys to make unauthorized decryption harder. Numerical simulation results verify the validity and the reliability of this scheme.
The MUSIC algorithm for sparse objects: a compressed sensing analysis
Fannjiang, Albert C.
2011-03-01
The multiple signal classification (MUSIC) algorithm, and its extension for imaging sparse extended objects, with noisy data is analyzed by compressed sensing (CS) techniques. A thresholding rule is developed to augment the standard MUSIC algorithm. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant (RIC) are employed to establish sufficient conditions for the exact localization by MUSIC with or without noise. In the noiseless case, the sufficient condition gives an upper bound on the numbers of random sampling and incident directions necessary for exact localization. In the noisy case, the sufficient condition assumes additionally an upper bound for the noise-to-object ratio in terms of the RIC and the dynamic range of objects. This bound points to the super-resolution capability of the MUSIC algorithm. Rigorous comparison of performance between MUSIC and the CS minimization principle, basis pursuit denoising (BPDN), is given. In general, the MUSIC algorithm guarantees to recover, with high probability, s scatterers with n= {O}(s^2) random sampling and incident directions and sufficiently high frequency. For the favorable imaging geometry where the scatterers are distributed on a transverse plane MUSIC guarantees to recover, with high probability, s scatterers with a median frequency and n= {O}(s) random sampling/incident directions. Moreover, for the problems of spectral estimation and source localizations both BPDN and MUSIC guarantee, with high probability, to identify exactly the frequencies of random signals with the number n= {O}(s) of sampling times. However, in the absence of abundant realizations of signals, BPDN is the preferred method for spectral estimation. Indeed, BPDN can identify the frequencies approximately with just one realization of signals with the recovery error at worst linearly proportional to the noise level. Numerical results confirm that BPDN outperforms MUSIC in the well
Il Yong Chun; Adcock, Ben; Talavage, Thomas M
2014-01-01
Magnetic resonance imaging (MRI) is considered a key modality for the future as it offers several advantages, including the use of non-ionizing radiation and having no known side effects on the human body, and has recently begun to serve as a key component of multi-modal neuroimaging. However, two major intrinsic problems exist: slow acquisition and intrusive acoustic noise. Parallel MRI (pMRI) techniques accelerate acquisition by reducing the duration and coverage of conventional gradient encoding. The under-sampled k-space data is detected with several receiver coils surrounding the object, using distinct spatial encoding information for each coil element to reconstruct the image. However, this scanning remains slow compared to typical clinical imaging (e.g. X-ray CT). Compressed Sensing (CS), a sampling theory based on random sub-sampling, has potential to further reduce the sampling used in pMRI, accelerating acquisition further. In this work, we propose a new CS SENSE pMRI reconstruction model promoting joint sparsity across channels and enhancing mutual incoherence to improve reconstruction accuracy from limited k-space data. For fast image reconstruction and fair comparisons, all reconstructions are computed with split-Bregman and variable splitting techniques. Numerical results show that, with the introduced methods, reconstruction performance can be crucially improved with limited amount of k-space data.
Compressed Sensing and Low-Rank Matrix Decomposition in Multisource Images Fusion
Kan Ren
2014-01-01
Full Text Available We propose a novel super-resolution multisource images fusion scheme via compressive sensing and dictionary learning theory. Under the sparsity prior of images patches and the framework of the compressive sensing theory, the multisource images fusion is reduced to a signal recovery problem from the compressive measurements. Then, a set of multiscale dictionaries are learned from several groups of high-resolution sample image’s patches via a nonlinear optimization algorithm. Moreover, a new linear weights fusion rule is proposed to obtain the high-resolution image. Some experiments are taken to investigate the performance of our proposed method, and the results prove its superiority to its counterparts.
Compressive sensing beamforming based on covariance for acoustic imaging with noisy measurements.
Zhong, Siyang; Wei, Qingkai; Huang, Xun
2013-11-01
Compressive sensing, a newly emerging method from information technology, is applied to array beamforming and associated acoustic applications. A compressive sensing beamforming method (CSB-II) is developed based on sampling covariance matrix, assuming spatially sparse and incoherent signals, and then examined using both simulations and aeroacoustic measurements. The simulation results clearly show that the proposed CSB-II method is robust to sensing noise. In addition, aeroacoustic tests of a landing gear model demonstrate the good performance in terms of resolution and sidelobe rejection.
A SPARSITY AND COMPRESSION RATIO JOINT ADJUSTMENT METHOD FOR COLLABORATIVE SPECTRUM SENSING
Chi Jingxiu; Zhang Jianwu; Xu Xiaorong
2012-01-01
Spectrum sensing is the fundamental task for Cognitive Radio (CR).To overcome the challenge of high sampling rate in traditional spectral estimation methods,Compressed Sensing (CS) theory is developed.A sparsity and compression ratio joint adjustment algorithm for compressed spectrum sensing in CR network is investigated,with the hypothesis that the sparsity level is unknown as priori knowledge at CR terminals.As perfect spectrum reconstruction is not necessarily required during spectrum detection process,the proposed algorithm only performs a rough estimate of sparsity level.Meanwhile,in order to further reduce the sensing measurement,different compression ratios for CR terminals with varying Signal-to-Noise Ratio (SNR) are considered.The proposed algorithm,which optimizes the compression ratio as well as the estimated sparsity level,can greatly reduce the sensing measurement without degrading the detection performance.It also requires less steps of iteration for convergence.Corroborating simulation results are presented to testify the effectiveness of the proposed algorithm for collaborative spectrum sensing.
Performance bounds for expander-based compressed sensing in Poisson noise
Raginsky, Maxim; Harmany, Zachary; Marcia, Roummel; Willett, Rebecca; Calderbank, Robert
2010-01-01
This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a MAP algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process.
Saligrama, Venkatesh
2008-01-01
In this paper we present a new family of discrete sequences having ``random like'' uniformly decaying auto-correlation properties. The new class of infinite length sequences are higher order chirps constructed using irrational numbers. Exploiting results from the theory of continued fractions and diophantine approximations, we show that the class of sequences so formed has the property that the worst-case auto-correlation coefficients for every finite length sequence decays at a polynomial rate. These sequences display doppler immunity as well. We also show that Toeplitz matrices formed from such sequences satisfy restricted-isometry-property (RIP), a concept that has played a central role recently in Compressed Sensing applications. Compressed sensing has conventionally dealt with sensing matrices with arbitrary components. Nevertheless, such arbitrary sensing matrices are not appropriate for linear system identification and one must employ Toeplitz structured sensing matrices. Linear system identification p...
Total Variation Minimization Based Compressive Wideband Spectrum Sensing for Cognitive Radios
Liu, Yipeng
2011-01-01
Wideband spectrum sensing is a critical component of a functioning cognitive radio system. Its major challenge is the too high sampling rate requirement. Compressive sensing (CS) promises to be able to deal with it. Nearly all the current CS based compressive wideband spectrum sensing methods exploit only the frequency sparsity to perform. Motivated by the achievement of a fast and robust detection of the wideband spectrum change, total variation mnimization is incorporated to exploit the temporal and frequency structure information to enhance the sparse level. As a sparser vector is obtained, the spectrum sensing period would be shorten and sensing accuracy would be enhanced. Both theoretical evaluation and numerical experiments can demonstrate the performance improvement.
2015-06-01
ARL-TR-7328 ● JUN 2015 US Army Research Laboratory The Use of Compressive Sensing to Reconstruct Radiation Characteristics of...Army Research Laboratory The Use of Compressive Sensing to Reconstruct Radiation Characteristics of Wide- Band Antennas from Sparse Measurements... Compressive Sensing to Reconstruct Radiation Characteristics of Wide-Band Antennas from Sparse Measurements 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c
Research on Differential Coding Method for Satellite Remote Sensing Data Compression
Lin, Z. J.; Yao, N.; Deng, B.; Wang, C. Z.; Wang, J. H.
2012-07-01
Data compression, in the process of Satellite Earth data transmission, is of great concern to improve the efficiency of data transmission. Information amounts inherent to remote sensing images provide a foundation for data compression in terms of information theory. In particular, distinct degrees of uncertainty inherent to distinct land covers result in the different information amounts. This paper first proposes a lossless differential encoding method to improve compression rates. Then a district forecast differential encoding method is proposed to further improve the compression rates. Considering the stereo measurements in modern photogrammetry are basically accomplished by means of automatic stereo image matching, an edge protection operator is finally utilized to appropriately filter out high frequency noises which could help magnify the signals and further improve the compression rates. The three steps were applied to a Landsat TM multispectral image and a set of SPOT-5 panchromatic images of four typical land cover types (i.e., urban areas, farm lands, mountain areas and water bodies). Results revealed that the average code lengths obtained by the differential encoding method, compared with Huffman encoding, were more close to the information amounts inherent to remote sensing images. And the compression rates were improved to some extent. Furthermore, the compression rates of the four land cover images obtained by the district forecast differential encoding method were nearly doubled. As for the images with the edge features preserved, the compression rates are average four times as large as those of the original images.
Compressed sensing for super-resolution spatial and temporal laser detection and ranging
Laurenzis, Martin; Schertzer, Stephane; Christnacher, Frank
2016-10-01
In the past decades, laser aided electro-optical sensing has reached high maturity and several commercial systems are available at the market for various but specific applications. These systems can be used for detection i.e. imaging as well as ranging. They cover laser scanning devices like LiDAR and staring full frame imaging systems like laser gated viewing or LADAR. The sensing capabilities of these systems is limited by physical parameter (like FPA array size, temporal band width, scanning rate, sampling rate) and is adapted to specific applications. Change of system parameter like an increase of spatial resolution implies the setup of a new sensing device with high development cost or the purchase and installation of a complete new sensor unit. Computational imaging approaches can help to setup sensor devices with flexible or adaptable sensing capabilities. Especially, compressed sensing is an emerging computational method which is a promising candidate to realize super-resolution sensing with the possibility to adapt its performance to various sensing tasks. It is possible to increase sensing capabilities with compressed sensing to gain either higher spatial and/or temporal resolution. Then, the sensing capabilities depend no longer only on the physical performance of the device but also on the computational effort and can be adapted to the application. In this paper, we demonstrate and discuss laser aided imaging using CS for super-resolution tempo-spatial imaging and ranging.
Li, Edward; Shafiee, Mohammad Javad; Haider, Masoom A; Wong, Alexander
2015-01-01
Magnetic Resonance Imaging (MRI) is a crucial medical imaging technology for the screening and diagnosis of frequently occurring cancers. However image quality may suffer by long acquisition times for MRIs due to patient motion, as well as result in great patient discomfort. Reducing MRI acquisition time can reduce patient discomfort and as a result reduces motion artifacts from the acquisition process. Compressive sensing strategies, when applied to MRI, have been demonstrated to be effective at decreasing acquisition times significantly by sparsely sampling the \\emph{k}-space during the acquisition process. However, such a strategy requires advanced reconstruction algorithms to produce high quality and reliable images from compressive sensing MRI. This paper proposes a new reconstruction approach based on cross-domain stochastically fully connected conditional random fields (CD-SFCRF) for compressive sensing MRI. The CD-SFCRF introduces constraints in both \\emph{k}-space and spatial domains within a stochas...
Compressive Sensing in Speech from LPC using Gradient Projection for Sparse Reconstruction
Viral Modha
2015-02-01
Full Text Available This paper presents compressive sensing technique used for speech reconstruction using linear predictive coding because the speech is more sparse in LPC. DCT of a speech is taken and the DCT points of sparse speech are thrown away arbitrarily. This is achieved by making some point in DCT domain to be zero by multiplying with mask functions. From the incomplete points in DCT domain, the original speech is reconstructed using compressive sensing and the tool used is Gradient Projection for Sparse Reconstruction. The performance of the result is compared with direct IDCT subjectively. The experiment is done and it is observed that the performance is better for compressive sensing than the DCT.
Zhou Jianming
2014-01-01
Full Text Available In mobile Internet of Tings, based on cross-layer design and resource-aware scheduling, the combination of light weight coding and compressed sensing is used to improve the real-time performance of acquisition of system resource and reliability of resource management in this paper. Compressed sensing scheme based on the adaptive frame format definition of lightweight coding is able to set up the parameters such as sample signal, signal and hops. The nonlinear relationship matrixes between resource information of sensors or system and quality of services are built to manage the global or local network resource scheduling. Experimental results show that the proposed scheme is better than the traditional scheme or resource management based on compressed sensing alone scheme, which can make the system be able to achieve optimal resource allocation.
Ke, Jun; Lam, Edmund Y
2016-05-02
Compressive measurements benefit low-light-level imaging (L3-imaging) due to the significantly improved measurement signal-to-noise ratio (SNR). However, as with other compressive imaging (CI) systems, compressive L3-imaging is slow. To accelerate the data acquisition, we develop an algorithm to compute the optimal binary sensing matrix that can minimize the image reconstruction error. First, we make use of the measurement SNR and the reconstruction mean square error (MSE) to define the optimal gray-value sensing matrix. Then, we construct an equality-constrained optimization problem to solve for a binary sensing matrix. From several experimental results, we show that the latter delivers a similar reconstruction performance as the former, while having a smaller dynamic range requirement to system sensors.
Non-convex prior image constrained compressed sensing (NC-PICCS)
Ramírez Giraldo, Juan Carlos; Trzasko, Joshua D.; Leng, Shuai; McCollough, Cynthia H.; Manduca, Armando
2010-04-01
The purpose of this paper is to present a new image reconstruction algorithm for dynamic data, termed non-convex prior image constrained compressed sensing (NC-PICCS). It generalizes the prior image constrained compressed sensing (PICCS) algorithm with the use of non-convex priors. Here, we concentrate on perfusion studies using computed tomography examples in simulated phantoms (with and without added noise) and in vivo data, to show how the NC-PICCS method holds potential for dramatic reductions in radiation dose for time-resolved CT imaging. We show that NC-PICCS can provide additional undersampling compared to conventional convex compressed sensing and PICCS, as well as, faster convergence under a quasi-Newton numerical solver.
Compressed Sensing-Based MRI Reconstruction Using Complex Double-Density Dual-Tree DWT
Zangen Zhu
2013-01-01
Full Text Available Undersampling k-space data is an efficient way to speed up the magnetic resonance imaging (MRI process. As a newly developed mathematical framework of signal sampling and recovery, compressed sensing (CS allows signal acquisition using fewer samples than what is specified by Nyquist-Shannon sampling theorem whenever the signal is sparse. As a result, CS has great potential in reducing data acquisition time in MRI. In traditional compressed sensing MRI methods, an image is reconstructed by enforcing its sparse representation with respect to a basis, usually wavelet transform or total variation. In this paper, we propose an improved compressed sensing-based reconstruction method using the complex double-density dual-tree discrete wavelet transform. Our experiments demonstrate that this method can reduce aliasing artifacts and achieve higher peak signal-to-noise ratio (PSNR and structural similarity (SSIM index.
压缩传感技术及其应用%Compressive Sensing and its Applications
2013-01-01
This paper introduced a new signal processing method —Compressive Sensing (CS ) . Recently , an emerging theory of signal acquirement named Compressive Sensing become one of the hottest topics of signal sampling and image processing .It is a novel signal sampling theory under the condition that the signal is sparse or compressible .It has the ability of compressing a signal during the process of sampling .It consists of three main areas :sparse representation matrix , measurement matrix and reconstruction algorithm . This paper mainly introduces the model of Compressive Sensing ,and the main reconstruction algorithms ,then analyses and compares the algorithms .Finally ,the paper lists the main applications of Compressive Sensing .% 本文综述了一种新的信号处理方法—压缩传感（Compressive Sensing ，CS），它是针对稀疏或者可压缩信号，在采样的同时即可对信号数据进行适当压缩的新理论。近年来，压缩传感理论成为信号采样及图像处理领域最新、最热点的问题之一。它主要包括三个方面：稀疏表示矩阵，非相干测量矩阵以及重建算法。本文介绍了压缩传感理论的模型，以及压缩传感的主要重建算法，并将实现方法进行了分析与比较。文章最后列举出了压缩传感的主要应用领域。
Photonic compressive sensing with a micro-ring-resonator-based microwave photonic filter
Chen, Ying; Ding, Yunhong; Zhu, Zhijing
2015-01-01
A novel approach to realize photonic compressive sensing (CS) with a multi-tap microwave photonic filter is proposed and demonstrated. The system takes both advantages of CS and photonics to capture wideband sparse signals with sub-Nyquist sampling rate. The low-pass filtering function required...... for a two-tone signal acquisition with frequencies of 350. MHz and 1.25. GHz is experimentally demonstrated with a compression factor up to 16....
Compressive spectrum sensing of radar pulses based on photonic techniques.
Guo, Qiang; Liang, Yunhua; Chen, Minghua; Chen, Hongwei; Xie, Shizhong
2015-02-23
We present a photonic-assisted compressive sampling (CS) system which can acquire about 10(6) radar pulses per second spanning from 500 MHz to 5 GHz with a 520-MHz analog-to-digital converter (ADC). A rectangular pulse, a linear frequency modulated (LFM) pulse and a pulse stream is respectively reconstructed faithfully through this system with a sliding window-based recovery algorithm, demonstrating the feasibility of the proposed photonic-assisted CS system in spectral estimation for radar pulses.
High capacity image steganography method based on framelet and compressive sensing
Xiao, Moyan; He, Zhibiao
2015-12-01
To improve the capacity and imperceptibility of image steganography, a novel high capacity and imperceptibility image steganography method based on a combination of framelet and compressive sensing (CS) is put forward. Firstly, SVD (Singular Value Decomposition) transform to measurement values obtained by compressive sensing technique to the secret data. Then the singular values in turn embed into the low frequency coarse subbands of framelet transform to the blocks of the cover image which is divided into non-overlapping blocks. Finally, use inverse framelet transforms and combine to obtain the stego image. The experimental results show that the proposed steganography method has a good performance in hiding capacity, security and imperceptibility.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks
Barranca, Victor J.; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks.
Barranca, Victor J; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Béché, Armand; Freitag, Bert; Verbeeck, Jo
2015-01-01
The concept of compressive sensing was recently proposed to significantly reduce the electron dose in scanning transmission electron microscopy (STEM) while still maintaining the main features in the image. Here, an experimental setup based on an electromagnetic shutter placed in the condenser plane of a STEM is proposed. The shutter blanks the beam following a random pattern while the scanning coils are moving the beam in the usual scan pattern. Experimental images at both medium scale and high resolution are acquired and then reconstructed based on a discrete cosine algorithm. The obtained results confirm the predicted usefulness of compressive sensing in experimental STEM even though some remaining artifacts need to be resolved.
Linear Program Relaxation of Sparse Nonnegative Recovery in Compressive Sensing Microarrays
Linxia Qin
2012-01-01
Full Text Available Compressive sensing microarrays (CSM are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l1 relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l1 relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.
Linear program relaxation of sparse nonnegative recovery in compressive sensing microarrays.
Qin, Linxia; Xiu, Naihua; Kong, Lingchen; Li, Yu
2012-01-01
Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the l₁ relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the l₁ relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.
Pilotless recovery of clipped OFDM signals by compressive sensing over reliable data carriers
Al-Safadi, Ebrahim B.
2012-06-01
In this paper we propose a novel method of clipping mitigation in OFDM using compressive sensing that completely avoids using reserved tones or channel-estimation pilots. The method builds on selecting the most reliable perturbations from the constellation lattice upon decoding at the receiver (in the frequency domain), and performs compressive sensing over these observations in order to completely recover the sparse nonlinear distortion in the time domain. As such, the method provides a practical solution to the problem of initial erroneous decoding decisions in iterative ML methods, and the ability to recover the distorted signal in one shot. © 2012 IEEE.
A compressive sensing approach to the calculation of the inverse data space
Khan, Babar Hasan
2012-01-01
Seismic processing in the Inverse Data Space (IDS) has its advantages like the task of removing the multiples simply becomes muting the zero offset and zero time data in the inverse domain. Calculation of the Inverse Data Space by sparse inversion techniques has seen mitigation of some artifacts. We reformulate the problem by taking advantage of some of the developments from the field of Compressive Sensing. The seismic data is compressed at the sensor level by recording projections of the traces. We then process this compressed data directly to estimate the inverse data space. Due to the smaller number of data set we also gain in terms of computational complexity.
An ECG Compressed Sensing Method of Low Power Body Area Network
Jizhong Liu
2013-07-01
Full Text Available Aimed at low power problem in body area network, an ECG compressed sensing method of low power body area network based on the compressed sensing theory was proposed. Random binary matrices were used as the sensing matrix to measure ECG signals on the sensor nodes. After measured value is transmitted to remote monitoring center, ECG signal sparse representation under the discrete cosine transform and block sparse Bayesian learning reconstruction algorithm is used to reconstruct the ECG signals. The simulation results show that the 30% of overall signal can get reconstruction signal which’s SNR is more than 60dB, each numbers in each rank of sensing matrix can be controlled below 5, which reduces the power of sensor node sampling, calculation and transmission. The method has the advantages of low power, high accuracy of signal reconstruction and easy to hardware implementation.
Robustly Stable Signal Recovery in Compressed Sensing with Structured Matrix Perturbation
Yang, Zai; Xie, Lihua
2011-01-01
The sparse signal recovery in standard compressed sensing (CS) requires that the sensing matrix be known a priori. The CS problem subject to perturbation in the sensing matrix is often encountered in practice and results in the literature have shown that the signal recovery error grows linearly with the perturbation level. This paper assumes a structure for the perturbation. Under mild conditions on the perturbed sensing matrix, it is shown that a sparse signal can be recovered by $\\ell_1$ minimization with the recovery error being at most proportional to the measurement noise level, similar to that in the standard CS. The recovery is exact in the special noise free case provided that the signal is sufficiently sparse with respect to the perturbation level. A similar result holds for compressible signals under an additional assumption of small perturbation. Algorithms are proposed for implementing the $\\ell_1$ minimization problem and numerical simulations are carried out that verify our analysis.
Compressed Sensing over $\\ell_p$-balls: Minimax Mean Square Error
Donoho, David; Maleki, Arian; Montanari, Andrea
2011-01-01
We consider the compressed sensing problem, where the object $x_0 \\in \\bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \\times N$ random matrix with iid Gaussian entries and $n 0$. We study an asymptotic regime in which $n$ and $N$ both tend to infinity with limiting ratio $n/N = \\delta \\in (0,1)$, both in the noisy ($z \
Application of Compressed Sensing to 2-D Ultrasonic Propagation Imaging System data
Mascarenas, David D. [Los Alamos National Laboratory; Farrar, Charles R. [Los Alamos National Laboratory; Chong, See Yenn [Engineering Institute-Korea; Lee, J.R. [Engineering Institute-Korea; Park, Gyu Hae [Los Alamos National Laboratory; Flynn, Eric B. [Los Alamos National Laboratory
2012-06-29
The Ultrasonic Propagation Imaging (UPI) System is a unique, non-contact, laser-based ultrasonic excitation and measurement system developed for structural health monitoring applications. The UPI system imparts laser-induced ultrasonic excitations at user-defined locations on a structure of interest. The response of these excitations is then measured by piezoelectric transducers. By using appropriate data reconstruction techniques, a time-evolving image of the response can be generated. A representative measurement of a plate might contain 800x800 spatial data measurement locations and each measurement location might be sampled at 500 instances in time. The result is a total of 640,000 measurement locations and 320,000,000 unique measurements. This is clearly a very large set of data to collect, store in memory and process. The value of these ultrasonic response images for structural health monitoring applications makes tackling these challenges worthwhile. Recently compressed sensing has presented itself as a candidate solution for directly collecting relevant information from sparse, high-dimensional measurements. The main idea behind compressed sensing is that by directly collecting a relatively small number of coefficients it is possible to reconstruct the original measurement. The coefficients are obtained from linear combinations of (what would have been the original direct) measurements. Often compressed sensing research is simulated by generating compressed coefficients from conventionally collected measurements. The simulation approach is necessary because the direct collection of compressed coefficients often requires compressed sensing analog front-ends that are currently not commercially available. The ability of the UPI system to make measurements at user-defined locations presents a unique capability on which compressed measurement techniques may be directly applied. The application of compressed sensing techniques on this data holds the potential to
Puy, Gilles; Gribonval, Rémi; Wiaux, Yves
2011-01-01
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, considering a whole class of sensing bases including the Fourier basis, we prove that the technique is universal in the sense that the required number of measurements for accurate recovery is optimal and independent of the sparsity basis. This universality stems from a drastic decrease of coherence between the sparsity and the sensing bases, which for a Fourier sensing basis relates to a spread of the original signal spectrum by the modulation (hence the name "spread spectrum"). The approach is also efficient as sensing matrices with fast matrix multiplication algorithms can be used, in particular in the case of Fourier measurements. Secondly, these results are confirmed by a numerical analysis of the phase transition of the l1- minimization problem. Finally, w...
Split Bregman's optimization method for image construction in compressive sensing
Skinner, D.; Foo, S.; Meyer-Bäse, A.
2014-05-01
The theory of compressive sampling (CS) was reintroduced by Candes, Romberg and Tao, and D. Donoho in 2006. Using a priori knowledge that a signal is sparse, it has been mathematically proven that CS can defY Nyquist sampling theorem. Theoretically, reconstruction of a CS image relies on the minimization and optimization techniques to solve this complex almost NP-complete problem. There are many paths to consider when compressing and reconstructing an image but these methods have remained untested and unclear on natural images, such as underwater sonar images. The goal of this research is to perfectly reconstruct the original sonar image from a sparse signal while maintaining pertinent information, such as mine-like object, in Side-scan sonar (SSS) images. Goldstein and Osher have shown how to use an iterative method to reconstruct the original image through a method called Split Bregman's iteration. This method "decouples" the energies using portions of the energy from both the !1 and !2 norm. Once the energies are split, Bregman iteration is used to solve the unconstrained optimization problem by recursively solving the problems simultaneously. The faster these two steps or energies can be solved then the faster the overall method becomes. While the majority of CS research is still focused on the medical field, this paper will demonstrate the effectiveness of the Split Bregman's methods on sonar images.
A joint image encryption and watermarking algorithm based on compressive sensing and chaotic map
Xiao, Di; Cai, Hong-Kun; Zheng, Hong-Ying
2015-06-01
In this paper, a compressive sensing (CS) and chaotic map-based joint image encryption and watermarking algorithm is proposed. The transform domain coefficients of the original image are scrambled by Arnold map firstly. Then the watermark is adhered to the scrambled data. By compressive sensing, a set of watermarked measurements is obtained as the watermarked cipher image. In this algorithm, watermark embedding and data compression can be performed without knowing the original image; similarly, watermark extraction will not interfere with decryption. Due to the characteristics of CS, this algorithm features compressible cipher image size, flexible watermark capacity, and lossless watermark extraction from the compressed cipher image as well as robustness against packet loss. Simulation results and analyses show that the algorithm achieves good performance in the sense of security, watermark capacity, extraction accuracy, reconstruction, robustness, etc. Project supported by the Open Research Fund of Chongqing Key Laboratory of Emergency Communications, China (Grant No. CQKLEC, 20140504), the National Natural Science Foundation of China (Grant Nos. 61173178, 61302161, and 61472464), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 106112013CDJZR180005 and 106112014CDJZR185501).
Spotlight SAR sparse sampling and imaging method based on compressive sensing
XU HuaPing; YOU YaNan; LI ChunSheng; ZHANG LvQian
2012-01-01
Spotlight synthetic aperture radar (SAR) emits a chirp signal and the echo bandwidth can be reduced through dechirp processing,where the A/D sampling rate decreases accordingly at the receiver.Compressive sensing allows the compressible signal to be reconstructed with a high probability using only a few samples by solving a linear program problem.This paper presents a novel signal sampling and imaging method for application to spotlight SAR based on compressive sensing.The signal is randomly sampled after dechirp processing to form a low-dimensional sample set,and the dechirp basis is imported to reconstruct the dechirp signal.Matching pursuit (MP) is used as a reconstruction algorithm.The reconstructed signal uses polar format algorithm (PFA) for imaging.Although our novel mechanism increases the system complexity to an extent,the data storage requirements can be compressed considerably. Several simulations verify the feasibility and accuracy of spotlight SAR signal processing via compressive sensing,and the method still obtains acceptable imaging results with 10％ of the original echo data.
Application of Compressive Sensing Theory for the Reconstruction of Signals in Plastic Scintillators
Raczyński, L; Bednarski, T; Białas, P; Czerwiński, E; Kapłon, Ł; Kochanowski, A; Korcyl, G; Kowal, J; Kozik, T; Krzemień, W; Molenda, M; Moskal, P; Niedźwiecki, Sz; Pałka, M; Pawlik, M; Rudy, Z; Salabura, P; Sharma, N G; Silarski, M; Słomski, A; Smyrski, J; Strzelecki, A; Wiślicki, W; Zieliński, M
2013-01-01
Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals from measurements of plastic scintillators. Sparse representation of obtained signals was found using SVD transform.
Foot and ankle compression improves joint position sense but not bipedal stance in older people
Hijmans, J.M.; Zijlstra, W.; Geertzen, J.H.; Hof, A.L.; Postema, K.
2009-01-01
This study investigates the effects of foot and ankle compression on joint position sense (JPS) and balance in older people and young adults. 12 independently living healthy older persons (77-93 years) were recruited from a senior accommodation facility. 15 young adults (19-24 years) also participat
Reducing the Computational Complexity of Reconstruction in Compressed Sensing Nonuniform Sampling
Grigoryan, Ruben; Jensen, Tobias Lindstrøm; Arildsen, Thomas
2013-01-01
This paper proposes a method that reduces the computational complexity of signal reconstruction in single-channel nonuniform sampling while acquiring frequency sparse multi-band signals. Generally, this compressed sensing based signal acquisition allows a decrease in the sampling rate of frequency...
Back to the sampling theory: a practical and less redundant alternative to Compressed sensing
Yaroslavsky, Leonid
2016-01-01
A method is suggested for restoration of images of N samples from their M
The extraction of motion-onset VEP BCI features based on deep learning and compressed sensing.
Ma, Teng; Li, Hui; Yang, Hao; Lv, Xulin; Li, Peiyang; Liu, Tiejun; Yao, Dezhong; Xu, Peng
2017-01-01
Motion-onset visual evoked potentials (mVEP) can provide a softer stimulus with reduced fatigue, and it has potential applications for brain computer interface(BCI)systems. However, the mVEP waveform is seriously masked in the strong background EEG activities, and an effective approach is needed to extract the corresponding mVEP features to perform task recognition for BCI control. In the current study, we combine deep learning with compressed sensing to mine discriminative mVEP information to improve the mVEP BCI performance. The deep learning and compressed sensing approach can generate the multi-modality features which can effectively improve the BCI performance with approximately 3.5% accuracy incensement over all 11 subjects and is more effective for those subjects with relatively poor performance when using the conventional features. Compared with the conventional amplitude-based mVEP feature extraction approach, the deep learning and compressed sensing approach has a higher classification accuracy and is more effective for subjects with relatively poor performance. According to the results, the deep learning and compressed sensing approach is more effective for extracting the mVEP feature to construct the corresponding BCI system, and the proposed feature extraction framework is easy to extend to other types of BCIs, such as motor imagery (MI), steady-state visual evoked potential (SSVEP)and P300. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Owodunni, Damilola S.
2014-04-01
In this paper, compressed sensing techniques are proposed to linearize commercial power amplifiers driven by orthogonal frequency division multiplexing signals. The nonlinear distortion is considered as a sparse phenomenon in the time-domain, and three compressed sensing based algorithms are presented to estimate and compensate for these distortions at the receiver using a few and, at times, even no frequency-domain free carriers (i.e. pilot carriers). The first technique is a conventional compressed sensing approach, while the second incorporates a priori information about the distortions to enhance the estimation. Finally, the third technique involves an iterative data-aided algorithm that does not require any pilot carriers and hence allows the system to work at maximum bandwidth efficiency. The performances of all the proposed techniques are evaluated on a commercial power amplifier and compared. The error vector magnitude and symbol error rate results show the ability of compressed sensing to compensate for the amplifier\\'s nonlinear distortions. © 2013 Elsevier B.V.
Compressed Sensing on the Image of Bilinear Maps
Walk, Philipp
2012-01-01
For several communication models, the dispersive part of a communication channel is described by a bilinear operation $T$ between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image $T(X,Y)$ of the input signal difference sets $X$ and the channel state sets $Y$. The main goal in this contribution is to characterize the compressibility of $T(X,Y)$ with respect to an ambient dimension $N$. In this paper we show that a restricted norm multiplicativity of $T$ on all canonical subspaces $X$ and $Y$ with dimension $S$ resp. $F$ is sufficient for the reconstruction of output signals with an overwhelming probability from $\\mathcal{O}((S+F)\\log N)$ random sub-Gaussian measurements.
Remotely sensed image compression based on wavelet transform
Kim, Seong W.; Lee, Heung K.; Kim, Kyung S.; Choi, Soon D.
1995-01-01
In this paper, we present an image compression algorithm that is capable of significantly reducing the vast amount of information contained in multispectral images. The developed algorithm exploits the spectral and spatial correlations found in multispectral images. The scheme encodes the difference between images after contrast/brightness equalization to remove the spectral redundancy, and utilizes a two-dimensional wavelet transform to remove the spatial redundancy. the transformed images are then encoded by Hilbert-curve scanning and run-length-encoding, followed by Huffman coding. We also present the performance of the proposed algorithm with the LANDSAT MultiSpectral Scanner data. The loss of information is evaluated by PSNR (peak signal to noise ratio) and classification capability.
Block Hadamard measurement matrix with arbitrary dimension in compressed sensing
Liu, Shaoqiang; Yan, Xiaoyan; Fan, Xiaoping; Li, Fei; Xu, Wen
2017-01-01
As Hadamard measurement matrix cannot be used for compressing signals with dimension of a non-integral power-of-2, this paper proposes a construction method of block Hadamard measurement matrix with arbitrary dimension. According to the dimension N of signals to be measured, firstly, construct a set of Hadamard sub matrixes with different dimensions and make the sum of these dimensions equals to N. Then, arrange the Hadamard sub matrixes in a certain order to form a block diagonal matrix. Finally, take the former M rows of the block diagonal matrix as the measurement matrix. The proposed measurement matrix which retains the orthogonality of Hadamard matrix and sparsity of block diagonal matrix has highly sparse structure, simple hardware implements and general applicability. Simulation results show that the performance of our measurement matrix is better than Gaussian matrix, Logistic chaotic matrix, and Toeplitz matrix.
Wu, Jiao; Liu, Fang; Jiao, L C; Wang, Xiaodong; Hou, Biao
2011-12-01
Most wavelet-based reconstruction methods of compressive sensing (CS) are developed under the independence assumption of the wavelet coefficients. However, the wavelet coefficients of images have significant statistical dependencies. Lots of multivariate prior models for the wavelet coefficients of images have been proposed and successfully applied to the image estimation problems. In this paper, the statistical structures of the wavelet coefficients are considered for CS reconstruction of images that are sparse or compressive in wavelet domain. A multivariate pursuit algorithm (MPA) based on the multivariate models is developed. Several multivariate scale mixture models are used as the prior distributions of MPA. Our method reconstructs the images by means of modeling the statistical dependencies of the wavelet coefficients in a neighborhood. The proposed algorithm based on these scale mixture models provides superior performance compared with many state-of-the-art compressive sensing reconstruction algorithms.
Arias, Fernando X.; Sierra, Heidy; Arzuaga, Emmanuel
2016-05-01
Compressive Sensing is an area of great recent interest for efficient signal acquisition, manipulation and reconstruction tasks in areas where sensor utilization is a scarce and valuable resource. The current work shows that approaches based on this technology can improve the efficiency of manipulation, analysis and storage processes already established for hyperspectral imagery, with little discernible loss in data performance upon reconstruction. We present the results of a comparative analysis of classification performance between a hyperspectral data cube acquired by traditional means, and one obtained through reconstruction from compressively sampled data points. To obtain a broad measure of the classification performance of compressively sensed cubes, we classify a commonly used scene in hyperspectral image processing algorithm evaluation using a set of five classifiers commonly used in hyperspectral image classification. Global accuracy statistics are presented and discussed, as well as class-specific statistical properties of the evaluated data set.
Block-Based Compressed Sensing for Neutron Radiation Image Using WDFB
Wei Jin
2015-01-01
Full Text Available An ideal compression method for neutron radiation image should have high compression ratio while keeping more details of the original image. Compressed sensing (CS, which can break through the restrictions of sampling theorem, is likely to offer an efficient compression scheme for the neutron radiation image. Combining wavelet transform with directional filter banks, a novel nonredundant multiscale geometry analysis transform named Wavelet Directional Filter Banks (WDFB is constructed and applied to represent neutron radiation image sparsely. Then, the block-based CS technique is introduced and a high performance CS scheme for neutron radiation image is proposed. By performing two-step iterative shrinkage algorithm the problem of L1 norm minimization is solved to reconstruct neutron radiation image from random measurements. The experiment results demonstrate that the scheme not only improves the quality of reconstructed image obviously but also retains more details of original image.
Energy and Quality Evaluation for Compressive Sensing of Fetal Electrocardiogram Signals.
Da Poian, Giulia; Brandalise, Denis; Bernardini, Riccardo; Rinaldo, Roberto
2016-12-22
This manuscript addresses the problem of non-invasive fetal Electrocardiogram (ECG) signal acquisition with low power/low complexity sensors. A sensor architecture using the Compressive Sensing (CS) paradigm is compared to a standard compression scheme using wavelets in terms of energy consumption vs. reconstruction quality, and, more importantly, vs. performance of fetal heart beat detection in the reconstructed signals. We show in this paper that a CS scheme based on reconstruction with an over-complete dictionary has similar reconstruction quality to one based on wavelet compression. We also consider, as a more important figure of merit, the accuracy of fetal beat detection after reconstruction as a function of the sensor power consumption. Experimental results with an actual implementation in a commercial device show that CS allows significant reduction of energy consumption in the sensor node, and that the detection performance is comparable to that obtained from original signals for compression ratios up to about 75%.
A LOSSLESS COMPRESSION ALGORITHM OF REMOTE SENSING IMAGE FOR SPACE APPLICATIONS
Sui Yuping; Yang Chengyu; Liu Yanjun; Wang Jun; Wei Zhonghui; He Xin
2008-01-01
A simple and adaptive lossless compression algorithm is proposed for remote sensing image compression,which includes integer wavelet transform and the Rice entropy coder. By analyzing the probability distribution of integer wavelet transform coefficients and the characteristics of Rice entropy coder,the divide and rule method is used for high-frequency sub-bands and low-frequency one.High-frequency sub-bands are coded by the Rice entropy coder,and low-frequency coefficients are predicted before coding. The role of predictor is to map the low-frequency coefficients into symbols suitable for the entropy coding. Experimental results show that the average Compression Ratio (CR) of our approach is about two,which is close to that of JPEG 2000. The algorithm is simple and easy to be implemented in hardware. Moreover,it has the merits of adaptability,and independent data packet. So the algorithm can adapt to space lossless compression applications.
Microwave spectrum sensing based on photonic time stretch and compressive sampling.
Chi, Hao; Chen, Ying; Mei, Yuan; Jin, Xiaofeng; Zheng, Shilie; Zhang, Xianmin
2013-01-15
An approach to realizing microwave spectrum sensing based on photonic time stretch and compressive sampling is proposed. The time stretch system is used to slow down the input high-speed signal and the compressive sampling based on random demodulation can further decrease the sampling rate. A spectrally sparse signal in a wide bandwidth can be captured with a sampling rate far lower than the Nyquist rate thanks to both time stretch and compressive sampling. It is demonstrated that a system with a time stretch factor 5 and a compression factor 8 can be used to capture a signal with multiple tones in a 50 GHz bandwidth, which means a sampling rate 40 times lower than the Nyquist rate. In addition, the time stretch of the microwave signal largely decreases the data rate of random data sequence and therefore the speed of the mixer in the random demodulator.
Bayesian nonparametric dictionary learning for compressed sensing MRI.
Huang, Yue; Paisley, John; Lin, Qin; Ding, Xinghao; Fu, Xueyang; Zhang, Xiao-Ping
2014-12-01
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.
Akoguz, A.; Bozkurt, S.; Gozutok, A. A.; Alp, G.; Turan, E. G.; Bogaz, M.; Kent, S.
2016-06-01
High resolution level in satellite imagery came with its fundamental problem as big amount of telemetry data which is to be stored after the downlink operation. Moreover, later the post-processing and image enhancement steps after the image is acquired, the file sizes increase even more and then it gets a lot harder to store and consume much more time to transmit the data from one source to another; hence, it should be taken into account that to save even more space with file compression of the raw and various levels of processed data is a necessity for archiving stations to save more space. Lossless data compression algorithms that will be examined in this study aim to provide compression without any loss of data holding spectral information. Within this objective, well-known open source programs supporting related compression algorithms have been implemented on processed GeoTIFF images of Airbus Defence & Spaces SPOT 6 & 7 satellites having 1.5 m. of GSD, which were acquired and stored by ITU Center for Satellite Communications and Remote Sensing (ITU CSCRS), with the algorithms Lempel-Ziv-Welch (LZW), Lempel-Ziv-Markov chain Algorithm (LZMA & LZMA2), Lempel-Ziv-Oberhumer (LZO), Deflate & Deflate 64, Prediction by Partial Matching (PPMd or PPM2), Burrows-Wheeler Transform (BWT) in order to observe compression performances of these algorithms over sample datasets in terms of how much of the image data can be compressed by ensuring lossless compression.
Compressive sensing for efficient health monitoring and effective damage detection of structures
Jayawardhana, Madhuka; Zhu, Xinqun; Liyanapathirana, Ranjith; Gunawardana, Upul
2017-02-01
Real world Structural Health Monitoring (SHM) systems consist of sensors in the scale of hundreds, each sensor generating extremely large amounts of data, often arousing the issue of the cost associated with data transfer and storage. Sensor energy is a major component included in this cost factor, especially in Wireless Sensor Networks (WSN). Data compression is one of the techniques that is being explored to mitigate the effects of these issues. In contrast to traditional data compression techniques, Compressive Sensing (CS) - a very recent development - introduces the means of accurately reproducing a signal by acquiring much less number of samples than that defined by Nyquist's theorem. CS achieves this task by exploiting the sparsity of the signal. By the reduced amount of data samples, CS may help reduce the energy consumption and storage costs associated with SHM systems. This paper investigates CS based data acquisition in SHM, in particular, the implications of CS on damage detection and localization. CS is implemented in a simulation environment to compress structural response data from a Reinforced Concrete (RC) structure. Promising results were obtained from the compressed data reconstruction process as well as the subsequent damage identification process using the reconstructed data. A reconstruction accuracy of 99% could be achieved at a Compression Ratio (CR) of 2.48 using the experimental data. Further analysis using the reconstructed signals provided accurate damage detection and localization results using two damage detection algorithms, showing that CS has not compromised the crucial information on structural damages during the compression process.
YAMPA: Yet Another Matching Pursuit Algorithm for compressive sensing
Lodhi, Muhammad A.; Voronin, Sergey; Bajwa, Waheed U.
2016-05-01
State-of-the-art sparse recovery methods often rely on the restricted isometry property for their theoretical guarantees. However, they cannot explicitly incorporate metrics such as restricted isometry constants within their recovery procedures due to the computational intractability of calculating such metrics. This paper formulates an iterative algorithm, termed yet another matching pursuit algorithm (YAMPA), for recovery of sparse signals from compressive measurements. YAMPA differs from other pursuit algorithms in that: (i) it adapts to the measurement matrix using a threshold that is explicitly dependent on two computable coherence metrics of the matrix, and (ii) it does not require knowledge of the signal sparsity. Performance comparisons of YAMPA against other matching pursuit and approximate message passing algorithms are made for several types of measurement matrices. These results show that while state-of-the-art approximate message passing algorithms outperform other algorithms (including YAMPA) in the case of well-conditioned random matrices, they completely break down in the case of ill-conditioned measurement matrices. On the other hand, YAMPA and comparable pursuit algorithms not only result in reasonable performance for well-conditioned matrices, but their performance also degrades gracefully for ill-conditioned matrices. The paper also shows that YAMPA uniformly outperforms other pursuit algorithms for the case of thresholding parameters chosen in a clairvoyant fashion. Further, when combined with a simple and fast technique for selecting thresholding parameters in the case of ill-conditioned matrices, YAMPA outperforms other pursuit algorithms in the regime of low undersampling, although some of these algorithms can outperform YAMPA in the regime of high undersampling in this setting.
WSNs data acquisition by combining hierarchical routing method and compressive sensing.
Zou, Zhiqiang; Hu, Cunchen; Zhang, Fei; Zhao, Hao; Shen, Shu
2014-09-09
We address the problem of data acquisition in large distributed wireless sensor networks (WSNs). We propose a method for data acquisition using the hierarchical routing method and compressive sensing for WSNs. Only a few samples are needed to recover the original signal with high probability since sparse representation technology is exploited to capture the similarities and differences of the original signal. To collect samples effectively in WSNs, a framework for the use of the hierarchical routing method and compressive sensing is proposed, using a randomized rotation of cluster-heads to evenly distribute the energy load among the sensors in the network. Furthermore, L1-minimization and Bayesian compressed sensing are used to approximate the recovery of the original signal from the smaller number of samples with a lower signal reconstruction error. We also give an extensive validation regarding coherence, compression rate, and lifetime, based on an analysis of the theory and experiments in the environment with real world signals. The results show that our solution is effective in a large distributed network, especially for energy constrained WSNs.
Tang, Gang; Hou, Wei; Wang, Huaqing; Luo, Ganggang; Ma, Jianwei
2015-10-09
The Shannon sampling principle requires substantial amounts of data to ensure the accuracy of on-line monitoring of roller bearing fault signals. Challenges are often encountered as a result of the cumbersome data monitoring, thus a novel method focused on compressed vibration signals for detecting roller bearing faults is developed in this study. Considering that harmonics often represent the fault characteristic frequencies in vibration signals, a compressive sensing frame of characteristic harmonics is proposed to detect bearing faults. A compressed vibration signal is first acquired from a sensing matrix with information preserved through a well-designed sampling strategy. A reconstruction process of the under-sampled vibration signal is then pursued as attempts are conducted to detect the characteristic harmonics from sparse measurements through a compressive matching pursuit strategy. In the proposed method bearing fault features depend on the existence of characteristic harmonics, as typically detected directly from compressed data far before reconstruction completion. The process of sampling and detection may then be performed simultaneously without complete recovery of the under-sampled signals. The effectiveness of the proposed method is validated by simulations and experiments.
A Novel Coherence Reduction Method in Compressed Sensing for DOA Estimation
Jing Liu
2013-01-01
Full Text Available A novel method named as coherent column replacement method is proposed to reduce the coherence of a partially deterministic sensing matrix, which is comprised of highly coherent columns and random Gaussian columns. The proposed method is to replace the highly coherent columns with random Gaussian columns to obtain a new sensing matrix. The measurement vector is changed accordingly. It is proved that the original sparse signal could be reconstructed well from the newly changed measurement vector based on the new sensing matrix with large probability. This method is then extended to a more practical condition when highly coherent columns and incoherent columns are considered, for example, the direction of arrival (DOA estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, where the compressed sensing method based on the original sensing matrix fails. The proposed method also obtains more precise estimation of DOA using one snapshot compared with the traditional estimation methods such as Capon, APES, and GLRT, based on hundreds of snapshots.
Model Identification of a Network as Compressing Sensing
Materassi, D; Giarré, L; Salapaka, M
2011-01-01
In many applications, it is important to derive information about the topology and the internal connections of dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology, and unveiling an unknown structure as the estimate of a "sparse Wiener filter". A geometric interpretation of the problem in a pre-Hilbert space for wide-sense stochastic processes is provided. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the solution that "better" satisfies the constraints according to the criterion of approximation. Applications starting from real data and numerical...
A Compressed Sensing Framework of Frequency-Sparse Signals through Chaotic Systems
Liu, Zhong; Xi, Feng
2011-01-01
This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system and the compressed measurement is obtained by downsampling the system output. The reconstruction is realized through the estimation of the excitation coefficients with principle of impulsive chaos synchronization. The -norm regularized nonlinear least squares is used to find the estimation. The proposed framework is easily implementable and creates secure measurements. The Henon map is used as an example to illustrate the principle and the performance.
Korde-Patel, Asmita (Inventor); Barry, Richard K.; Mohsenin, Tinoosh
2016-01-01
Compressive Sensing is a technique for simultaneous acquisition and compression of data that is sparse or can be made sparse in some domain. It is currently under intense development and has been profitably employed for industrial and medical applications. We here describe the use of this technique for the processing of astronomical data. We outline the procedure as applied to exoplanet gravitational microlensing and analyze measurement results and uncertainty values. We describe implications for on-spacecraft data processing for space observatories. Our findings suggest that application of these techniques may yield significant, enabling benefits especially for power and volume-limited space applications such as miniaturized or micro-constellation satellites.
A new backtracking-based sparsity adaptive algorithm for distributed compressed sensing
徐勇; 张玉洁; 邢婧; 李宏伟
2015-01-01
A new iterative greedy algorithm based on the backtracking technique was proposed for distributed compressed sensing (DCS) problem. The algorithm applies two mechanisms for precise recovery soft thresholding and cutting. It can reconstruct several compressed signals simultaneously even without any prior information of the sparsity, which makes it a potential candidate for many practical applications, but the numbers of non-zero (significant) coefficients of signals are not available. Numerical experiments are conducted to demonstrate the validity and high performance of the proposed algorithm, as compared to other existing strong DCS algorithms.
Optical information authentication via compressed sensing and double random phase encoding
Chen, Junxin; Bao, Nan; Zhu, Zhi-liang
2017-10-01
This paper presents a novel information authentication scheme via compressed sensing and double random phase encoding. Two alternative architectures have been investigated, in which significantly compressed data with micro percentage is sufficient for authentication. At the decoder end, a noise-like image with no leakage of the plaintext is recovered and subsequently authenticated using a nonlinear optical correlation approach. The authentication effectiveness, noise resistance and security performance of the proposed scheme have been experimentally validated. This work was supported by the Fundamental Research Funds for the Central Universities (N162410002-4, N151904002), the National Natural Science Foundation of China (No. 61374178).
Detection of Modified Matrix Encoding Using Machine Learning and Compressed Sensing
Allen, Josef D [ORNL
2011-01-01
In recent years, driven by the development of steganalysis methods, steganographic algorithms have been evolved rapidly with the ultimate goal of an unbreakable embedding procedure, resulting in recent steganographic algorithms with minimum distortions, exemplified by the recent family of Modified Matrix Encoding (MME) algorithms, which has shown to be most difficult to be detected. In this paper we propose a compressed sensing based on approach for intrinsic steganalysis to detect MME stego messages. Compressed sensing is a recently proposed mathematical framework to represent an image (in general, a signal) using a sparse representation relative to an overcomplete dictionary by minimizing the l1-norm of resulting coefficients. Here we first learn a dictionary from a training set so that the performance will be optimized using the KSVD algorithm; since JPEG images are processed by 8x8 blocks, the training examples are 8x8 patches, rather than the entire images and this increases the generalization of compressed sensing. For each 8x8 block, we compute its sparse representation using OMP (orthogonal matching pursuit) algorithm. Using computed sparse representations, we train a support vector machine (SVM) to classify 8x8 blocks into stego and non-stego classes. Then given an input image, we first divide it into 8x8 blocks. For each 8x8 block, we compute its sparse representation and classify it using the trained SVM. After all the 8x8 blocks are classified, the entire image is classified based on the majority rule of 8x8 block classification results. This allows us to achieve a robust decision even when 8x8 blocks can be classified only with relatively low accuracy. We have tested the proposed algorithm on two datasets (Corel-1000 dataset and a remote sensing image dataset) and have achieved 100% accuracy on classifying images, even though the accuracy of classifying 8x8 blocks is only 80.89%. Key Words Compressed Sensing, Sparcity, Data Dictionary, Steganography
Hatay, Gokce Hale; Yildirim, Muhammed; Ozturk-Isik, Esin
2017-08-01
The purpose of this study was to apply compressed sensing method for accelerated phosphorus MR spectroscopic imaging ((31)P-MRSI) of human brain in vivo at 3T. Fast (31)P-MRSI data of five volunteers were acquired on a 3T clinical MR scanner using pulse-acquire sequence with a pseudorandom undersampling pattern for a data reduction factor of 5.33 and were reconstructed using compressed sensing. Additionally, simulated (31)P-MRSI human brain tumor datasets were created to analyze the effects of k-space sampling pattern, data matrix size, regularization parameters of the reconstruction, and noise on the compressed sensing accelerated (31)P-MRSI data. The (31)P metabolite peak ratios of the full and compressed sensing accelerated datasets of healthy volunteers in vivo were similar according to the results of a Bland-Altman test. The estimated effective spatial resolution increased with reduction factor and sampling more at the k-space center. A lower regularization parameter for both total variation and L1-norm penalties resulted in a better compressed sensing reconstruction of (31)P-MRSI. Although the root-mean-square error increased with noise levels, the compressed sensing reconstruction was robust for up to a reduction factor of 10 for the simulated data that had sharply defined tumor borders. As a result, compressed sensing was successfully applied to accelerate (31)P-MRSI of human brain in vivo at 3T.
Experimental study of a compressive line sensing imaging system in a turbulent environment.
Ouyang, Bing; Hou, Weilin; Gong, Cuiling; Dalgleish, Fraser R; Caimi, Frank M; Vuorenkoski, Anni K; Nootz, Gero; Xiao, Xifeng; Voelz, David G
2016-10-20
Turbulence poses challenges in many atmospheric and underwater surveillance applications. The compressive line sensing (CLS) active imaging scheme has been demonstrated in simulations and test tank experiments to be effective in scattering media such as turbid coastal water, fog, and mist. The CLS sensing model adopts the distributed compressive sensing theoretical framework that exploits both intrasignal sparsity and the highly correlated nature of adjacent areas in a natural scene. During sensing operation, the laser illuminates the spatial light modulator digital micromirror device to generate a series of one-dimensional binary sensing patterns from a codebook to encode the current target line segment. A single element detector photomultiplier tube acquires target reflections as the encoder output. The target can then be recovered using the encoder output and a predicted on-target codebook that reflects the environmental interference of original codebook entries. In this work, we investigated the effectiveness of the CLS imaging system in a turbulent environment. The development of a compact CLS prototype will be discussed, as will a series of experiments using various turbulence intensities at the Naval Research Lab's Simulated Turbulence and Turbidity Environment. The experimental results showed that the time-averaged measurements improved both the signal-to-noise radio and the resolution of the reconstructed image in the extreme turbulence environment. The contributing factors for this intriguing and promising result will be discussed.
Jinesh, Mathew; MacPherson, William N.; Hand, Duncan P.; Maier, Robert R. J.
2016-05-01
A smart metal component having the potential for high temperature strain sensing capability is reported. The stainless steel (SS316) structure is made by selective laser melting (SLM). A fiber Bragg grating (FBG) is embedded in to a 3D printed U-groove by high temperature brazing using a silver based alloy, achieving an axial FBG compression of 13 millistrain at room temperature. Initial results shows that the test component can be used for up to 700°C for sensing applications.
A compressed sensing based method with support refinement for impulse noise cancelation in DSL
Quadeer, Ahmed Abdul
2013-06-01
This paper presents a compressed sensing based method to suppress impulse noise in digital subscriber line (DSL). The proposed algorithm exploits the sparse nature of the impulse noise and utilizes the carriers, already available in all practical DSL systems, for its estimation and cancelation. Specifically, compressed sensing is used for a coarse estimate of the impulse position, an a priori information based maximum aposteriori probability (MAP) metric for its refinement, followed by least squares (LS) or minimum mean square error (MMSE) estimation for estimating the impulse amplitudes. Simulation results show that the proposed scheme achieves higher rate as compared to other known sparse estimation algorithms in literature. The paper also demonstrates the superior performance of the proposed scheme compared to the ITU-T G992.3 standard that utilizes RS-coding for impulse noise refinement in DSL signals. © 2013 IEEE.
Nakanishi-Ohno, Yoshinori; Haze, Masahiro; Yoshida, Yasuo; Hukushima, Koji; Hasegawa, Yukio; Okada, Masato
2016-09-01
We applied a method of compressed sensing to the observation of quasi-particle interference (QPI) by scanning tunneling microscopy/spectroscopy to improve efficiency and save measurement time. To solve an ill-posed problem owing to the scarcity of data, the compressed sensing utilizes the sparseness of QPI patterns in momentum space. We examined the performance of a sparsity-inducing algorithm called least absolute shrinkage and selection operator (LASSO), and demonstrated that LASSO enables us to recover a double-circle QPI pattern of the Ag(111) surface from a dataset whose size is less than that necessary for the conventional Fourier transformation method. In addition, the smallest number of data required for the recovery is discussed on the basis of cross validation.
Zhou, Fei [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nielson, Weston [Univ. of California, Los Angeles, CA (United States); Xia, Yi [Univ. of California, Los Angeles, CA (United States); Ozoliņš, Vidvuds [Univ. of California, Los Angeles, CA (United States)
2014-10-01
First-principles prediction of lattice thermal conductivity κ_{L} of strongly anharmonic crystals is a long-standing challenge in solid-state physics. Making use of recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics. Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Nonintuitively, high accuracy is achieved when the model is trained on first-principles forces in quasirandom atomic configurations. The method is demonstrated for Si, NaCl, and Cu_{12}Sb_{4}S_{13}, an earth-abundant thermoelectric with strong phonon-phonon interactions that limit the room-temperature κ_{L} to values near the amorphous limit.
Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
Donoho, David; Montanari, Andrea
2011-01-01
Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important both for theory and practice. We present a formula precisely delineating the allowable degree of of undersampling of generalized sparse objects. The formula applies to Approximate Message Passing (AMP) algorithms for compressed sensing, which are here generalized to employ denoising operators besides the traditional scalar shrinkers (soft thresholding, positive soft thresholding and capping). This paper gives several examples including scalar shrinkers not derivable from convex optimization -- the firm shrinkage nonlinearity and the minimax} nonlinearity -- and also nonscalar denoisers -- block thresholding (both block soft and block James-Stein), monotone regression, and total variation minimization. Let the variables \\epsilon = k/N and \\delta = n/N denote the generalized sparsity and undersampling fractions for sampling the k-gene...
Compressed Sensing Imaging Algorithm for High-squint SAR Based on NCS Operator
Gu Fufei
2016-02-01
Full Text Available A novel compressed sensing imaging algorithm for high-squint Synthetic Aperture Radar (SAR based on a Nonlinear Chirp-Scaling (NCS operator is proposed. First, the echo signal of high-squint SAR is analyzed, and a novel imaging method based on the Nyquist-sampled echo signal is proposed. With the proposed method, the range migration is corrected and the coupling problem in the range and azimuth directions is solved. Then, to solve the problem of high-squint SAR imaging using undersampled echo signals, the NCS operator and compressed sensing algorithm based on this operator are constructed. Imaging results are obtained by solving an optimization problem. The proposed method can recover a sparse scene using undersampled echo data. Furthermore, it can recover a nonsparse scene using fully sampled data. Finally, simulations show the effectiveness of the proposed method.
Ali, Anum Z.
2013-12-01
Linearization of user equipment power amplifiers driven by orthogonal frequency division multiplexing signals is addressed in this paper. Particular attention is paid to the power efficient operation of an orthogonal frequency division multiple access cognitive radio system and realization of such a system using compressed sensing. Specifically, precompensated overdriven amplifiers are employed at the mobile terminal. Over-driven amplifiers result in in-band distortions and out of band interference. Out of band interference mostly occupies the spectrum of inactive users, whereas the in-band distortions are mitigated using compressed sensing at the receiver. It is also shown that the performance of the proposed scheme can be further enhanced using multiple measurements of the distortion signal in single-input multi-output systems. Numerical results verify the ability of the proposed setup to improve error vector magnitude, bit error rate, outage capacity and mean squared error. © 2011 IEEE.
Effect of downsampling and compressive sensing on audio-based continuous cough monitoring.
Casaseca-de-la-Higuera, Pablo; Lesso, Paul; McKinstry, Brian; Pinnock, Hilary; Rabinovich, Roberto; McCloughan, Lucy; Monge-Álvarez, Jesús
2015-01-01
This paper presents an efficient cough detection system based on simple decision-tree classification of spectral features from a smartphone audio signal. Preliminary evaluation on voluntary coughs shows that the system can achieve 98% sensitivity and 97.13% specificity when the audio signal is sampled at full rate. With this baseline system, we study possible efficiency optimisations by evaluating the effect of downsampling below the Nyquist rate and how the system performance at low sampling frequencies can be improved by incorporating compressive sensing reconstruction schemes. Our results show that undersampling down to 400 Hz can still keep sensitivity and specificity values above 90% despite of aliasing. Furthermore, the sparsity of cough signals in the time domain allows keeping performance figures close to 90% when sampling at 100 Hz using compressive sensing schemes.
Zhou, Fei; Nielson, Weston; Xia, Yi; Ozoliņš, Vidvuds
2014-10-31
First-principles prediction of lattice thermal conductivity κ(L) of strongly anharmonic crystals is a long-standing challenge in solid-state physics. Making use of recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics. Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Nonintuitively, high accuracy is achieved when the model is trained on first-principles forces in quasirandom atomic configurations. The method is demonstrated for Si, NaCl, and Cu(12)Sb(4)S(13), an earth-abundant thermoelectric with strong phonon-phonon interactions that limit the room-temperature κ(L) to values near the amorphous limit.
Channel estimation based on distributed compressed sensing in amplify-and-forward relay networks
WANG Dong-hao; NIU Kai; HE Zhi-qiang; TIAN Bao-yu
2010-01-01
In orthogonal frequency-division multiplexing(OFDM)amplify-and-forward(AF)relay networks,in order to exploit diversity gains over frequency-selective fading channels,the receiver needs to acquire the knowledge of channel state information(CSI).In this article,based on the recent methodology of distributed compressed sensing(DCS),a novel channel estimation scheme is proposed.The joint sparsity model 2(JSM-2)in DCS theory and simultaneous orthogonal matching pursuit(SOMP)are both introduced to improve the estimation performance and increase the spectral efficiency.Simulation results show that compared with current compressed sensing(CS)methods,the estimation error of our scheme is reduced dramatically in high SNR region while the pilot number is still kept small.
An algorithm for 252Cf-Source-Driven neutron signal denoising based on Compressive Sensing
李鹏程; 魏彪; 冯鹏; 何鹏; 米德伶
2015-01-01
As photoelectrically detected 252Cf-source-driven neutron signals always contain noise, a denoising algorithm is proposed based on compressive sensing for the noised neutron signal. In the algorithm, Empirical Mode Decomposition (EMD) is applied to decompose the noised neutron signal and then find out the noised Intrinsic Mode Function (IMF) automatically. Thus, we only need to use the basis pursuit denoising (BPDN) algorithm to denoise these IMFs. For this reason, the proposed algorithm can be called EMDCSDN (Empirical Mode Decomposition Compressive Sensing Denoising). In addition, five indicators are employed to evaluate the denoising effect. The results show that the EMDCSDN algorithm is more effective than the other denoising algorithms including BPDN. This study provides a new approach for signal denoising at the front-end.
Compressive Sensing in High-resolution 3D SAR Tomography of Urban Scenarios
Liao Ming-sheng
2015-04-01
Full Text Available In modern high resolution SAR data, due to the intrinsic side-looking geometry of SAR sensors, layover and foreshortening issues inevitably arise, especially in dense urban areas. SAR tomography provides a new way of overcoming these problems by exploiting the back-scattering property for each pixel. However, traditional non-parametric spectral estimators, e.g. Truncated Singular Value Decomposition (TSVD, are limited by their poor elevation resolution, which is not comparable to the azimuth and slant-range resolution. In this paper, the Compressive Sensing (CS approach using Basis Pursuit (BP and TWo-step Iterative Shrinkage/Thresholding (TWIST are introduced. Experimental studies with real spotlight-mode TerraSAR-X dataset are carried out using both BP and TWIST, to demonstrate the merits of compressive sensing approaches in terms of robustness, computational efficiency, and super-resolution capability.
Primary User Localization Algorithm Based on Compressive Sensing in Cognitive Radio Networks
Fang Ye
2016-04-01
Full Text Available In order to locate source signal more accurately in authorized frequency bands, a novel primary user localization algorithm based on compressive sensing (PU-CSL in cognitive radio networks (CRNs is proposed in this paper. In comparison to existing centroid locating algorithms, PU-CSL shows higher locating accuracy for integrally exploring correlation between source signal and secondary users (SUs. Energy detection is first adopted for collecting the energy fingerprint of source signal at each SU, then degree of correlation between source signal and SUs is reconstructed based on compressive sensing (CS, which determines weights of centroid coordinates. A weighted centroid scheme is finally utilized to estimate source position. Simulation results show that PU-CSL has smaller maximum error of positioning and root-mean-square error. Moreover, the proposed PU-CSL algorithm possess excellent location accuracy and strong anti-noise performance.
Geethanath, Sairam; Gulaka, Praveen K; Kodibagkar, Vikram D
2014-01-01
Dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) has become a valuable clinical tool for cancer diagnosis and prognosis. DCE MRI provides pharmacokinetic parameters dependent on the extravasation of small molecular contrast agents, and thus high temporal resolution and/or spatial resolution is required for accurate estimation of parameters. In this article we investigate the efficacy of 2 undersampling approaches to speed up DCE MRI: a conventional keyhole approach and compressed sensing-based imaging. Data reconstructed from variants of these methods has been compared with the full k-space reconstruction with respect to data quality and pharmacokinetic parameters Ktrans and ve. Overall, compressive sensing provides better data quality and reproducible parametric maps than key-hole methods with higher acceleration factors. In particular, an undersampling mask based on a priori precontrast data showed high fidelity of reconstructed data and parametric maps up to 5× acceleration.
A Compressive Sensing SAR Imaging Approach Based on Wavelet Package Algorithm
Shi Yan
2013-06-01
Full Text Available Compressive sensing SAR imaging can significantly reduce the sampling rate and the amount of data,but it is essential only in the case where the reflection coefficients of SAR scene are sparse. This paper proposed a compressive sensing SAR imaging method based on wavelet packet sparse representation. The wavelet packet algorithm is used to choose the most sparse representation of the SAR scene by training the same type of SAR images. By solving for the minimum 1 l norm optimization, the SAR scene reflection coefficients can be reconstructed. Unambiguous SAR image can be produced with the proposed method even with fewer samples. SAR data simulation experiments demonstrate the efficiency of the proposed method.
Simultaneous Greedy Analysis Pursuit for compressive sensing of multi-channel ECG signals.
Avonds, Yurrit; Liu, Yipeng; Van Huffel, Sabine
2014-01-01
This paper addresses compressive sensing for multi-channel ECG. Compared to the traditional sparse signal recovery approach which decomposes the signal into the product of a dictionary and a sparse vector, the recently developed cosparse approach exploits sparsity of the product of an analysis matrix and the original signal. We apply the cosparse Greedy Analysis Pursuit (GAP) algorithm for compressive sensing of ECG signals. Moreover, to reduce processing time, classical signal-channel GAP is generalized to the multi-channel GAP algorithm, which simultaneously reconstructs multiple signals with similar support. Numerical experiments show that the proposed method outperforms the classical sparse multi-channel greedy algorithms in terms of accuracy and the single-channel cosparse approach in terms of processing speed.
Li, Qiyue; Qu, Xiaobo; Liu, Yunsong; Guo, Di; Lai, Zongying; Ye, Jing; Chen, Zhong
2015-06-01
Compressed sensing MRI (CS-MRI) is a promising technology to accelerate magnetic resonance imaging. Both improving the image quality and reducing the computation time are important for this technology. Recently, a patch-based directional wavelet (PBDW) has been applied in CS-MRI to improve edge reconstruction. However, this method is time consuming since it involves extensive computations, including geometric direction estimation and numerous iterations of wavelet transform. To accelerate computations of PBDW, we propose a general parallelization of patch-based processing by taking the advantage of multicore processors. Additionally, two pertinent optimizations, excluding smooth patches and pre-arranged insertion sort, that make use of sparsity in MR images are also proposed. Simulation results demonstrate that the acceleration factor with the parallel architecture of PBDW approaches the number of central processing unit cores, and that pertinent optimizations are also effective to make further accelerations. The proposed approaches allow compressed sensing MRI reconstruction to be accomplished within several seconds.
Parallel computing of patch-based nonlocal operator and its application in compressed sensing MRI.
Li, Qiyue; Qu, Xiaobo; Liu, Yunsong; Guo, Di; Ye, Jing; Zhan, Zhifang; Chen, Zhong
2014-01-01
Magnetic resonance imaging has been benefited from compressed sensing in improving imaging speed. But the computation time of compressed sensing magnetic resonance imaging (CS-MRI) is relatively long due to its iterative reconstruction process. Recently, a patch-based nonlocal operator (PANO) has been applied in CS-MRI to significantly reduce the reconstruction error by making use of self-similarity in images. But the two major steps in PANO, learning similarities and performing 3D wavelet transform, require extensive computations. In this paper, a parallel architecture based on multicore processors is proposed to accelerate computations of PANO. Simulation results demonstrate that the acceleration factor approaches the number of CPU cores and overall PANO-based CS-MRI reconstruction can be accomplished in several seconds.
LFP-SPECK: an improved SPECK compression algorithm of remote sensing image
Zhang, Xubing; Guan, Zequn; Han, Wei
2009-10-01
SPECK has been found to be competitive in compression of the remote sensing images with abundant texture, while the visual importance of DWT LL sub-band has not been utilized in the SPECK. To improve the compression capability of the SPECK further, this paper presents the LFP-SPECK (Low Frequency Prior SPECK) algorithm. By lifting the bit planes of low frequency sub-band coefficients LFP-SPECK algorithm encodes low frequency sub-band firstly. The double LSP (List of Significant Pixels) lists are adopted here to avoid increasing bits by lifting bit planes. In addition, the optimal single-value linear prediction method is used to decrease the redundancy of the LL sub band. The experimental results with remote sensing and aerial images show that LFP-SPECK algorithm is better than SPECK and the LSPECK (Lifting SEPCK) algorithms.
Effects of ADC Nonlinearity on the Spurious Dynamic Range Performance of Compressed Sensing
Rongzong Kang
2014-01-01
Full Text Available Analog-to-information converter (AIC plays an important role in the compressed sensing system; it has the potential to significantly extend the capabilities of conventional analog-to-digital converter. This paper evaluates the impact of AIC nonlinearity on the dynamic performance in practical compressed sensing system, which included the nonlinearity introduced by quantization as well as the circuit non-ideality. It presents intuitive yet quantitative insights into the harmonics of quantization output of AIC, and the effect of other AIC nonlinearity on the spurious dynamic range (SFDR performance is also analyzed. The analysis and simulation results demonstrated that, compared with conventional ADC-based system, the measurement process decorrelates the input signal and the quantization error and alleviate the effect of other decorrelates of AIC, which results in a dramatic increase in spurious free dynamic range (SFDR.
Efficient High-Dimensional Entanglement Imaging with a Compressive-Sensing Double-Pixel Camera
Gregory A. Howland
2013-02-01
Full Text Available We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n^{2}/log(n for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the entangled photons’ classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates that compressive sensing can be especially effective for higher-order measurements on correlated systems.
Less is more: how compressed sensing is transforming metrology in chemistry.
Holland, Daniel J; Gladden, Lynn F
2014-12-01
Mathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways. With the advent of the digital age, the subject of information theory has grown hugely in importance. In particular, over the last two decades significant advances in our understanding of sampling and function reconstruction have culminated in the development of an idea known as compressed sensing. What seems like an abstract idea is now having a profound impact throughout the scientific world-from enabling high-resolution imaging of pediatric patients in clinical medicine through to advancing 3D electron tomography images of nanoparticle catalysts and NMR spectroscopy studies of proteins. In this Minireview, we summarize these applications and provide an outlook on how the principles of compressed sensing are leading to entirely new approaches to measurement throughout the physical and life sciences. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Cabrelli, Carlos; Jaffard, Stephane; Molter, Ursula
2016-01-01
This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and covers both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Sejdić, Ervin; Movahedi, Faezeh; Zhang, Zhenwei; Kurosu, Atsuko; Coyle, James L.
2016-05-01
Acquiring swallowing accelerometry signals using a comprehensive sensing scheme may be a desirable approach for monitoring swallowing safety for longer periods of time. However, it needs to be insured that signal characteristics can be recovered accurately from compressed samples. In this paper, we considered this issue by examining the effects of the number of acquired compressed samples on the calculated swallowing accelerometry signal features. We used tri-axial swallowing accelerometry signals acquired from seventeen stroke patients (106 swallows in total). From acquired signals, we extracted typically considered signal features from time, frequency and time-frequency domains. Next, we compared these features from the original signals (sampled using traditional sampling schemes) and compressively sampled signals. Our results have shown we can obtain accurate estimates of signal features even by using only a third of original samples.
Sejdić, Ervin; Movahedi, Faezeh; Zhang, Zhenwei; Kurosu, Atsuko; Coyle, James L
2016-04-17
Acquiring swallowing accelerometry signals using a comprehensive sensing scheme may be a desirable approach for monitoring swallowing safety for longer periods of time. However, it needs to be insured that signal characteristics can be recovered accurately from compressed samples. In this paper, we considered this issue by examining the effects of the number of acquired compressed samples on the calculated swallowing accelerometry signal features. We used tri-axial swallowing accelerometry signals acquired from seventeen stroke patients (106 swallows in total). From acquired signals, we extracted typically considered signal features from time, frequency and time-frequency domains. Next, we compared these features from the original signals (sampled using traditional sampling schemes) and compressively sampled signals. Our results have shown we can obtain accurate estimates of signal features even by using only a third of original samples.
Mejia, Yuri H.; Arguello, Henry
2016-05-01
Compressive sensing state-of-the-art proposes random Gaussian and Bernoulli as measurement matrices. Nev- ertheless, often the design of the measurement matrix is subject to physical constraints, and therefore it is frequently not possible that the matrix follows a Gaussian or Bernoulli distribution. Examples of these lim- itations are the structured and sparse matrices of the compressive X-Ray, and compressive spectral imaging systems. A standard algorithm for recovering sparse signals consists in minimizing an objective function that includes a quadratic error term combined with a sparsity-inducing regularization term. This problem can be solved using the iterative algorithms for solving linear inverse problems. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity. However, current algorithms are slow for getting a high quality image reconstruction because they do not exploit the structured and sparsity characteristics of the compressive measurement matrices. This paper proposes the development of a gradient-based algorithm for compressive sensing reconstruction by including a filtering step that yields improved quality using less iterations. This algorithm modifies the iterative solution such that it forces to converge to a filtered version of the residual AT y, where y is the measurement vector and A is the compressive measurement matrix. We show that the algorithm including the filtering step converges faster than the unfiltered version. We design various filters that are motivated by the structure of AT y. Extensive simulation results using various sparse and structured matrices highlight the relative performance gain over the existing iterative process.
Moré, G.; Pesquer, L.; Blanes, I.; Serra-Sagristà, J.; Pons, X.
2012-12-01
World coverage Digital Elevation Models (DEM) have progressively increased their spatial resolution (e.g., ETOPO, SRTM, or Aster GDEM) and, consequently, their storage requirements. On the other hand, lossy data compression facilitates accessing, sharing and transmitting large spatial datasets in environments with limited storage. However, since lossy compression modifies the original information, rigorous studies are needed to understand its effects and consequences. The present work analyzes the influence of DEM quality -modified by lossy compression-, on the radiometric correction of remote sensing imagery, and the eventual propagation of the uncertainty in the resulting land cover classification. Radiometric correction is usually composed of two parts: atmospheric correction and topographical correction. For topographical correction, DEM provides the altimetry information that allows modeling the incidence radiation on terrain surface (cast shadows, self shadows, etc). To quantify the effects of the DEM lossy compression on the radiometric correction, we use radiometrically corrected images for classification purposes, and compare the accuracy of two standard coding techniques for a wide range of compression ratios. The DEM has been obtained by resampling the DEM v.2 of Catalonia (ICC), originally having 15 m resolution, to the Landsat TM resolution. The Aster DEM has been used to fill the gaps beyond the administrative limits of Catalonia. The DEM has been lossy compressed with two coding standards at compression ratios 5:1, 10:1, 20:1, 100:1 and 200:1. The employed coding standards have been JPEG2000 and CCSDS-IDC; the former is an international ISO/ITU-T standard for almost any type of images, while the latter is a recommendation of the CCSDS consortium for mono-component remote sensing images. Both techniques are wavelet-based followed by an entropy-coding stage. Also, for large compression ratios, both techniques need a post processing for correctly
Real time network traffic monitoring for wireless local area networks based on compressed sensing
Balouchestani, Mohammadreza
2017-05-01
A wireless local area network (WLAN) is an important type of wireless networks which connotes different wireless nodes in a local area network. WLANs suffer from important problems such as network load balancing, large amount of energy, and load of sampling. This paper presents a new networking traffic approach based on Compressed Sensing (CS) for improving the quality of WLANs. The proposed architecture allows reducing Data Delay Probability (DDP) to 15%, which is a good record for WLANs. The proposed architecture is increased Data Throughput (DT) to 22 % and Signal to Noise (S/N) ratio to 17 %, which provide a good background for establishing high qualified local area networks. This architecture enables continuous data acquisition and compression of WLAN's signals that are suitable for a variety of other wireless networking applications. At the transmitter side of each wireless node, an analog-CS framework is applied at the sensing step before analog to digital converter in order to generate the compressed version of the input signal. At the receiver side of wireless node, a reconstruction algorithm is applied in order to reconstruct the original signals from the compressed signals with high probability and enough accuracy. The proposed algorithm out-performs existing algorithms by achieving a good level of Quality of Service (QoS). This ability allows reducing 15 % of Bit Error Rate (BER) at each wireless node.
基于压缩感知理论的图像压缩技术研究%Study on Image Compressed Technology Based on Compressed Sensing
王辛悦; 周德全
2013-01-01
压缩感知理论是近年来信号处理领域诞生的一种新的信号处理理论.相较于传统的奈奎斯特采样定率,压缩感知理论采样数据量少,节省了后续处理时间和存储空间,这使其在信号处理领域有着广阔的应用前景.首先讨论了应用压缩感知理论的三个关键问题:信号稀疏表示、随机测量矩阵设计、信号重构算法,初步研究了压缩感知理论在图像压缩技术中的应用,给出了在不同压缩率下的重构图像和PSNR.计算机模拟结果表明了理论的可行性.%Compressed sensing theory,as a new signal processing theory appearing in recent years,can capture and represent compressible signals at a rate significantly below the Nyquist sampling rate.Compressed sensing theory provides outstanding advantages,such as less sampled data,shorter processing time and smaller storage space,which shows a good prospect of application in signal processing.During application of compressed sensing theory,three key points are discussed firstly.Secondly,the application of compressed sensing in the field of image compression technology is studied,the reconstructed images and PSNR at different compress rates are given.The computer simulation proves the feasibility of compressed sensing theory.
Accelerated high-frame-rate mouse heart cine-MRI using compressed sensing reconstruction.
Motaal, Abdallah G; Coolen, Bram F; Abdurrachim, Desiree; Castro, Rui M; Prompers, Jeanine J; Florack, Luc M J; Nicolay, Klaas; Strijkers, Gustav J
2013-04-01
We introduce a new protocol to obtain very high-frame-rate cinematographic (Cine) MRI movies of the beating mouse heart within a reasonable measurement time. The method is based on a self-gated accelerated fast low-angle shot (FLASH) acquisition and compressed sensing reconstruction. Key to our approach is that we exploit the stochastic nature of the retrospective triggering acquisition scheme to produce an undersampled and random k-t space filling that allows for compressed sensing reconstruction and acceleration. As a standard, a self-gated FLASH sequence with a total acquisition time of 10 min was used to produce single-slice Cine movies of seven mouse hearts with 90 frames per cardiac cycle. Two times (2×) and three times (3×) k-t space undersampled Cine movies were produced from 2.5- and 1.5-min data acquisitions, respectively. The accelerated 90-frame Cine movies of mouse hearts were successfully reconstructed with a compressed sensing algorithm. The movies had high image quality and the undersampling artifacts were effectively removed. Left ventricular functional parameters, i.e. end-systolic and end-diastolic lumen surface areas and early-to-late filling rate ratio as a parameter to evaluate diastolic function, derived from the standard and accelerated Cine movies, were nearly identical. Copyright © 2012 John Wiley & Sons, Ltd.
A novel 3D Cartesian random sampling strategy for Compressive Sensing Magnetic Resonance Imaging.
Valvano, Giuseppe; Martini, Nicola; Santarelli, Maria Filomena; Chiappino, Dante; Landini, Luigi
2015-01-01
In this work we propose a novel acquisition strategy for accelerated 3D Compressive Sensing Magnetic Resonance Imaging (CS-MRI). This strategy is based on a 3D cartesian sampling with random switching of the frequency encoding direction with other K-space directions. Two 3D sampling strategies are presented. In the first strategy, the frequency encoding direction is randomly switched with one of the two phase encoding directions. In the second strategy, the frequency encoding direction is randomly chosen between all the directions of the K-Space. These strategies can lower the coherence of the acquisition, in order to produce reduced aliasing artifacts and to achieve a better image quality after Compressive Sensing (CS) reconstruction. Furthermore, the proposed strategies can reduce the typical smoothing of CS due to the limited sampling of high frequency locations. We demonstrated by means of simulations that the proposed acquisition strategies outperformed the standard Compressive Sensing acquisition. This results in a better quality of the reconstructed images and in a greater achievable acceleration.
Reconstructing high-dimensional two-photon entangled states via compressive sensing.
Tonolini, Francesco; Chan, Susan; Agnew, Megan; Lindsay, Alan; Leach, Jonathan
2014-10-13
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to d = 17, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems.
Efficient Reconstruction of Heterogeneous Networks from Time Series via Compressed Sensing.
Long Ma
Full Text Available Recent years have witnessed a rapid development of network reconstruction approaches, especially for a series of methods based on compressed sensing. Although compressed-sensing based methods require much less data than conventional approaches, the compressed sensing for reconstructing heterogeneous networks has not been fully exploited because of hubs. Hub neighbors require much more data to be inferred than small-degree nodes, inducing a cask effect for the reconstruction of heterogeneous networks. Here, a conflict-based method is proposed to overcome the cast effect to considerably reduce data amounts for achieving accurate reconstruction. Moreover, an element elimination method is presented to use the partially available structural information to reduce data requirements. The integration of both methods can further improve the reconstruction performance than separately using each technique. These methods are validated by exploring two evolutionary games taking place in scale-free networks, where individual information is accessible and an attempt to decode the network structure from measurable data is made. The results demonstrate that for all of the cases, much data are saved compared to that in the absence of these two methods. Due to the prevalence of heterogeneous networks in nature and society and the high cost of data acquisition in large-scale networks, these approaches have wide applications in many fields and are valuable for understanding and controlling the collective dynamics of a variety of heterogeneous networked systems.
Efficient Reconstruction of Heterogeneous Networks from Time Series via Compressed Sensing.
Ma, Long; Han, Xiao; Shen, Zhesi; Wang, Wen-Xu; Di, Zengru
2015-01-01
Recent years have witnessed a rapid development of network reconstruction approaches, especially for a series of methods based on compressed sensing. Although compressed-sensing based methods require much less data than conventional approaches, the compressed sensing for reconstructing heterogeneous networks has not been fully exploited because of hubs. Hub neighbors require much more data to be inferred than small-degree nodes, inducing a cask effect for the reconstruction of heterogeneous networks. Here, a conflict-based method is proposed to overcome the cast effect to considerably reduce data amounts for achieving accurate reconstruction. Moreover, an element elimination method is presented to use the partially available structural information to reduce data requirements. The integration of both methods can further improve the reconstruction performance than separately using each technique. These methods are validated by exploring two evolutionary games taking place in scale-free networks, where individual information is accessible and an attempt to decode the network structure from measurable data is made. The results demonstrate that for all of the cases, much data are saved compared to that in the absence of these two methods. Due to the prevalence of heterogeneous networks in nature and society and the high cost of data acquisition in large-scale networks, these approaches have wide applications in many fields and are valuable for understanding and controlling the collective dynamics of a variety of heterogeneous networked systems.
Wood defect detection method with PCA feature fusion and compressed sensing
Yizhuo Zhang; Chao Xu; Chao Li; Huiling Yu; Jun Cao
2015-01-01
We used principal component analysis (PCA) and compressed sensing to detect wood defects from wood plate images. PCA makes it possible to reduce data redundancy and feature dimensions and compressed sensing, used as a clas-sifier, improves identification accuracy. We extracted 25 features, including geometry and regional features, gray-scale texture features, and invariant moment features, from wood board images and then integrated them using PCA, and se-lected eight principal components to express defects. After the fusion process, we used the features to construct a data dic-tionary, and realized the classification of defects by computing the optimal solution of the data dictionary in l1 norm using the least square method. We tested 50 Xylosma samples of live knots, dead knots, and cracks. The average detection time with PCA feature fusion and without were 0.2015 and 0.7125 ms, respectively. The original detection accuracy by SOM neural network was 87%, but after compressed sensing, it was 92%.
Xu Xiaorong; Zhang Jianwu; Huang Aiping; Jiang Bin
2012-01-01
An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS)theory in Cognitive Wireless Sensor Network (C-WSN).Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors,and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals.Adaptive measurement matrix is designed in AMS,which is based on maximum energy subset selection.Energy subset is calculated with sparse transformation of sensing information,and maximum energy subset is selected as the row vector of adaptive measurement matrix.In addition,the measurement matrix is constructed by orthogonalization of those selected row vectors,which also satisfies the Restricted Isometry Property (RIP) in CS theory.Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information.Simulation results are performed with the comparison of Random Measurement Scheme (RMS).It is revealed that,signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement.Moreover,AMS has better detection performance than RMS at lower compression rate region,and it is suitable for large-scale C-WSN wideband spectrum sensing.
Efficient Sparse Signal Transmission over a Lossy Link Using Compressive Sensing.
Wu, Liantao; Yu, Kai; Cao, Dongyu; Hu, Yuhen; Wang, Zhi
2015-08-13
Reliable data transmission over lossy communication link is expensive due to overheads for error protection. For signals that have inherent sparse structures, compressive sensing (CS) is applied to facilitate efficient sparse signal transmissions over lossy communication links without data compression or error protection. The natural packet loss in the lossy link is modeled as a random sampling process of the transmitted data, and the original signal will be reconstructed from the lossy transmission results using the CS-based reconstruction method at the receiving end. The impacts of packet lengths on transmission efficiency under different channel conditions have been discussed, and interleaving is incorporated to mitigate the impact of burst data loss. Extensive simulations and experiments have been conducted and compared to the traditional automatic repeat request (ARQ) interpolation technique, and very favorable results have been observed in terms of both accuracy of the reconstructed signals and the transmission energy consumption. Furthermore, the packet length effect provides useful insights for using compressed sensing for efficient sparse signal transmission via lossy links.
Efficient Sparse Signal Transmission over a Lossy Link Using Compressive Sensing
Liantao Wu
2015-08-01
Full Text Available Reliable data transmission over lossy communication link is expensive due to overheads for error protection. For signals that have inherent sparse structures, compressive sensing (CS is applied to facilitate efficient sparse signal transmissions over lossy communication links without data compression or error protection. The natural packet loss in the lossy link is modeled as a random sampling process of the transmitted data, and the original signal will be reconstructed from the lossy transmission results using the CS-based reconstruction method at the receiving end. The impacts of packet lengths on transmission efficiency under different channel conditions have been discussed, and interleaving is incorporated to mitigate the impact of burst data loss. Extensive simulations and experiments have been conducted and compared to the traditional automatic repeat request (ARQ interpolation technique, and very favorable results have been observed in terms of both accuracy of the reconstructed signals and the transmission energy consumption. Furthermore, the packet length effect provides useful insights for using compressed sensing for efficient sparse signal transmission via lossy links.
Atubga, David; Wu, Huijuan; Lu, Lidong; Sun, Xiaoyan
2017-02-01
Typical fully distributed optical fiber sensors (DOFS) with dozens of kilometers are equivalent to tens of thousands of point sensors along the whole monitoring line, which means tens of thousands of data will be generated for one pulse launching period. Therefore, in an all-day nonstop monitoring, large volumes of data are created thereby triggering the demand for large storage space and high speed for data transmission. In addition, when the monitoring length and channel numbers increase, the data also increase extensively. The task of mitigating large volumes of data accumulation, large storage capacity, and high-speed data transmission is, therefore, the aim of this paper. To demonstrate our idea, we carried out a comparative study of two lossless methods, Huffman and Lempel Ziv Welch (LZW), with a lossy data compression algorithm, fast wavelet transform (FWT) based on three distinctive DOFS sensing data, such as Φ-OTDR, P-OTDR, and B-OTDA. Our results demonstrated that FWT yielded the best compression ratio with good consumption time, irrespective of errors in signal construction of the three DOFS data. Our outcomes indicate the promising potentials of FWT which makes it more suitable, reliable, and convenient for real-time compression of the DOFS data. Finally, it was observed that differences in the DOFS data structure have some influence on both the compression ratio and computational cost.
Ouyang, Bing; Hou, Weilin; Gong, Cuiling; Caimi, Frank M.; Dalgleish, Fraser R.; Vuorenkoski, Anni K.; Xiao, Xifeng; Voelz, David G.
2016-02-01
The Compressive Line Sensing (CLS) active imaging system has been demonstrated to be effective in scattering mediums, such as coastal turbid water, fog and mist, through simulations and test tank experiments. The CLS prototype hardware consists of a CW laser, a DMD, a photomultiplier tube, and a data acquisition instrument. CLS employs whiskbroom imaging formation that is compatible with traditional survey platforms. The sensing model adopts the distributed compressive sensing theoretical framework that exploits both intra-signal sparsity and highly correlated nature of adjacent areas in a natural scene. During sensing operation, the laser illuminates the spatial light modulator DMD to generate a series of 1D binary sensing pattern from a codebook to "encode" current target line segment. A single element detector PMT acquires target reflections as encoder output. The target can then be recovered using the encoder output and a predicted on-target codebook that reflects the environmental interference of original codebook entries. In this work, we investigated the effectiveness of the CLS imaging system in a turbulence environment. Turbulence poses challenges in many atmospheric and underwater surveillance applications. A series of experiments were conducted in the Naval Research Lab's optical turbulence test facility with the imaging path subjected to various turbulence intensities. The total-variation minimization sparsifying basis was used in imaging reconstruction. The preliminary experimental results showed that the current imaging system was able to recover target information under various turbulence strengths. The challenges of acquiring data through strong turbulence environment and future enhancements of the system will be discussed.
IDMA-Based Compressed Sensing for Ocean Monitoring Information Acquisition with Sensor Networks
Gongliang Liu
2014-01-01
Full Text Available The ocean monitoring sensor network is a typically energy-limited and bandwidth-limited system, and the technical bottleneck of which is the asymmetry between the demand for large-scale and high-resolution information acquisition and the limited network resources. The newly arising compressed sensing theory provides a chance for breaking through the bottleneck. In view of this and considering the potential advantages of the emerging interleave-division multiple access (IDMA technology in underwater channels, this paper proposes an IDMA-based compressed sensing scheme in underwater sensor networks with applications to environmental monitoring information acquisition. Exploiting the sparse property of the monitored objects, only a subset of sensors is required to measure and transmit the measurements to the monitoring center for accurate information reconstruction, reducing the requirements for channel bandwidth and energy consumption significantly. Furthermore, with the aid of the semianalytical technique of IDMA, the optimal sensing probability of each sensor is determined to minimize the reconstruction error of the information map. Simulation results with real oceanic monitoring data validate the efficiency of the proposed scheme.
Shihua Cao
2014-03-01
Full Text Available Anomaly event detection is one of the research hotspots in wireless sensor networks. Aiming at the disadvantages of current detection solutions, a novel anomaly event detection algorithm based on compressed sensing and iteration is proposed. Firstly, a measured value can be sensed in each node, based on the compressed sensing. Then the problem of anomaly event detection is modeled as the minimization problem of weighted l1 norm, and OMP algorithm is adopted for solving the problem iteratively. And then the result of problem solving is judged according to detection functions. Finally, in the light of the judgment results, the weight value is updated for beginning a new round iteration. The loop won't stop until all the anomaly events are detected in wireless sensor networks. Simulation experimental results show the proposed algorithm has a better omission detection rate and false alarm rate in different noisy environments. In addition, the detection quality of this algorithm is higher than those of the traditional ones.
Compressed RSS Measurement for Communication and Sensing in the Internet of Things
Yanchao Zhao
2017-01-01
Full Text Available The receiving signal strength (RSS is crucial for the Internet of Things (IoT, as it is the key foundation for communication resource allocation, localization, interference management, sensing, and so on. Aside from its significance, the measurement process could be tedious, time consuming, inaccurate, and involving human operations. The state-of-the-art works usually applied the fashion of “measure a few, predict many,” which use measurement calibrated models to generate the RSS for the whole networks. However, this kind of methods still cannot provide accurate results in a short duration with low measurement cost. In addition, they also require careful scheduling of the measurement which is vulnerable to measurement conflict. In this paper, we propose a compressive sensing- (CS- based RSS measurement solution, which is conflict-tolerant, time-efficient, and accuracy-guaranteed without any model-calibrate operation. The CS-based solution takes advantage of compressive sensing theory to enable simultaneous measurement in the same channel, which reduces the time cost to the level of O(logN (where N is the network size and works well for sparse networks. Extensive experiments based on real data trace are conducted to show the efficiency of the proposed solutions.
Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging
Pastuszczak, Anna; Szczygieł, Bartłomiej; Mikołajczyk, Michał; Kotyński, Rafał
2016-07-01
Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally-efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.
Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain
Liu, Xingbin; Mei, Wenbo; Du, Huiqian
2014-11-01
We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.
Model-based compressive sensing for damage localization in Lamb wave inspection.
Perelli, Alessandro; Di Ianni, Tommaso; Marzani, Alessandro; De Marchi, Luca; Masetti, Guido
2013-10-01
Compressive sensing (CS) has emerged as a potentially viable technique for the efficient compression and analysis of high-resolution signals that have a sparse representation in a fixed basis. In this work, we have developed a CS approach for ultrasonic signal decomposition suitable to achieve high performance in Lamb-wave-based defect detection procedures. In the proposed approach, a CS algorithm based on an alternating minimization (AM) procedure is adopted to extract the information about both the system impulse response and the reflectivity function. The implemented tool exploits the dispersion compensation properties of the warped frequency transform as a means to generate the sparsifying basis for the signal representation. The effectiveness of the decomposition task is demonstrated on synthetic signals and successfully tested on experimental Lamb waves propagating in an aluminum plate. Compared with available strategies, the proposed approach provides an improvement in the accuracy of wave propagation path length estimation, a fundamental step in defect localization procedures.
Spatio-temporal Compressed Sensing with Coded Apertures and Keyed Exposures
Harmany, Zachary T; Willett, Rebecca M
2011-01-01
Optical systems which measure independent random projections of a scene according to compressed sensing (CS) theory face a myriad of practical challenges related to the size of the physical platform, photon efficiency, the need for high temporal resolution, and fast reconstruction in video settings. This paper describes a coded aperture and keyed exposure approach to compressive measurement in optical systems. The proposed projections satisfy the Restricted Isometry Property for sufficiently sparse scenes, and hence are compatible with theoretical guarantees on the video reconstruction quality. These concepts can be implemented in both space and time via either amplitude modulation or phase shifting, and this paper describes the relative merits of the two approaches in terms of theoretical performance, noise and hardware considerations, and experimental results. Fast numerical algorithms which account for the nonnegativity of the projections and temporal correlations in a video sequence are developed and appl...
Li, Jiaosheng; Zhong, Liyun; Zhang, Qinnan; Zhou, Yunfei; Xiong, Jiaxiang; Tian, Jindong; Lu, Xiaoxu
2017-01-01
We propose an optical image hiding method based on dual-channel simultaneous phase-shifting interferometry (DCSPSI) and compressive sensing (CS) in all-optical domain. In the DCSPSI architecture, a secret image is firstly embedded in the host image without destroying the original host's form, and a pair of interferograms with the phase shifts of π/2 is simultaneously generated by the polarization components and captured by two CCDs. Then, the holograms are further compressed sampling to the less data by CS. The proposed strategy will provide a useful solution for the real-time optical image security transmission and largely reducing data volume of interferogram. The experimental result demonstrates the validity and feasibility of the proposed method.
Demonstration of a compressive-sensing Fourier-transform on-chip spectrometer.
Podmore, Hugh; Scott, Alan; Cheben, Pavel; Velasco, Aitor V; Schmid, Jens H; Vachon, Martin; Lee, Regina
2017-04-01
We demonstrate compressive-sensing (CS) spectroscopy in a planar-waveguide Fourier-transform spectrometer (FTS) device. The spectrometer is implemented as an array of Mach-Zehnder interferometers (MZIs) integrated on a photonic chip. The signal from a set of MZIs is composed of an undersampled discrete Fourier interferogram, which we invert using l1-norm minimization to retrieve a sparse input spectrum. To implement this technique, we use a subwavelength-engineered spatial heterodyne FTS on a chip composed of 32 independent MZIs. We demonstrate the retrieval of three sparse input signals by collecting data from restricted sets (8 and 14) of MZIs and applying common CS reconstruction techniques to this data. We show that this retrieval maintains the full resolution and bandwidth of the original device, despite a sampling factor as low as one-fourth of a conventional (non-compressive) design.
Spencer, Austin P; Spokoyny, Boris; Ray, Supratim; Sarvari, Fahad; Harel, Elad
2016-01-25
Compressive sensing allows signals to be efficiently captured by exploiting their inherent sparsity. Here we implement sparse sampling to capture the electronic structure and ultrafast dynamics of molecular systems using phase-resolved 2D coherent spectroscopy. Until now, 2D spectroscopy has been hampered by its reliance on array detectors that operate in limited spectral regions. Combining spatial encoding of the nonlinear optical response and rapid signal modulation allows retrieval of state-resolved correlation maps in a photosynthetic protein and carbocyanine dye. We report complete Hadamard reconstruction of the signals and compression factors as high as 10, in good agreement with array-detected spectra. Single-point array reconstruction by spatial encoding (SPARSE) Spectroscopy reduces acquisition times by about an order of magnitude, with further speed improvements enabled by fast scanning of a digital micromirror device. We envision unprecedented applications for coherent spectroscopy using frequency combs and super-continua in diverse spectral regions.
Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging
Pastuszczak, Anna; Mikołajczyk, Michał; Kotyński, Rafał
2016-01-01
Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally-efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.
Chen, Luoyang; Liu, Jiansheng; cheng, Jiangtao; Liu, Haitao; Zhou, Hongwen
2017-03-01
3D optical coherence tomography imaging (OCT) combined with compressive sensing (CS) has been proved to be an attractive and effective tool in a variety of fields, such as medicine and biology. To achieve high quality imaging while using as less CS sampling rate as possible is the goal of this approach. Here we present an innovative single step fully 3D CS-OCT volumetric image recovery method, in which 3D OCT volumetric image of the object is compressively sampled via our proposed CS coding strategies in all three dimensions while its sparsity is simultaneously taken into consideration in every direction. The object can be directly recovered as the whole volume reconstruction via our advanced full 3D CS reconstruction algorithm. The numerical simulations of a human retina OCT volumetric image reconstruction by our method demonstrate a PSNR of as high as 38dB at a sampling rate of less than 10%.
Photonic compressive sensing with a micro-ring-resonator-based microwave photonic filter
Chen, Ying; Ding, Yunhong; Zhu, Zhijing; Chi, Hao; Zheng, Shilie; Zhang, Xianmin; Jin, Xiaofeng; Galili, Michael; Yu, Xianbin
2016-08-01
A novel approach to realize photonic compressive sensing (CS) with a multi-tap microwave photonic filter is proposed and demonstrated. The system takes both advantages of CS and photonics to capture wideband sparse signals with sub-Nyquist sampling rate. The low-pass filtering function required in the CS is realized in a photonic way by using a frequency comb and a dispersive element. The frequency comb is realized by shaping an amplified spontaneous emission (ASE) source with an on-chip micro-ring resonator, which is beneficial to the integration of photonic CS. A proof-of-concept experiment for a two-tone signal acquisition with frequencies of 350 MHz and 1.25 GHz is experimentally demonstrated with a compression factor up to 16.
Wang, Chuanyun; Song, Fei; Qin, Shiyin
2017-02-01
Addressing the problems of infrared small target tracking in forward looking infrared (FLIR) system, a new infrared small target tracking method is presented, in which features binding of both target gray intensity and spatial relationship is implemented by compressive sensing so as to construct the Gaussian mixture model of compressive appearance distribution. Subsequently, naive Bayesian classification is carried out over testing samples acquired with non-uniform sampling probability to identify the most credible location of targets from background scene. A series of experiments are carried out over four infrared small target image sequences with more than 200 images for each sequence, the results demonstrate the effectiveness and advantages of the proposed method in both success rate and precision rate.
Fast, accurate 2D-MR relaxation exchange spectroscopy (REXSY): Beyond compressed sensing
Bai, Ruiliang; Benjamini, Dan; Cheng, Jian; Basser, Peter J.
2016-10-01
Previously, we showed that compressive or compressed sensing (CS) can be used to reduce significantly the data required to obtain 2D-NMR relaxation and diffusion spectra when they are sparse or well localized. In some cases, an order of magnitude fewer uniformly sampled data were required to reconstruct 2D-MR spectra of comparable quality. Nonetheless, this acceleration may still not be sufficient to make 2D-MR spectroscopy practicable for many important applications, such as studying time-varying exchange processes in swelling gels or drying paints, in living tissue in response to various biological or biochemical challenges, and particularly for in vivo MRI applications. A recently introduced framework, marginal distributions constrained optimization (MADCO), tremendously accelerates such 2D acquisitions by using a priori obtained 1D marginal distribution as powerful constraints when 2D spectra are reconstructed. Here we exploit one important intrinsic property of the 2D-MR relaxation exchange spectra: the fact that the 1D marginal distributions of each 2D-MR relaxation exchange spectrum in both dimensions are equal and can be rapidly estimated from a single Carr-Purcell-Meiboom-Gill (CPMG) or inversion recovery prepared CPMG measurement. We extend the MADCO framework by further proposing to use the 1D marginal distributions to inform the subsequent 2D data-sampling scheme, concentrating measurements where spectral peaks are present and reducing them where they are not. In this way we achieve compression or acceleration that is an order of magnitude greater than that in our previous CS method while providing data in reconstructed 2D-MR spectral maps of comparable quality, demonstrated using several simulated and real 2D T2 - T2 experimental data. This method, which can be called "informed compressed sensing," is extendable to other 2D- and even ND-MR exchange spectroscopy.
Arias, Fernando X.; Sierra, Heidy; Rajadhyaksha, Milind; Arzuaga, Emmanuel
2016-03-01
Compressive Sensing (CS)-based technologies have shown potential to improve the efficiency of acquisition, manipulation, analysis and storage processes on signals and imagery with slight discernible loss in data performance. The CS framework relies on the reconstruction of signals that are presumed sparse in some domain, from a significantly small data collection of linear projections of the signal of interest. As a result, a solution to the underdetermined linear system resulting from this paradigm makes it possible to estimate the original signal with high accuracy. One common approach to solve the linear system is based on methods that minimize the L1-norm. Several fast algorithms have been developed for this purpose. This paper presents a study on the use of CS in high-resolution reflectance confocal microscopy (RCM) images of the skin. RCM offers a cell resolution level similar to that used in histology to identify cellular patterns for diagnosis of skin diseases. However, imaging of large areas (required for effective clinical evaluation) at such high-resolution can turn image capturing, processing and storage processes into a time consuming procedure, which may pose a limitation for use in clinical settings. We present an analysis on the compression ratio that may allow for a simpler capturing approach while reconstructing the required cellular resolution for clinical use. We provide a comparative study in compressive sensing and estimate its effectiveness in terms of compression ratio vs. image reconstruction accuracy. Preliminary results show that by using as little as 25% of the original number of samples, cellular resolution may be reconstructed with high accuracy.
Ling Yongfa
2016-01-01
Full Text Available The paper proposes a mobile control sink node data collection method in the wireless sensor network based on compressive sensing. This method, with regular track, selects the optimal data collection points in the monitoring area via the disc method, calcu-lates the shortest path by using the quantum genetic algorithm, and hence determines the data collection route. Simulation results show that this method has higher network throughput and better energy efficiency, capable of collecting a huge amount of data with balanced energy consumption in the network.
Xu, Daguang; Huang, Yong; Kang, Jin U
2014-09-01
In this work, we propose a novel dispersion compensation method that enables real-time compressive sensing (CS) spectral domain optical coherence tomography (SD OCT) image reconstruction. We show that dispersion compensation can be incorporated into CS SD OCT by multiplying the dispersion-correcting terms by the undersampled spectral data before CS reconstruction. High-quality SD OCT imaging with dispersion compensation was demonstrated at a speed in excess of 70 frames per s using 40% of the spectral measurements required by the well-known Shannon/Nyquist theory. The data processing and image display were performed on a conventional workstation having three graphics processing units.
Fast algorithms for nonconvex compression sensing: MRI reconstruction from very few data
Chartrand, Rick [Los Alamos National Laboratory
2009-01-01
Compressive sensing is the reconstruction of sparse images or signals from very few samples, by means of solving a tractable optimization problem. In the context of MRI, this can allow reconstruction from many fewer k-space samples, thereby reducing scanning time. Previous work has shown that nonconvex optimization reduces still further the number of samples required for reconstruction, while still being tractable. In this work, we extend recent Fourier-based algorithms for convex optimization to the nonconvex setting, and obtain methods that combine the reconstruction abilities of previous nonconvex approaches with the computational speed of state-of-the-art convex methods.
Watermark Detection in Impulsive Noise Environment Based on the Compressive Sensing Reconstruction
B. Lutovac
2017-04-01
Full Text Available The watermark detection procedure for images corrupted by impulsive noise is proposed. The procedure is based on the compressive sensing (CS method for the reconstruction of corrupted pixels. It is shown that the proposed procedure can extract watermark with a moderate impulsive noise level. It is well known that most of the images are approximately sparse in the 2D DCT domain. Moreover, we can force sparsity in the watermarking procedure and obtain almost strictly sparse image as a desirable input to the CS based reconstruction algorithms. Compared to the state-of-the-art methods for impulse noise removal, the proposed solution provides much better performance in watermark extraction.
LP Decoding meets LP Decoding: A Connection between Channel Coding and Compressed Sensing
Dimakis, Alexandros G
2009-01-01
This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present paper is to show that there is a tight connection between, on the one hand, CS-LPD based on a zero-one measurement matrix over the reals and, on the other hand, CC-LPD of the binary linear code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows one to translate performance guarantees from one setup to the other.
Compact all-CMOS spatiotemporal compressive sensing video camera with pixel-wise coded exposure.
Zhang, Jie; Xiong, Tao; Tran, Trac; Chin, Sang; Etienne-Cummings, Ralph
2016-04-18
We present a low power all-CMOS implementation of temporal compressive sensing with pixel-wise coded exposure. This image sensor can increase video pixel resolution and frame rate simultaneously while reducing data readout speed. Compared to previous architectures, this system modulates pixel exposure at the individual photo-diode electronically without external optical components. Thus, the system provides reduction in size and power compare to previous optics based implementations. The prototype image sensor (127 × 90 pixels) can reconstruct 100 fps videos from coded images sampled at 5 fps. With 20× reduction in readout speed, our CMOS image sensor only consumes 14μW to provide 100 fps videos.
Zhao Ruizhen; Ren Xiaoxin; Han Xuelian; Hu Shaohai
2012-01-01
Sparsity Adaptive Matching Pursuit (SAMP) algorithm is a widely used reconstruction algorithm for compressive sensing in the case that the sparsity is unknown.In order to match the sparsity more accurately,we presented an improved SAMP algorithm based on Regularized Backtracking (SAMP-RB).By adapting a regularized backtracking step to SAMP algorithm in each iteration stage,the proposed algorithm can flexibly remove the inappropriate atoms.The experimental results show that SAMP-RB reconstruction algorithm greatly improves SAMP algorithm both in reconstruction quality and computational time.It has better reconstruction efficiency than most of the available matching pursuit algorithms.
Li, Li; Xiao, Wei; Jian, Weijian
2014-11-20
Three-dimensional (3D) laser imaging combining compressive sensing (CS) has an advantage in lower power consumption and less imaging sensors; however, it brings enormous stress to subsequent calculation devices. In this paper we proposed a fast 3D imaging reconstruction algorithm to deal with time-slice images sampled by single-pixel detectors. The algorithm implements 3D imaging reconstruction before CS recovery, thus it saves plenty of runtime of CS recovery. Several experiments are conducted to verify the performance of the algorithm. Simulation results demonstrated that the proposed algorithm has better performance in terms of efficiency compared to an existing algorithm.
New Compressed Sensing ISAR Imaging Algorithm Based on Log-Sum Minimization
Ping, Cheng; Jiaqun, Zhao
2016-12-01
To improve the performance of inverse synthetic aperture radar (ISAR) imaging based on compressed sensing (CS), a new algorithm based on log-sum minimization is proposed. A new interpretation of the algorithm is also provided. Compared with the conventional algorithm, the new algorithm can recover signals based on fewer measurements, in looser sparsity condition, with smaller recovery error, and it has obtained better sinusoidal signal spectrum and imaging result for real ISAR data. Therefore, the proposed algorithm is a promising imaging algorithm in CS ISAR.
Sliding window and compressive sensing for low-field dynamic magnetic resonance imaging
Toraci, Cristian; Ceriani, Stefano; Wilson, David; Fato, Marco; Piana, Michele
2014-01-01
We describe an acquisition/processing procedure for image reconstruction in dynamic Magnetic Resonance Imaging (MRI). The approach requires sliding window to record a set of trajectories in the k-space, standard regularization to reconstruct an estimate of the object and compressed sensing to recover image residuals. We validated this approach in the case of specific simulated experiments and, in the case of real measurements, we showed that the procedure is reliable even in the case of data acquired by means of a low-field scanner.
A novel reconstruction algorithm for bioluminescent tomography based on Bayesian compressive sensing
Wang, Yaqi; Feng, Jinchao; Jia, Kebin; Sun, Zhonghua; Wei, Huijun
2016-03-01
Bioluminescence tomography (BLT) is becoming a promising tool because it can resolve the biodistribution of bioluminescent reporters associated with cellular and subcellular function through several millimeters with to centimeters of tissues in vivo. However, BLT reconstruction is an ill-posed problem. By incorporating sparse a priori information about bioluminescent source, enhanced image quality is obtained for sparsity based reconstruction algorithm. Therefore, sparsity based BLT reconstruction algorithm has a great potential. Here, we proposed a novel reconstruction method based on Bayesian compressive sensing and investigated its feasibility and effectiveness with a heterogeneous phantom. The results demonstrate the potential and merits of the proposed algorithm.
Weng, Jiawen; Clark, David C.; Kim, Myung K.
2016-05-01
A numerical reconstruction method based on compressive sensing (CS) for self-interference incoherent digital holography (SIDH) is proposed to achieve sectional imaging by single-shot in-line self-interference incoherent hologram. The sensing operator is built up based on the physical mechanism of SIDH according to CS theory, and a recovery algorithm is employed for image restoration. Numerical simulation and experimental studies employing LEDs as discrete point-sources and resolution targets as extended sources are performed to demonstrate the feasibility and validity of the method. The intensity distribution and the axial resolution along the propagation direction of SIDH by angular spectrum method (ASM) and by CS are discussed. The analysis result shows that compared to ASM the reconstruction by CS can improve the axial resolution of SIDH, and achieve sectional imaging. The proposed method may be useful to 3D analysis of dynamic systems.
Micro-Doppler Ambiguity Resolution Based on Short-Time Compressed Sensing
Jing-bo Zhuang
2015-01-01
Full Text Available When using a long range radar (LRR to track a target with micromotion, the micro-Doppler embodied in the radar echoes may suffer from ambiguity problem. In this paper, we propose a novel method based on compressed sensing (CS to solve micro-Doppler ambiguity. According to the RIP requirement, a sparse probing pulse train with its transmitting time random is designed. After matched filtering, the slow-time echo signals of the micromotion target can be viewed as randomly sparse sampling of Doppler spectrum. Select several successive pulses to form a short-time window and the CS sensing matrix can be built according to the time stamps of these pulses. Then performing Orthogonal Matching Pursuit (OMP, the unambiguous micro-Doppler spectrum can be obtained. The proposed algorithm is verified using the echo signals generated according to the theoretical model and the signals with micro-Doppler signature produced using the commercial electromagnetic simulation software FEKO.
Hologram Compression Based on Compressive Sensing%基于压缩传感的全息图压缩研究
李科; 李军
2012-01-01
提出将压缩传感理论用于数字全息图的压缩研究.研究了2种不同交换域对全息图稀疏化的影响,针对全息图的特点选取合适的稀疏域,然后根据压缩传感理论直接获取图像的压缩表示,最后利用得到的压缩数据采用2种不同算法重构全息图并对比其重构效果.实验证实这种压缩方法是可行的,并且在傅里叶稀疏域下使用正交匹配追踪(OMP)重构算法能获得1.5％的压缩率.%Hologram is the image that contains the amplitude and phase information of an object, and the compression of hologram is different from the nature image. This paper presents a new theory for digital hologram compression using compressive sensing. A study of the impact of two transform domains to the hologram sparse is first presented, which selects the appropriate transform domain according to the character of hologram, then it directly acquires the compression data of hologram using compressive sensing theory, recovery the hologram using these compression data by two reconstruction algorithms and make a comparison of their construction effects. The main purpose of this paper is to explore the feasibility of the CS framework for hologram compression. The experiments demonstrate that the method proposed is available and it can achieve the compression ratio of 5% when the OMP reconstruction algorithm is used in Fourier transform domain.
Performance of 2D Compressive Sensing on Wide-Beam Through-the-Wall Imaging
Edison Cristofani
2013-01-01
Full Text Available Compressive sensing has become an accepted and powerful alternative to conventional data sampling schemes. Hardware simplicity, data, and measurement time reduction and simplified imagery are some of its most attractive strengths. This work aims at exploring the possibilities of using sparse vector recovery theory for actual engineering and defense- and security-oriented applications. Conventional through-the-wall imaging using a synthetic aperture configuration can also take advantage of compressive sensing by reducing data acquisition rates and omitting certain azimuth scanning positions. An ultra-wideband stepped frequency system carrying wide beam antennas performs through-the-wall imaging of a real scene, including a hollow concrete block wall and a corner reflector behind it. Random downsampling rates lower than those announced by Nyquist’s theorem both in the fast-time and azimuth domains are studied, as well as downsampling limitations for accurate imaging. Separate dictionaries are considered and modeled depending on the objects to be reconstructed: walls or point targets. Results show that an easy interpretation of through-the-wall scenes using the -norm and orthogonal matching pursuit algorithms is possible thanks to the simplification of the reconstructed scene, for which only as low as 25% of the conventional SAR data are needed.
Amina Noor
2013-01-01
Full Text Available This paper proposes a novel algorithm for inferring gene regulatory networks which makes use of cubature Kalman filter (CKF and Kalman filter (KF techniques in conjunction with compressed sensing methods. The gene network is described using a state-space model. A nonlinear model for the evolution of gene expression is considered, while the gene expression data is assumed to follow a linear Gaussian model. The hidden states are estimated using CKF. The system parameters are modeled as a Gauss-Markov process and are estimated using compressed sensing-based KF. These parameters provide insight into the regulatory relations among the genes. The Cramér-Rao lower bound of the parameter estimates is calculated for the system model and used as a benchmark to assess the estimation accuracy. The proposed algorithm is evaluated rigorously using synthetic data in different scenarios which include different number of genes and varying number of sample points. In addition, the algorithm is tested on the DREAM4 in silico data sets as well as the in vivo data sets from IRMA network. The proposed algorithm shows superior performance in terms of accuracy, robustness, and scalability.
Direct inference of protein-DNA interactions using compressed sensing methods.
AlQuraishi, Mohammed; McAdams, Harley H
2011-09-06
Compressed sensing has revolutionized signal acquisition, by enabling complex signals to be measured with remarkable fidelity using a small number of so-called incoherent sensors. We show that molecular interactions, e.g., protein-DNA interactions, can be analyzed in a directly analogous manner and with similarly remarkable results. Specifically, mesoscopic molecular interactions act as incoherent sensors that measure the energies of microscopic interactions between atoms. We combine concepts from compressed sensing and statistical mechanics to determine the interatomic interaction energies of a molecular system exclusively from experimental measurements, resulting in a "de novo" energy potential. In contrast, conventional methods for estimating energy potentials are based on theoretical models premised on a priori assumptions and extensive domain knowledge. We determine the de novo energy potential for pairwise interactions between protein and DNA atoms from (i) experimental measurements of the binding affinity of protein-DNA complexes and (ii) crystal structures of the complexes. We show that the de novo energy potential can be used to predict the binding specificity of proteins to DNA with approximately 90% accuracy, compared to approximately 60% for the best performing alternative computational methods applied to this fundamental problem. This de novo potential method is directly extendable to other biomolecule interaction domains (enzymes and signaling molecule interactions) and to other classes of molecular interactions.
A COMPRESSED SENSING METHOD WITH ANALYTICAL RESULTS FOR LIDAR FEATURE CLASSIFICATION
Allen, Josef D [ORNL
2011-01-01
We present an innovative way to autonomously classify LiDAR points into bare earth, building, vegetation, and other categories. One desirable product of LiDAR data is the automatic classification of the points in the scene. Our algorithm automatically classifies scene points using Compressed Sensing Methods via Orthogonal Matching Pursuit algorithms utilizing a generalized K-Means clustering algorithm to extract buildings and foliage from a Digital Surface Models (DSM). This technology reduces manual editing while being cost effective for large scale automated global scene modeling. Quantitative analyses are provided using Receiver Operating Characteristics (ROC) curves to show Probability of Detection and False Alarm of buildings vs. vegetation classification. Histograms are shown with sample size metrics. Our inpainting algorithms then fill the voids where buildings and vegetation were removed, utilizing Computational Fluid Dynamics (CFD) techniques and Partial Differential Equations (PDE) to create an accurate Digital Terrain Model (DTM) [6]. Inpainting preserves building height contour consistency and edge sharpness of identified inpainted regions. Qualitative results illustrate other benefits such as Terrain Inpainting s unique ability to minimize or eliminate undesirable terrain data artifacts. Keywords: Compressed Sensing, Sparsity, Data Dictionary, LiDAR, ROC, K-Means, Clustering, K-SVD, Orthogonal Matching Pursuit
Robust group compressive sensing for DOA estimation with partially distorted observations
Wang, Ben; Zhang, Yimin D.; Wang, Wei
2016-12-01
In this paper, we propose a robust direction-of-arrival (DOA) estimation algorithm based on group sparse reconstruction algorithm utilizing signals observed at multiple frequencies. The group sparse reconstruction scheme for DOA estimation is solved through the complex multitask Bayesian compressive sensing algorithm by exploiting the group sparse property of the received multi-frequency signals. Then, we propose a robust reconstruction algorithm in the presence of distorted signals. In particular, we consider a problem where the observed data in some frequencies are distorted due to, e.g., interference contamination. In this case, the residual error will follow the impulsive Gaussian mixture distribution instead of the Gaussian distribution due to the fact that some of the estimation errors significantly depart from the mean value of the estimation error distribution. Thus, the minimum least square restriction used in the conventional sparse reconstruction algorithm may lead to a failed reconstruction result. By exploiting the maximum correntropy criterion which is inherently insensitive to the impulsive noise, a weighting vector is derived to automatically mitigate the effect of the distorted narrowband signals, and a robust group compressive sensing approach is developed to achieve reliable DOA estimation. The robustness and effectiveness of the proposed algorithm are verified using simulation results.
Compressive Sensing Based Opportunistic Protocol for Throughput Improvement in Wireless Networks
Qaseem, Syed T
2009-01-01
A key feature in the design of any MAC protocol is the throughput it can provide. In wireless networks, the channel of a user is not fixed but varies randomly. Thus, in order to maximize the throughput of the MAC protocol at any given time, only users with large channel gains should be allowed to transmit. In this paper, compressive sensing based opportunistic protocol for throughput improvement in wireless networks is proposed. The protocol is based on the traditional protocol of R-ALOHA which allows users to compete for channel access before reserving the channel to the best user. We use compressive sensing to find the best user, and show that the proposed protocol requires less time for reservation and so it outperforms other schemes proposed in literature. This makes the protocol particularly suitable for enhancing R-ALOHA in fast fading environments. We consider both analog and digital versions of the protocol where the channel gains sent by the user are analog and digital, respectively.
Optical scanning holography based on compressive sensing using a digital micro-mirror device
A-qian, Sun; Ding-fu, Zhou; Sheng, Yuan; You-jun, Hu; Peng, Zhang; Jian-ming, Yue; xin, Zhou
2017-02-01
Optical scanning holography (OSH) is a distinct digital holography technique, which uses a single two-dimensional (2D) scanning process to record the hologram of a three-dimensional (3D) object. Usually, these 2D scanning processes are in the form of mechanical scanning, and the quality of recorded hologram may be affected due to the limitation of mechanical scanning accuracy and unavoidable vibration of stepper motor's start-stop. In this paper, we propose a new framework, which replaces the 2D mechanical scanning mirrors with a Digital Micro-mirror Device (DMD) to modulate the scanning light field, and we call it OSH based on Compressive Sensing (CS) using a digital micro-mirror device (CS-OSH). CS-OSH can reconstruct the hologram of an object through the use of compressive sensing theory, and then restore the image of object itself. Numerical simulation results confirm this new type OSH can get a reconstructed image with favorable visual quality even under the condition of a low sample rate.
High-resolution MRI of spinal cords by compressive sensing parallel imaging.
Peng Li; Xiangdong Yu; Griffin, Jay; Levine, Jonathan M; Jim Ji
2015-08-01
Spinal Cord Injury (SCI) is a common injury due to diseases or accidents. Noninvasive imaging methods play a critical role in diagnosing SCI and monitoring the response to therapy. Magnetic Resonance Imaging (MRI), by the virtue of providing excellent soft tissue contrast, is the most promising imaging method for this application. However, spinal cord has a very small cross-section, which needs high-resolution images for better visualization and diagnosis. Acquiring high-resolution spinal cord MRI images requires long acquisition time due to the physical and physiological constraints. Moreover, long acquisition time makes MRI more susceptible to motion artifacts. In this paper, we studied the application of compressive sensing (CS) and parallel imaging to achieve high-resolution imaging from sparsely sampled and reduced k-space data acquired by parallel receive arrays. In particular, the studies are limited to the effects of 2D Cartesian sampling with different subsampling schemes and reduction factors. The results show that compressive sensing parallel MRI has the potential to provide high-resolution images of the spinal cord in 1/3 of the acquisition time required by the conventional methods.
Gui, Guan; Xu, Li; Shan, Lin; Adachi, Fumiyuki
2014-01-01
In orthogonal frequency division modulation (OFDM) communication systems, channel state information (CSI) is required at receiver due to the fact that frequency-selective fading channel leads to disgusting intersymbol interference (ISI) over data transmission. Broadband channel model is often described by very few dominant channel taps and they can be probed by compressive sensing based sparse channel estimation (SCE) methods, for example, orthogonal matching pursuit algorithm, which can take the advantage of sparse structure effectively in the channel as for prior information. However, these developed methods are vulnerable to both noise interference and column coherence of training signal matrix. In other words, the primary objective of these conventional methods is to catch the dominant channel taps without a report of posterior channel uncertainty. To improve the estimation performance, we proposed a compressive sensing based Bayesian sparse channel estimation (BSCE) method which cannot only exploit the channel sparsity but also mitigate the unexpected channel uncertainty without scarifying any computational complexity. The proposed method can reveal potential ambiguity among multiple channel estimators that are ambiguous due to observation noise or correlation interference among columns in the training matrix. Computer simulations show that proposed method can improve the estimation performance when comparing with conventional SCE methods.
Microwave-induced thermal acoustic tomography for breast tumor based on compressive sensing.
Zhu, Xiaozhang; Zhao, Zhiqin; Wang, Jinguo; Song, Jian; Liu, Qing Huo
2013-05-01
Microwave-induced thermal acoustic tomography (MITAT) is an innovative technique to image biomedical tissues based on their electric properties. It has the advantages of both high contrast and high spatial resolution. Image reconstruction method in MITAT is always a critical issue. In this paper, a CS-MITAT (CS: compressive sensing) imaging method is proposed. Compressive sensing (CS) is a recently developed sparse signal representation and analysis framework which handles medical imaging measurements using low sampling rate or increasing imaging quality. The CS-MITAT imaging method applies CS theory to the MITAT for breast tumor imaging. In this method, an over-complete dictionary is established to make sparse measurements in the spatial domain. This treatment greatly saves measurement time. Simulations and experiments with real breast tumor tissues demonstrate the feasibility and effectiveness of the method. Compared with conventional time reversal mirror method which has been used in MITAT research, CS-MITAT provides the same peak signal-to-noise ratio imaging quality by using significantly fewer acoustic sensor positions or scanning times.
Zhu Yanping; Song Yaoliang; Chen Jinli; Zhao Delin
2012-01-01
Compressed Sensing (CS) theory is a great breakthrough of the traditional Nyquist sampling theory.It can accomplish compressive sampling and signal recovery based on the sparsity of interested signal,the randomness of measurement matrix and nonlinear optimization method of signal recovery.Firstly,the CS principle is reviewed.Then the ambiguity function of Multiple-Input Multiple-Output (MIMO) radar is deduced.After that,combined with CS theory,the ambiguity function of MIMO radar is analyzed and simulated in detail.At last,the resolutions of coherent and non-coherent MIMO radars on the CS theory are discussed.Simulation results show that the coherent MIMO radar has better resolution performance than the non-coherent.But the coherent ambiguity function has higher side lobes,which caused a deterioration in radar target detection performances.The stochastic embattling method of sparse array based on minimizing the statistical coherence of sensing matrix is proposed.And simulation results show that it could effectively suppress side lobes of the ambiguity function and improve the capability of weak target detection.
Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging.
Liu, Yunsong; Cai, Jian-Feng; Zhan, Zhifang; Guo, Di; Ye, Jing; Chen, Zhong; Qu, Xiaobo
2015-01-01
Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an image is sparse after the application of an analysis operator. Balanced model is a new sparse model that bridges analysis and synthesis models by introducing a penalty term on the distance of frame coefficients to the range of the analysis operator. In this paper, we study the performance of the balanced model in tight frame based compressed sensing magnetic resonance imaging and propose a new efficient numerical algorithm to solve the optimization problem. By tuning the balancing parameter, the new model achieves solutions of three models. It is found that the balanced model has a comparable performance with the analysis model. Besides, both of them achieve better results than the synthesis model no matter what value the balancing parameter is. Experiment shows that our proposed numerical algorithm constrained split augmented Lagrangian shrinkage algorithm for balanced model (C-SALSA-B) converges faster than previously proposed algorithms accelerated proximal algorithm (APG) and alternating directional method of multipliers for balanced model (ADMM-B).
Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging.
Yunsong Liu
Full Text Available Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an image is sparse after the application of an analysis operator. Balanced model is a new sparse model that bridges analysis and synthesis models by introducing a penalty term on the distance of frame coefficients to the range of the analysis operator. In this paper, we study the performance of the balanced model in tight frame based compressed sensing magnetic resonance imaging and propose a new efficient numerical algorithm to solve the optimization problem. By tuning the balancing parameter, the new model achieves solutions of three models. It is found that the balanced model has a comparable performance with the analysis model. Besides, both of them achieve better results than the synthesis model no matter what value the balancing parameter is. Experiment shows that our proposed numerical algorithm constrained split augmented Lagrangian shrinkage algorithm for balanced model (C-SALSA-B converges faster than previously proposed algorithms accelerated proximal algorithm (APG and alternating directional method of multipliers for balanced model (ADMM-B.
Continuous Compressed Sensing for Surface Dynamical Processes with Helium Atom Scattering
Jones, Alex; Tamtögl, Anton; Calvo-Almazán, Irene; Hansen, Anders
2016-06-01
Compressed Sensing (CS) techniques are used to measure and reconstruct surface dynamical processes with a helium spin-echo spectrometer for the first time. Helium atom scattering is a well established method for examining the surface structure and dynamics of materials at atomic sized resolution and the spin-echo technique opens up the possibility of compressing the data acquisition process. CS methods demonstrating the compressibility of spin-echo spectra are presented for several measurements. Recent developments on structured multilevel sampling that are empirically and theoretically shown to substantially improve upon the state of the art CS techniques are implemented. In addition, wavelet based CS approximations, founded on a new continuous CS approach, are used to construct continuous spectra. In order to measure both surface diffusion and surface phonons, which appear usually on different energy scales, standard CS techniques are not sufficient. However, the new continuous CS wavelet approach allows simultaneous analysis of surface phonons and molecular diffusion while reducing acquisition times substantially. The developed methodology is not exclusive to Helium atom scattering and can also be applied to other scattering frameworks such as neutron spin-echo and Raman spectroscopy.
Eslahi, Nasser; Aghagolzadeh, Ali
2016-07-01
Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which suggests a new framework for the simultaneous sampling and compression of sparse or compressible signals at a rate significantly below the Nyquist rate. Maybe, designing an effective regularization term reflecting the image sparse prior information plays a critical role in CS image restoration. Recently, both local smoothness and nonlocal self-similarity have led to superior sparsity prior for CS image restoration. In this paper, first, an adaptive curvelet thresholding criterion is developed, trying to adaptively remove the perturbations appeared in recovered images during CS recovery process, imposing sparsity. Furthermore, a new sparsity measure called joint adaptive sparsity regularization (JASR) is established, which enforces both local sparsity and nonlocal 3-D sparsity in transform domain, simultaneously. Then, a novel technique for high-fidelity CS image recovery via JASR is proposed-CS-JASR. To efficiently solve the proposed corresponding optimization problem, we employ the split Bregman iterations. Extensive experimental results are reported to attest the adequacy and effectiveness of the proposed method comparing with the current state-of-the-art methods in CS image restoration.
Block sparsity-based joint compressed sensing recovery of multi-channel ECG signals.
Singh, Anurag; Dandapat, Samarendra
2017-04-01
In recent years, compressed sensing (CS) has emerged as an effective alternative to conventional wavelet based data compression techniques. This is due to its simple and energy-efficient data reduction procedure, which makes it suitable for resource-constrained wireless body area network (WBAN)-enabled electrocardiogram (ECG) telemonitoring applications. Both spatial and temporal correlations exist simultaneously in multi-channel ECG (MECG) signals. Exploitation of both types of correlations is very important in CS-based ECG telemonitoring systems for better performance. However, most of the existing CS-based works exploit either of the correlations, which results in a suboptimal performance. In this work, within a CS framework, the authors propose to exploit both types of correlations simultaneously using a sparse Bayesian learning-based approach. A spatiotemporal sparse model is employed for joint compression/reconstruction of MECG signals. Discrete wavelets transform domain block sparsity of MECG signals is exploited for simultaneous reconstruction of all the channels. Performance evaluations using Physikalisch-Technische Bundesanstalt MECG diagnostic database show a significant gain in the diagnostic reconstruction quality of the MECG signals compared with the state-of-the art techniques at reduced number of measurements. Low measurement requirement may lead to significant savings in the energy-cost of the existing CS-based WBAN systems.
A Compressed Sensing-Based Wearable Sensor Network for Quantitative Assessment of Stroke Patients
Lei Yu
2016-02-01
Full Text Available Clinical rehabilitation assessment is an important part of the therapy process because it is the premise for prescribing suitable rehabilitation interventions. However, the commonly used assessment scales have the following two drawbacks: (1 they are susceptible to subjective factors; (2 they only have several rating levels and are influenced by a ceiling effect, making it impossible to exactly detect any further improvement in the movement. Meanwhile, energy constraints are a primary design consideration in wearable sensor network systems since they are often battery-operated. Traditionally, for wearable sensor network systems that follow the Shannon/Nyquist sampling theorem, there are many data that need to be sampled and transmitted. This paper proposes a novel wearable sensor network system to monitor and quantitatively assess the upper limb motion function, based on compressed sensing technology. With the sparse representation model, less data is transmitted to the computer than with traditional systems. The experimental results show that the accelerometer signals of Bobath handshake and shoulder touch exercises can be compressed, and the length of the compressed signal is less than 1/3 of the raw signal length. More importantly, the reconstruction errors have no influence on the predictive accuracy of the Brunnstrom stage classification model. It also indicated that the proposed system can not only reduce the amount of data during the sampling and transmission processes, but also, the reconstructed accelerometer signals can be used for quantitative assessment without any loss of useful information.
A Compressed Sensing-Based Wearable Sensor Network for Quantitative Assessment of Stroke Patients
Yu, Lei; Xiong, Daxi; Guo, Liquan; Wang, Jiping
2016-01-01
Clinical rehabilitation assessment is an important part of the therapy process because it is the premise for prescribing suitable rehabilitation interventions. However, the commonly used assessment scales have the following two drawbacks: (1) they are susceptible to subjective factors; (2) they only have several rating levels and are influenced by a ceiling effect, making it impossible to exactly detect any further improvement in the movement. Meanwhile, energy constraints are a primary design consideration in wearable sensor network systems since they are often battery-operated. Traditionally, for wearable sensor network systems that follow the Shannon/Nyquist sampling theorem, there are many data that need to be sampled and transmitted. This paper proposes a novel wearable sensor network system to monitor and quantitatively assess the upper limb motion function, based on compressed sensing technology. With the sparse representation model, less data is transmitted to the computer than with traditional systems. The experimental results show that the accelerometer signals of Bobath handshake and shoulder touch exercises can be compressed, and the length of the compressed signal is less than 1/3 of the raw signal length. More importantly, the reconstruction errors have no influence on the predictive accuracy of the Brunnstrom stage classification model. It also indicated that the proposed system can not only reduce the amount of data during the sampling and transmission processes, but also, the reconstructed accelerometer signals can be used for quantitative assessment without any loss of useful information. PMID:26861337
A Compressed Sensing-Based Wearable Sensor Network for Quantitative Assessment of Stroke Patients.
Yu, Lei; Xiong, Daxi; Guo, Liquan; Wang, Jiping
2016-02-05
Clinical rehabilitation assessment is an important part of the therapy process because it is the premise for prescribing suitable rehabilitation interventions. However, the commonly used assessment scales have the following two drawbacks: (1) they are susceptible to subjective factors; (2) they only have several rating levels and are influenced by a ceiling effect, making it impossible to exactly detect any further improvement in the movement. Meanwhile, energy constraints are a primary design consideration in wearable sensor network systems since they are often battery-operated. Traditionally, for wearable sensor network systems that follow the Shannon/Nyquist sampling theorem, there are many data that need to be sampled and transmitted. This paper proposes a novel wearable sensor network system to monitor and quantitatively assess the upper limb motion function, based on compressed sensing technology. With the sparse representation model, less data is transmitted to the computer than with traditional systems. The experimental results show that the accelerometer signals of Bobath handshake and shoulder touch exercises can be compressed, and the length of the compressed signal is less than 1/3 of the raw signal length. More importantly, the reconstruction errors have no influence on the predictive accuracy of the Brunnstrom stage classification model. It also indicated that the proposed system can not only reduce the amount of data during the sampling and transmission processes, but also, the reconstructed accelerometer signals can be used for quantitative assessment without any loss of useful information.
An infrared-visible image fusion scheme based on NSCT and compressed sensing
Zhang, Qiong; Maldague, Xavier
2015-05-01
Image fusion, as a research hot point nowadays in the field of infrared computer vision, has been developed utilizing different varieties of methods. Traditional image fusion algorithms are inclined to bring problems, such as data storage shortage and computational complexity increase, etc. Compressed sensing (CS) uses sparse sampling without knowing the priori knowledge and greatly reconstructs the image, which reduces the cost and complexity of image processing. In this paper, an advanced compressed sensing image fusion algorithm based on non-subsampled contourlet transform (NSCT) is proposed. NSCT provides better sparsity than the wavelet transform in image representation. Throughout the NSCT decomposition, the low-frequency and high-frequency coefficients can be obtained respectively. For the fusion processing of low-frequency coefficients of infrared and visible images , the adaptive regional energy weighting rule is utilized. Thus only the high-frequency coefficients are specially measured. Here we use sparse representation and random projection to obtain the required values of high-frequency coefficients, afterwards, the coefficients of each image block can be fused via the absolute maximum selection rule and/or the regional standard deviation rule. In the reconstruction of the compressive sampling results, a gradient-based iterative algorithm and the total variation (TV) method are employed to recover the high-frequency coefficients. Eventually, the fused image is recovered by inverse NSCT. Both the visual effects and the numerical computation results after experiments indicate that the presented approach achieves much higher quality of image fusion, accelerates the calculations, enhances various targets and extracts more useful information.
Xu, Daguang; Huang, Yong; Kang, Jin U
2013-01-01
We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.
Chen, Xiao; Yang, Yang; Cai, Xiaoying; Auger, Daniel A; Meyer, Craig H; Salerno, Michael; Epstein, Frederick H
2016-06-14
Cine Displacement Encoding with Stimulated Echoes (DENSE) provides accurate quantitative imaging of cardiac mechanics with rapid displacement and strain analysis; however, image acquisition times are relatively long. Compressed sensing (CS) with parallel imaging (PI) can generally provide high-quality images recovered from data sampled below the Nyquist rate. The purposes of the present study were to develop CS-PI-accelerated acquisition and reconstruction methods for cine DENSE, to assess their accuracy for cardiac imaging using retrospective undersampling, and to demonstrate their feasibility for prospectively-accelerated 2D cine DENSE imaging in a single breathhold. An accelerated cine DENSE sequence with variable-density spiral k-space sampling and golden angle rotations through time was implemented. A CS method, Block LOw-rank Sparsity with Motion-guidance (BLOSM), was combined with sensitivity encoding (SENSE) for the reconstruction of under-sampled multi-coil spiral data. Seven healthy volunteers and 7 patients underwent 2D cine DENSE imaging with fully-sampled acquisitions (14-26 heartbeats in duration) and with prospectively rate-2 and rate-4 accelerated acquisitions (14 and 8 heartbeats in duration). Retrospectively- and prospectively-accelerated data were reconstructed using BLOSM-SENSE and SENSE. Image quality of retrospectively-undersampled data was quantified using the relative root mean square error (rRMSE). Myocardial displacement and circumferential strain were computed for functional assessment, and linear correlation and Bland-Altman analyses were used to compare accelerated acquisitions to fully-sampled reference datasets. For retrospectively-undersampled data, BLOSM-SENSE provided similar or lower rRMSE at rate-2 and lower rRMSE at rate-4 acceleration compared to SENSE (p cine DENSE provided good image quality and expected values of displacement and strain. BLOSM-SENSE-accelerated spiral cine DENSE imaging with 2D displacement encoding can be
Computational Complexity Reduction in Nonuniform Compressed Sensing by Multi-Coset Emulation
Grigoryan, Ruben; Jensen, Tobias Lindstrøm; Larsen, Torben
2017-01-01
and positions of the frequency bands and different levels of noise in the signals. For the \\{SNS\\} reconstruction, we consider the accelerated iterative hard thresholding algorithm; for the \\{MCS\\} reconstruction, the multiple signal classification and focal underdetermined system solver algorithms are used......Abstract Single-channel Nonuniform Sampling (SNS) is a Compressed Sensing (CS) approach that allows sub-Nyquist sampling of frequency sparse signals. The relatively simple architecture, comprising one wide-band sampling channel, makes it an attractive solution for applications such as signal...... analyzers and telecommunications. However, a high computational cost of the \\{SNS\\} signal reconstruction is an obstacle for real-time applications. This paper proposes to emulate Multi-Coset Sampling (MCS) in \\{SNS\\} acquisition as a means to decrease the computational costs. Such an emulation introduces...
Quantitative Inspection of Remanence of Broken Wire Rope Based on Compressed Sensing
Zhang, Juwei; Tan, Xiaojiang
2016-01-01
Most traditional strong magnetic inspection equipment has disadvantages such as big excitation devices, high weight, low detection precision, and inconvenient operation. This paper presents the design of a giant magneto-resistance (GMR) sensor array collection system. The remanence signal is collected to acquire two-dimensional magnetic flux leakage (MFL) data on the surface of wire ropes. Through the use of compressed sensing wavelet filtering (CSWF), the image expression of wire ropes MFL on the surface was obtained. Then this was taken as the input of the designed back propagation (BP) neural network to extract three kinds of MFL image geometry features and seven invariant moments of defect images. Good results were obtained. The experimental results show that nondestructive inspection through the use of remanence has higher accuracy and reliability compared with traditional inspection devices, along with smaller volume, lighter weight and higher precision. PMID:27571077
Biological application of Compressed Sensing Tomography in the Scanning Electron Microscope
Ferroni, Matteo; Signoroni, Alberto; Sanzogni, Andrea; Masini, Luca; Migliori, Andrea; Ortolani, Luca; Pezza, Alessandro; Morandi, Vittorio
2016-01-01
The three-dimensional tomographic reconstruction of a biological sample, namely collagen fibrils in human dermal tissue, was obtained from a set of projection-images acquired in the Scanning Electron Microscope. A tailored strategy for the transmission imaging mode was implemented in the microscope and proved effective in acquiring the projections needed for the tomographic reconstruction. Suitable projection alignment and Compressed Sensing formulation were used to overcome the limitations arising from the experimental acquisition strategy and to improve the reconstruction of the sample. The undetermined problem of structure reconstruction from a set of projections, limited in number and angular range, was indeed supported by exploiting the sparsity of the object projected in the electron microscopy images. In particular, the proposed system was able to preserve the reconstruction accuracy even in presence of a significant reduction of experimental projections. PMID:27646194
Flame four-dimensional deflection tomography with compressed-sensing-revision reconstruction
Zhang, Bin; Zhao, Minmin; Liu, Zhigang; Wu, Zhaohang
2016-08-01
Deflection tomography with limited angle projections was investigated to visualize a premixed flame. A projection sampling system for deflection tomography was used to obtain chronological deflectogram arrays at six view angles with only a pair of gratings. A new iterative reconstruction algorithm with deflection angle compressed-sensing revision was developed to improve reconstruction-distribution quality from incomplete projection data. Numerical simulation and error analysis provided a good indication of algorithm precision and convergence. In the experiment, 150 fringes were processed, and temperature distributions in 20 cross-sections were reconstructed from projection data in four instants. Four-dimensional flame structures and temperature distributions in the flame interior were visualized using the visualization toolkit. The experimental reconstruction was then compared with the result obtained from computational fluid dynamic analysis.
Cylindrical Three-Dimensional Millimeter-Wave Imaging via Compressive Sensing
Guoqiang Zhao
2015-01-01
Full Text Available Millimeter-wave (MMW imaging techniques have been used for the detection of concealed weapons and contraband carried by personnel. However, the future application of the new technology may be limited by its large number of antennas. In order to reduce the complexity of the hardware, a novel MMW imaging method based on compressive sensing (CS is proposed in this paper. The MMW images can be reconstructed from the significantly undersampled backscattered data via the CS approach. Thus the number of antennas and the cost of system can be further reduced than those based on the traditional imaging methods that obey the Nyquist sampling theorem. The effectiveness of the proposed method is validated by numerical simulations as well as by real measured data of objects.
Sparse-View Ultrasound Diffraction Tomography Using Compressed Sensing with Nonuniform FFT
Shaoyan Hua
2014-01-01
Full Text Available Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT. In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed.
Yuan, Haiying; Wang, Xiuyu; Sun, Xun; Ju, Zijian
2017-06-01
Bearing fault diagnosis collects massive amounts of vibration data about a rotating machinery system, whose fault classification largely depends on feature extraction. Features reflecting bearing work states are directly extracted using time-frequency analysis of vibration signals, which leads to high dimensional feature data. To address the problem of feature dimension reduction, a compressive sensing-based feature extraction algorithm is developed to construct a concise fault feature set. Next, a heuristic PSO-BP neural network, whose learning process perfectly combines particle swarm optimization and the Levenberg-Marquardt algorithm, is constructed for fault classification. Numerical simulation experiments are conducted on four datasets sampled under different severity levels and load conditions, which verify that the proposed fault diagnosis method achieves efficient feature extraction and high classification accuracy.
Accelerate Single-shot Data Acquisitions Using Compressed Sensing and FRONSAC Imaging
Wang, Haifeng; Galiana, Gigi
2015-01-01
Nonlinear spatial encoding magnetic (SEM) fields have been studied to complement multichannel RF encoding and accelerate MRI scans. Published schemes include PatLoc, O-Space, Null Space, 4D-RIO, and others, but the large variety of possible approaches to exploiting nonlinear SEMs remains mostly unexplored. Before, we have presented a new approach, Fast ROtary Nonlinear Spatial ACquisition (FRONSAC) imaging, where the nonlinear fields provide a small rotating perturbation to standard linear trajectories. While FRONSAC encoding greatly improves image quality, at the highest accelerations or weakest FRONSAC fields, some undersampling artifacts remain. However, the under-sampling artifacts that occur with FRONSAC encoding are relatively incoherent and well suited to the compressed sensing (CS) reconstruction. CS provides a sparsity-promoting convex strategy to reconstruct images from highly undersampled datasets. The work presented here combines the benefits of FRONSAC and CS. Simulations illustrate that this com...
Dafu, Shen; Leihong, Zhang; Dong, Liang; Bei, Li; Yi, Kang
2017-07-01
The purpose of this study is to improve the reconstruction precision and better copy the color of spectral image surfaces. A new spectral reflectance reconstruction algorithm based on an iterative threshold combined with weighted principal component space is presented in this paper, and the principal component with weighted visual features is the sparse basis. Different numbers of color cards are selected as the training samples, a multispectral image is the testing sample, and the color differences in the reconstructions are compared. The channel response value is obtained by a Mega Vision high-accuracy, multi-channel imaging system. The results show that spectral reconstruction based on weighted principal component space is superior in performance to that based on traditional principal component space. Therefore, the color difference obtained using the compressive-sensing algorithm with weighted principal component analysis is less than that obtained using the algorithm with traditional principal component analysis, and better reconstructed color consistency with human eye vision is achieved.
Shechtman, Yoav; Szameit, Alexander; Segev, Mordechai
2011-01-01
We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.
Weijian Si
2015-01-01
Full Text Available A novel direction of arrival (DOA estimation method in compressed sensing (CS is proposed, in which the DOA estimation problem is cast as the joint sparse reconstruction from multiple measurement vectors (MMV. The proposed method is derived through transforming quadratically constrained linear programming (QCLP into unconstrained convex optimization which overcomes the drawback that l1-norm is nondifferentiable when sparse sources are reconstructed by minimizing l1-norm. The convergence rate and estimation performance of the proposed method can be significantly improved, since the steepest descent step and Barzilai-Borwein step are alternately used as the search step in the unconstrained convex optimization. The proposed method can obtain satisfactory performance especially in these scenarios with low signal to noise ratio (SNR, small number of snapshots, or coherent sources. Simulation results show the superior performance of the proposed method as compared with existing methods.
Si, Weijian; Qu, Xinggen; Liu, Lutao
2014-01-01
A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV). The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP) and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR), small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB) of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP). The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results.
Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing
Weijian Si
2015-08-01
Full Text Available This paper presents a novel off-grid direction of arrival (DOA estimation method to achieve the superior performance in compressed sensing (CS, in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods.
Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing.
Si, Weijian; Qu, Xinggen; Qu, Zhiyu
2015-08-27
This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods.
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
Ziniel, Justin
2012-01-01
In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracl...
Reduced Complexity Angle-Doppler-Range Estimation for MIMO Radar That Employs Compressive Sensing
Yu, Yao; Poor, H Vincent
2009-01-01
The authors recently proposed a MIMO radar system that is implemented by a small wireless network. By applying compressive sensing (CS) at the receive nodes, the MIMO radar super-resolution can be achieved with far fewer observations than conventional approaches. This previous work considered the estimation of direction of arrival and Doppler. Since the targets are sparse in the angle-velocity space, target information can be extracted by solving an l1 minimization problem. In this paper, the range information is exploited by introducing step frequency to MIMO radar with CS. The proposed approach is able to achieve high range resolution and also improve the ambiguous velocity. However, joint angle-Doppler-range estimation requires discretization of the angle-Doppler-range space which causes a sharp rise in the computational burden of the l1 minimization problem. To maintain an acceptable complexity, a technique is proposed to successively estimate angle, Doppler and range in a decoupled fashion. The proposed ...
Wide-field fluorescence molecular tomography with compressive sensing based preconditioning.
Yao, Ruoyang; Pian, Qi; Intes, Xavier
2015-12-01
Wide-field optical tomography based on structured light illumination and detection strategies enables efficient tomographic imaging of large tissues at very fast acquisition speeds. However, the optical inverse problem based on such instrumental approach is still ill-conditioned. Herein, we investigate the benefit of employing compressive sensing-based preconditioning to wide-field structured illumination and detection approaches. We assess the performances of Fluorescence Molecular Tomography (FMT) when using such preconditioning methods both in silico and with experimental data. Additionally, we demonstrate that such methodology could be used to select the subset of patterns that provides optimal reconstruction performances. Lastly, we compare preconditioning data collected using a normal base that offers good experimental SNR against that directly acquired with optimal designed base. An experimental phantom study is provided to validate the proposed technique.
Optimal Arrays for Compressed Sensing in Snapshot-Mode Radio Interferometry
Fannjiang, Clara
2015-01-01
Radio interferometry has always faced the problem of incomplete sampling of the Fourier plane. A possible remedy can be found in the promising new theory of compressed sensing (CS), which allows for the accurate recovery of sparse signals from sub-Nyquist sampling given certain measurement conditions. We provide an introductory assessment of optimal arrays for CS in snapshot-mode radio interferometry, using orthogonal matching pursuit (OMP), a widely used CS recovery algorithm similar in some respects to CLEAN. We focus on centrally condensed (specifically, Gaussian) arrays versus uniform arrays, and the principle of randomization versus deterministic arrays such as the VLA. The theory of CS is grounded in $a)$ sparse representation of signals and $b)$ measurement matrices of low coherence. We calculate a related quantity, mutual coherence (MC), as a theoretical indicator of arrays' suitability for OMP based on the recovery error bounds in (Donoho et al. 2006). OMP reconstructions of both point and extended o...
Suppressing azimuth ambiguity in spaceborne SAR images based on compressed sensing
YU Ze; LIU Min
2012-01-01
In spaceborne synthetic aperture radar,undersampling at the rate of the pulse repetition frequency causes azimuth ambiguity,which induces ghost into the images.This paper introduces compressed sensing for azimuth ambiguity suppression and presents two novel methods from the perspectives of system design and image formation,known as azimuth random sampling and ambiguity separation,respectively.The first method makes the imaging results for the ambiguity zones as disperse as possible while ensuring that the imaging results for the main scene are affected as little as possible.The second method separates the ambiguity signals from the echoes and achieves imaging results without the ambiguity effect.Simulation results show that the two methods can reduce the ambiguity levels by about 16 dB and 99.37％,respectively.
Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery
Lingjun Liu
2017-01-01
Full Text Available This paper presents a variant of the iterative shrinkage-thresholding (IST algorithm, called backtracking-based adaptive IST (BAIST, for image compressive sensing (CS reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the BAIST method backtracks to the previous noisy image using L2 norm minimization, i.e., minimizing the Euclidean distance between the current solution and the previous ones. Through this modification, the BAIST method achieves superior performance while maintaining the low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive regularizor to automatically detect the sparsity level of an image. Experimental results show that our algorithm outperforms the original IST method and several excellent CS techniques.
Compressive sensing of full wave field data for structural health monitoring applications.
Di Ianni, Tommaso; De Marchi, Luca; Perelli, Alessandro; Marzani, Alessandro
2015-07-01
Numerous nondestructive evaluations and structural health monitoring approaches based on guide waves rely on analysis of wave fields recorded through scanning laser Doppler vibrometers (SLDVs) or ultrasonic scanners. The informative content which can be extracted from these inspections is relevant; however, the acquisition process is generally time-consuming, posing a limit in the applicability of such approaches. To reduce the acquisition time, we use a random sampling scheme based on compressive sensing (CS) to minimize the number of points at which the field is measured. The CS reconstruction performance is mostly influenced by the choice of a proper decomposition basis to exploit the sparsity of the acquired signal. Here, different bases have been tested to recover the guided waves wave field acquired on both an aluminum and a composite plate. Experimental results show that the proposed approach allows a reduction of the measurement locations required for accurate signal recovery to less than 34% of the original sampling grid.
High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing.
Yang, Fugang; Ozturk, Mehmet S; Zhao, Lingling; Cong, Wenxiang; Wang, Ge; Intes, Xavier
2015-01-01
Mesoscopic fluorescence molecular tomography (MFMT) is new imaging modality aiming at 3-D imaging of molecular probes in a few millimeter thick biological samples with high-spatial resolution. In this paper, we develop a compressive sensing-based reconstruction method with l1-norm regularization for MFMT with the goal of improving spatial resolution and stability of the optical inverse problem. Three-dimensional numerical simulations of anatomically accurate microvasculature and real data obtained from phantom experiments are employed to evaluate the merits of the proposed method. Experimental results show that the proposed method can achieve 80 μm spatial resolution for a biological sample of 3 mm thickness and more accurate quantifications of concentrations and locations for the fluorophore distribution than those of the conventional methods.
Ahmed M. Khedr
2015-10-01
Full Text Available In designing wireless sensor networks (WSNs, it is important to reduce energy dissipation and prolong network lifetime. Clustering of nodes is one of the most effective approaches for conserving energy in WSNs. Cluster formation protocols generally consider the heterogeneity of sensor nodes in terms of energy difference of nodes but ignore the different transmission ranges of them. In this paper, we propose an effective data acquisition clustered protocol using compressive sensing (EDACP-CS for heterogeneous WSNs that aims to conserve the energy of sensor nodes in the presence of energy and transmission range heterogeneity. In EDACP-CS, cluster heads are selected based on the distance from the base station and sensor residual energy. Simulation results show that our protocol offers a much better performance than the existing protocols in terms of energy consumption, stability, network lifetime, and throughput.
Jørgensen, Jakob H; Pan, Xiaochuan
2011-01-01
Discrete-to-discrete imaging models for computed tomography (CT) are becoming increasingly ubiquitous as the interest in iterative image reconstruction algorithms has heightened. Despite this trend, all the intuition for algorithm and system design derives from analysis of continuous-to-continuous models such as the X-ray and Radon transform. While the similarity between these models justifies some crossover, questions such as what are sufficient sampling conditions can be quite different for the two models. This sampling issue is addressed extensively in the first half of the article using singular value decomposition analysis for determining sufficient number of views and detector bins. The question of full sampling for CT is particularly relevant to current attempts to adapt compressive sensing (CS) motivated methods to application in CT image reconstruction. The second half goes in depth on this subject and discusses the link between object sparsity and sufficient sampling for accurate reconstruction. Par...
Accelerating PS model-based dynamic cardiac MRI using compressed sensing.
Zhang, Xiaoyong; Xie, Guoxi; Shi, Caiyun; Su, Shi; Zhang, Yongqin; Liu, Xin; Qiu, Bensheng
2016-02-01
High spatiotemporal resolution MRI is a challenging topic in dynamic MRI field. Partial separability (PS) model has been successfully applied to dynamic cardiac MRI by exploiting data redundancy. However, the model requires substantial preprocessing data to accurately estimate the model parameters before image reconstruction. Since compressed sensing (CS) is a potential technique to accelerate MRI by reducing the number of acquired data, the combination of PS and CS, named as Stepped-SparsePS, was introduced to accelerate the preprocessing data acquisition of PS in this work. The proposed Stepped-SparsePS method sequentially reconstructs a set of aliased dynamic images in each channel based on PS model and then the final dynamic images from the aliased images using CS. The results from numerical simulations and in vivo experiments demonstrate that Stepped-SparsePS could significantly reduce data acquisition time while preserving high spatiotemporal resolution. Copyright © 2015 Elsevier Inc. All rights reserved.
CSSF MIMO RADAR: Low-Complexity Compressive Sensing Based MIMO Radar That Uses Step Frequency
Yu, Yao; Poor, H Vincent
2011-01-01
A new approach is proposed, namely CSSF MIMO radar, which applies the technique of step frequency (SF) to compressive sensing (CS) based multi-input multi-output (MIMO) radar. The proposed approach enables high resolution range, angle and Doppler estimation, while transmitting narrowband pulses. The problem of joint angle-Doppler-range estimation is first formulated to fit the CS framework, i.e., as an L1 optimization problem. Direct solution of this problem entails high complexity as it employs a basis matrix whose construction requires discretization of the angle-Doppler-range space. Since high resolution requires fine space discretization, the complexity of joint range, angle and Doppler estimation can be prohibitively high. For the case of slowly moving targets, a technique is proposed that achieves significant complexity reduction by successively estimating angle-range and Doppler in a decoupled fashion and by employing initial estimates obtained via matched filtering to further reduce the space that nee...
Aharchaou, M.; Levander, A.
2016-11-01
We propose a new approach to the linear Radon transform (LRT) based on compressive sensing (CS) theory. This method can be used to extract signals of interest embedded in teleseismic measurements recorded by regional seismic arrays. We pose the problem of enhancing the resolution of the LRT as an inverse problem formulated in the frequency domain and solved according to a CS framework. We show how irregularity in the measurements along with sparsity constraints can be used to reach very compact and meaningful representations in the Radon domain, offering a benefit for both signal isolation and spatial interpolation during data reconstruction. We demonstrate the effectiveness of our approach and its benefits on both synthetic and USArray seismograms. This CS-based version of the LRT presents a valuable tool relevant for both global and exploration seismic processing, and which can be used as a basis for signal enhancement techniques exploiting irregularly sampled data.
Jiang, Hai; Zhang, Bingchen; Lin, Yueguan; Hong, Wen; Wu, Yirong
2011-11-01
Recent theory of compressed sensing (CS) has been widely used in many application areas. In this paper, we mainly concentrate on the CS in radar and analyze the distinguishing ability of CS radar image based on information theory model. The information content contained in the CS radar echoes is analyzed by simplifying the information transmission channel as a parallel Gaussian channel, and the relationship among the signal-to-noise ratio (SNR) of the echo signal, the number of required samples, the length of the sparse targets and the distinguishing level of the radar image is gotten. Based on this result, we introduced the distinguishing ability of the CS radar image and some of its properties are also gotten. Real IECAS advanced scanning two-dimensional railway observation (ASTRO) data experiment demonstrates our conclusions.
Compressive sensing based spinning mode detections by in-duct microphone arrays
Yu, Wenjun; Huang, Xun
2016-05-01
This paper presents a compressive sensing based experimental method for detecting spinning modes of sound waves propagating inside a cylindrical duct system. This method requires fewer dynamic pressure sensors than the number required by the Shannon-Nyquist sampling theorem so long as the incident waves are sparse in spinning modes. In this work, the proposed new method is firstly validated by preparing some of the numerical simulations with representative set-ups. Then, a duct acoustic testing rig with a spinning mode synthesiser and an in-duct microphone array is built to experimentally demonstrate the new approach. Both the numerical simulations and the experiment results are satisfactory, even when the practical issue of the background noise pollution is taken into account. The approach is beneficial for sensory array tests of silent aeroengines in particular and some other engineering systems with duct acoustics in general.
An infrared image super-resolution reconstruction method based on compressive sensing
Mao, Yuxing; Wang, Yan; Zhou, Jintao; Jia, Haiwei
2016-05-01
Limited by the properties of infrared detector and camera lens, infrared images are often detail missing and indistinct in vision. The spatial resolution needs to be improved to satisfy the requirements of practical application. Based on compressive sensing (CS) theory, this thesis presents a single image super-resolution reconstruction (SRR) method. With synthetically adopting image degradation model, difference operation-based sparse transformation method and orthogonal matching pursuit (OMP) algorithm, the image SRR problem is transformed into a sparse signal reconstruction issue in CS theory. In our work, the sparse transformation matrix is obtained through difference operation to image, and, the measurement matrix is achieved analytically from the imaging principle of infrared camera. Therefore, the time consumption can be decreased compared with the redundant dictionary obtained by sample training such as K-SVD. The experimental results show that our method can achieve favorable performance and good stability with low algorithm complexity.
Quantitative Inspection of Remanence of Broken Wire Rope Based on Compressed Sensing
Juwei Zhang
2016-08-01
Full Text Available Most traditional strong magnetic inspection equipment has disadvantages such as big excitation devices, high weight, low detection precision, and inconvenient operation. This paper presents the design of a giant magneto-resistance (GMR sensor array collection system. The remanence signal is collected to acquire two-dimensional magnetic flux leakage (MFL data on the surface of wire ropes. Through the use of compressed sensing wavelet filtering (CSWF, the image expression of wire ropes MFL on the surface was obtained. Then this was taken as the input of the designed back propagation (BP neural network to extract three kinds of MFL image geometry features and seven invariant moments of defect images. Good results were obtained. The experimental results show that nondestructive inspection through the use of remanence has higher accuracy and reliability compared with traditional inspection devices, along with smaller volume, lighter weight and higher precision.
Novel Covert Data Channel in Wireless Sensor Networks Using Compressive Sensing
Jiping Xiong
2012-10-01
Full Text Available Wireless sensor networks (WSN is a novel data centered self-organizing network that can be used in acquiring and processing information. With the limited energy of sensor nodes and the increasing requirement of secure data transmission, how to save nodes energy as well as realize a transmission of sensitive information in WSN effectively is becoming an interesting research problem recently. In this paper, we present a novel scheme to transmit sensitive information in the pattern of energy efficient way by utilizing compressive sensing (CS which is an emerging technology in recent years. In this method, sensor nodes need not to do complex computing but simple linear operations which can save the energy extensively, and thus extend the life time of the wireless sensor networks. Theory analysis and detail simulation results demonstrate the effective of our method, and the sensitive information can be accurately reconstructed even when the communication channel is lossy.
Multidimensional dictionary learning algorithm for compressive sensing-based hyperspectral imaging
Zhao, Rongqiang; Wang, Qiang; Shen, Yi; Li, Jia
2016-11-01
The sparsifying representation plays a significant role in compressive sensing (CS)-based hyperspectral (HS) imaging. Training the dictionaries for each dimension from HS samples is very beneficial to accurate reconstruction. However, the tensor dictionary learning algorithms are limited by a great amount of computation and convergence difficulties. We propose a least squares (LS) type multidimensional dictionary learning algorithm for CS-based HS imaging. We develop a practical method for the dictionary updating stage, which avoids the use of the Kronecker product and thus has lower computation complexity. To guarantee the convergence, we add a pruning stage to the algorithm to ensure the similarity and relativity among data in the spectral dimension. Our experimental results demonstrated that the dictionaries trained using the proposed algorithm performed better at CS-based HS image reconstruction than those trained with traditional LS-type dictionary learning algorithms and the commonly used analytical dictionaries.
Fast Compressed Sensing MRI Based on Complex Double-Density Dual-Tree Discrete Wavelet Transform
Shanshan Chen
2017-01-01
Full Text Available Compressed sensing (CS has been applied to accelerate magnetic resonance imaging (MRI for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT with fast iterative shrinkage/soft thresholding algorithm (FISTA to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR, larger signal-to-noise ratio (SNR, better structural similarity index (SSIM, and lower relative error.
An adaptive fusion approach for infrared and visible images based on NSCT and compressed sensing
Zhang, Qiong; Maldague, Xavier
2016-01-01
A novel nonsubsampled contourlet transform (NSCT) based image fusion approach, implementing an adaptive-Gaussian (AG) fuzzy membership method, compressed sensing (CS) technique, total variation (TV) based gradient descent reconstruction algorithm, is proposed for the fusion computation of infrared and visible images. Compared with wavelet, contourlet, or any other multi-resolution analysis method, NSCT has many evident advantages, such as multi-scale, multi-direction, and translation invariance. As is known, a fuzzy set is characterized by its membership function (MF), while the commonly known Gaussian fuzzy membership degree can be introduced to establish an adaptive control of the fusion processing. The compressed sensing technique can sparsely sample the image information in a certain sampling rate, and the sparse signal can be recovered by solving a convex problem employing gradient descent based iterative algorithm(s). In the proposed fusion process, the pre-enhanced infrared image and the visible image are decomposed into low-frequency subbands and high-frequency subbands, respectively, via the NSCT method as a first step. The low-frequency coefficients are fused using the adaptive regional average energy rule; the highest-frequency coefficients are fused using the maximum absolute selection rule; the other high-frequency coefficients are sparsely sampled, fused using the adaptive-Gaussian regional standard deviation rule, and then recovered by employing the total variation based gradient descent recovery algorithm. Experimental results and human visual perception illustrate the effectiveness and advantages of the proposed fusion approach. The efficiency and robustness are also analyzed and discussed through different evaluation methods, such as the standard deviation, Shannon entropy, root-mean-square error, mutual information and edge-based similarity index.
Tongfeng Zhang
2016-01-01
Full Text Available A one-dimensional (1D hybrid chaotic system is constructed by three different 1D chaotic maps in parallel-then-cascade fashion. The proposed chaotic map has larger key space and exhibits better uniform distribution property in some parametric range compared with existing 1D chaotic map. Meanwhile, with the combination of compressive sensing (CS and Fibonacci-Lucas transform (FLT, a novel image compression and encryption scheme is proposed with the advantages of the 1D hybrid chaotic map. The whole encryption procedure includes compression by compressed sensing (CS, scrambling with FLT, and diffusion after linear scaling. Bernoulli measurement matrix in CS is generated by the proposed 1D hybrid chaotic map due to its excellent uniform distribution. To enhance the security and complexity, transform kernel of FLT varies in each permutation round according to the generated chaotic sequences. Further, the key streams used in the diffusion process depend on the chaotic map as well as plain image, which could resist chosen plaintext attack (CPA. Experimental results and security analyses demonstrate the validity of our scheme in terms of high security and robustness against noise attack and cropping attack.
Hesham Mahrous
2016-02-01
Full Text Available This paper proposes a compressive sensing (CS method for multi-channel electroencephalogram (EEG signals in Wireless Body Area Network (WBAN applications, where the battery life of sensors is limited. For the single EEG channel case, known as the single measurement vector (SMV problem, the Block Sparse Bayesian Learning-BO (BSBL-BO method has been shown to yield good results. This method exploits the block sparsity and the intra-correlation (i.e., the linear dependency within the measurement vector of a single channel. For the multichannel case, known as the multi-measurement vector (MMV problem, the Spatio-Temporal Sparse Bayesian Learning (STSBL-EM method has been proposed. This method learns the joint correlation structure in the multichannel signals by whitening the model in the temporal and the spatial domains. Our proposed method represents the multi-channels signal data as a vector that is constructed in a specific way, so that it has a better block sparsity structure than the conventional representation obtained by stacking the measurement vectors of the different channels. To reconstruct the multichannel EEG signals, we modify the parameters of the BSBL-BO algorithm, so that it can exploit not only the linear but also the non-linear dependency structures in a vector. The modified BSBL-BO is then applied on the vector with the better sparsity structure. The proposed method is shown to significantly outperform existing SMV and also MMV methods. It also shows significant lower compression errors even at high compression ratios such as 10:1 on three different datasets.
MAP Support Detection for Greedy Sparse Signal Recovery Algorithms in Compressive Sensing
Lee, Namyoon
2016-10-01
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred to as "\\textit{maximum a posteriori (MAP) support detection}". Unlike existing support detection methods that identify support indices with the largest correlation value in magnitude per iteration, the proposed method selects them with the largest likelihood ratios computed under the true and null support hypotheses by simultaneously exploiting the distributions of sensing matrix, sparse signal, and noise. Leveraging this technique, MAP-Matching Pursuit (MAP-MP) is first presented to show the advantages of exploiting the proposed support detection method, and a sufficient condition for perfect signal recovery is derived for the case when the sparse signal is binary. Subsequently, a set of iterative greedy algorithms, called MAP-generalized Orthogonal Matching Pursuit (MAP-gOMP), MAP-Compressive Sampling Matching Pursuit (MAP-CoSaMP), and MAP-Subspace Pursuit (MAP-SP) are presented to demonstrate the applicability of the proposed support detection method to existing greedy algorithms. From empirical results, it is shown that the proposed greedy algorithms with highly reliable support detection can be better, faster, and easier to implement than basis pursuit via linear programming.
On the Feedback Reduction of Relay Multiuser Networks using Compressive Sensing
Elkhalil, Khalil
2016-01-29
This paper presents a comprehensive performance analysis of full-duplex multiuser relay networks employing opportunistic scheduling with noisy and compressive feedback. Specifically, two feedback techniques based on compressive sensing (CS) theory are introduced and their effect on the system performance is analyzed. The problem of joint user identity and signal-tonoise ratio (SNR) estimation at the base-station is casted as a block sparse signal recovery problem in CS. Using existing CS block recovery algorithms, the identity of the strong users is obtained and their corresponding SNRs are estimated using the best linear unbiased estimator (BLUE). To minimize the effect of feedback noise on the estimated SNRs, a back-off strategy that optimally backs-off on the noisy estimated SNRs is introduced, and the error covariance matrix of the noise after CS recovery is derived. Finally, closed-form expressions for the end-to-end SNRs of the system are derived. Numerical results show that the proposed techniques drastically reduce the feedback air-time and achieve a rate close to that obtained by scheduling techniques that require dedicated error-free feedback from all network users. Key findings of this paper suggest that the choice of half-duplex or full-duplex SNR feedback is dependent on the channel coherence interval, and on low coherence intervals, full-duplex feedback is superior to the interference-free half-duplex feedback.
Robust Watermarking Using Compressed Sensing Framework with Application to MP3 Audio
Mohamed Waleed Fakhr
2012-12-01
Full Text Available In this paper a watermark embedding and recovery technique is proposed based on the compressed sensing framework. Both the watermark and the host signal are sparse, each in its own domain. In recovery, the L1-minimization is used to recover the watermark and the host signal almost perfectly in clean conditions. The proposed technique is tested on MP3 audio compression-decompression attack and additive noise attack. Bit error rates are compared with standard spread spectrum embedding. The proposed technique is implemented for both time domain and frequency domain embedding with a unified approach. The WalshHadamard transform (WHT, the discrete cosine transform (DCT and the Karhunen-Loeve transform (KLT are compared in the host signal sparsifying process. Significant performance improvements in all tested conditions are achieved against the spread spectrum embedding. A payload as high as 172bps in additive noise attacks, 86bps in 128kbps MP3 attacks and 11bps in 64kbps MP3 attacks are achieved at small bit error rates and acceptable MP3 audio signal quality.
Depth map resolution enhancement for 2D/3D imaging system via compressive sensing
Han, Juanjuan; Loffeld, Otmar; Hartmann, Klaus
2011-08-01
This paper introduces a novel approach for post-processing of depth map which enhances the depth map resolution in order to achieve visually pleasing 3D models from a new monocular 2D/3D imaging system consists of a Photonic mixer device (PMD) range camera and a standard color camera. The proposed method adopts the revolutionary inversion theory framework called Compressive Sensing (CS). The depth map of low resolution is considered as the result of applying blurring and down-sampling techniques to that of high-resolution. Based on the underlying assumption that the high-resolution depth map is compressible in frequency domain and recent theoretical work on CS, the high-resolution version can be estimated and furthermore reconstructed via solving non-linear optimization problem. And therefore the improved depth map reconstruction provides a useful help to build an improved 3D model of a scene. The experimental results on the real data are presented. In the meanwhile the proposed scheme opens new possibilities to apply CS to a multitude of potential applications on various multimodal data analysis and processing.
Lei You
2013-05-01
Full Text Available The lifetime of the emerging Wireless visual sensor network (WVSN is seriously dependent on the energy shored in the battery of its sensor nodes as well as the compression and resource allocation scheme. In this paper, the energy harvesting technology was adopted to provide almost perpetual operation of the WVSN and compressed-sensing-based encoding was used to decrease the power consumption of acquiring visual information at the front-end sensors. A Dynamic Source and Transmission Control Algorithm (DSTCA was proposed to jointly determine source rate, source energy consumption, and the allocation of transmission energy and available bandwidth under energy harvesting and queue stability constraints. A virtual energy queue was introduced to control the resource allocation and the measurement rate in each time slot. The algorithm can guarantee the stability of the visual data queues in all sensors and achieve near-optimal performance. The distributed implementation of the proposed algorithm was discussed and the achievable performance theorem was also given.
Valenzise G
2009-01-01
Full Text Available In the past few years, a large amount of techniques have been proposed to identify whether a multimedia content has been illegally tampered or not. Nevertheless, very few efforts have been devoted to identifying which kind of attack has been carried out, especially due to the large data required for this task. We propose a novel hashing scheme which exploits the paradigms of compressive sensing and distributed source coding to generate a compact hash signature, and we apply it to the case of audio content protection. The audio content provider produces a small hash signature by computing a limited number of random projections of a perceptual, time-frequency representation of the original audio stream; the audio hash is given by the syndrome bits of an LDPC code applied to the projections. At the content user side, the hash is decoded using distributed source coding tools. If the tampering is sparsifiable or compressible in some orthonormal basis or redundant dictionary, it is possible to identify the time-frequency position of the attack, with a hash size as small as 200 bits/second; the bit saving obtained by introducing distributed source coding ranges between 20% to 70%.
Statistical Prior Aided Separate Compressed Image Sensing for Green Internet of Multimedia Things
Shaohua Wu
2017-01-01
Full Text Available In this paper, we aim to propose an image compression and reconstruction strategy under the compressed sensing (CS framework to enable the green computation and communication for the Internet of Multimedia Things (IoMT. The core idea is to explore the statistics of image representations in the wavelet domain to aid the reconstruction method design. Specifically, the energy distribution of natural images in the wavelet domain is well characterized by an exponential decay model and then used in the two-step separate image reconstruction method, by which the row-wise (or column-wise intermediates and column-wise (or row-wise final results are reconstructed sequentially. Both the intermediates and the final results are constrained to conform with the statistical prior by using a weight matrix. Two recovery strategies with different levels of complexity, namely, the direct recovery with fixed weight matrix (DR-FM and the iterative recovery with refined weight matrix (IR-RM, are designed to obtain different quality of recovery. Extensive simulations show that both DR-FM and IR-RM can achieve much better image reconstruction quality with much faster recovery speed than traditional methods.
Estimation of multipath parameters in wireless communications using multi-way compressive sensing
Fangqing Wen; Gong Zhang; De Ben
2015-01-01
This paper addresses the problem of joint angle and delay estimation (JADE) in a multipath communication scenario. A low-complexity multi-way compressive sensing (MCS) estimation algorithm is proposed. The received data are firstly stacked up to a trilinear tensor model. To reduce the computational complexity, three random compression matrices are individual y used to re-duce each tensor to a much smal er one. JADE then is linked to a low-dimensional trilinear model. Our algorithm has an estima-tion performance very close to that of the paral el factor analysis (PARAFAC) algorithm and automatic pairing of the two parameter sets. Compared with other methods, such as multiple signal classi-fication (MUSIC), the estimation of signal parameters via rotational invariance techniques (ESPRIT), the MCS algorithm requires nei-ther eigenvalue decomposition of the received signal covariance matrix nor spectral peak searching. It also does not require the channel fading information, which means the proposed algorithm is blind and robust, therefore it has a higher working efficiency. Simulation results indicate the proposed algorithm have a bright future in wireless communications.
G. Valenzise
2009-02-01
Full Text Available In the past few years, a large amount of techniques have been proposed to identify whether a multimedia content has been illegally tampered or not. Nevertheless, very few efforts have been devoted to identifying which kind of attack has been carried out, especially due to the large data required for this task. We propose a novel hashing scheme which exploits the paradigms of compressive sensing and distributed source coding to generate a compact hash signature, and we apply it to the case of audio content protection. The audio content provider produces a small hash signature by computing a limited number of random projections of a perceptual, time-frequency representation of the original audio stream; the audio hash is given by the syndrome bits of an LDPC code applied to the projections. At the content user side, the hash is decoded using distributed source coding tools. If the tampering is sparsifiable or compressible in some orthonormal basis or redundant dictionary, it is possible to identify the time-frequency position of the attack, with a hash size as small as 200 bits/second; the bit saving obtained by introducing distributed source coding ranges between 20% to 70%.
Performance assessment of a single-pixel compressive sensing imaging system
Du Bosq, Todd W.; Preece, Bradley L.
2016-05-01
Conventional electro-optical and infrared (EO/IR) systems capture an image by measuring the light incident at each of the millions of pixels in a focal plane array. Compressive sensing (CS) involves capturing a smaller number of unconventional measurements from the scene, and then using a companion process known as sparse reconstruction to recover the image as if a fully populated array that satisfies the Nyquist criteria was used. Therefore, CS operates under the assumption that signal acquisition and data compression can be accomplished simultaneously. CS has the potential to acquire an image with equivalent information content to a large format array while using smaller, cheaper, and lower bandwidth components. However, the benefits of CS do not come without compromise. The CS architecture chosen must effectively balance between physical considerations (SWaP-C), reconstruction accuracy, and reconstruction speed to meet operational requirements. To properly assess the value of such systems, it is necessary to fully characterize the image quality, including artifacts and sensitivity to noise. Imagery of the two-handheld object target set at range was collected using a passive SWIR single-pixel CS camera for various ranges, mirror resolution, and number of processed measurements. Human perception experiments were performed to determine the identification performance within the trade space. The performance of the nonlinear CS camera was modeled with the Night Vision Integrated Performance Model (NV-IPM) by mapping the nonlinear degradations to an equivalent linear shift invariant model. Finally, the limitations of CS modeling techniques will be discussed.
Wang, Yishan; Doleschel, Sammy; Wunderlich, Ralf; Heinen, Stefan
2016-07-01
In this paper, a wearable and wireless ECG system is firstly designed with Bluetooth Low Energy (BLE). It can detect 3-lead ECG signals and is completely wireless. Secondly the digital Compressed Sensing (CS) is implemented to increase the energy efficiency of wireless ECG sensor. Different sparsifying basis, various compression ratio (CR) and several reconstruction algorithms are simulated and discussed. Finally the reconstruction is done by the android application (App) on smartphone to display the signal in real time. The power efficiency is measured and compared with the system without CS. The optimum satisfying basis built by 3-level decomposed db4 wavelet coefficients, 1-bit Bernoulli random matrix and the most suitable reconstruction algorithm are selected by the simulations and applied on the sensor node and App. The signal is successfully reconstructed and displayed on the App of smartphone. Battery life of sensor node is extended from 55 h to 67 h. The presented wireless ECG system with CS can significantly extend the battery life by 22 %. With the compact characteristic and long term working time, the system provides a feasible solution for the long term homecare utilization.
郭喜峰; 王大志; 刘炜
2012-01-01
More and more information are needed in social life and commercial production, causing significant pressure on the sampling and too much time spent on signal sampling. Compressed sensing is one emerging hotspot in signal processing which employs a special sampling method to capture and represent compressible signals at a rate significantly below the Nyquist rate. In this paper, a Takagi-Sugeno-Kang (TSK) Model based on compressed-sensing sampling theorem is proposed for grinding power. It is further tested by using the actual production data, and the algorithm performance in grinding power model is also analyzed. The experiments show the validity and effectiveness of the proposed modeling method and its bright application foreground in other fields with similar features, such as power, metallurgy and so on.
Leung, Chung Ming; Or, Siu Wing; Ho, S L
2013-12-01
A force sensing device capable of sensing dc (or static) compressive forces is developed based on a NAS106N stainless steel compressive spring, a sintered NdFeB permanent magnet, and a coil-wound Tb(0.3)Dy(0.7)Fe(1.92)/Pb(Zr, Ti)O3 magnetostrictive∕piezoelectric laminate. The dc compressive force sensing in the device is evaluated theoretically and experimentally and is found to originate from a unique force-induced, position-dependent, current-driven dc magnetoelectric effect. The sensitivity of the device can be increased by increasing the spring constant of the compressive spring, the size of the permanent magnet, and/or the driving current for the coil-wound laminate. Devices of low-force (20 N) and high-force (200 N) types, showing high output voltages of 262 and 128 mV peak, respectively, are demonstrated at a low driving current of 100 mA peak by using different combinations of compressive spring and permanent magnet.
Ji Yunyun; Yang Zhen; Xu Qian
2012-01-01
Structural and statistical characteristics of signals can improve the performance of Compressed Sensing (CS).Two kinds of features of Discrete Cosine Transform (DCT) coefficients of voiced speech signals are discussed in this paper.The first one is the block sparsity of DCT coefficients of voiced speech formulated from two different aspects which are the distribution of the DCT coefficients of voiced speech and the comparison of reconstruction performance between the mixed l2 /l1 program and Basis Pursuit (BP).The block sparsity of DCT coefficients of voiced speech means that some algorithms of block-sparse CS can be used to improve the recovery performance of speech signals.It is proved by the simulation results of the l2 / reweighted l1 mixed program which is an improved version of the mixed l2 /l1 program.The second one is the well known large DCT coefficients of voiced speech focus on low frequency.In line with this feature,a special Gaussian and Partial Identity Joint (GPIJ)matrix is constructed as the sensing matrix for voiced speech signals.Simulation results show that the GPIJ matrix outperforms the classical Gaussian matrix for speech signals of male and female adults.
Mode separation in frequency-wavenumber domain through compressed sensing of far-field Lamb waves
Gao, Fei; Zeng, Liang; Lin, Jing; Luo, Zhi
2017-07-01
This method based on Lamb waves shows great potential for long-range damage detection. Mode superposition resulting from multi-modal and dispersive characteristics makes signal interpretation and damage feature extraction difficult. Mode separation in the frequency-wavenumber (f-k) domain using a 1D sparse sensing array is a promising solution. However, due to the lack of prior knowledge about damage location, this method based on 1D linear measurement, for the mode extraction of arbitrary reflections caused by defects that are not in line with the sensor array, is restricted. In this paper, an improved compressed sensing method under the far-field assumption is established, which is beneficial to the reconstruction of reflections in the f-k domain. Hence, multiple components consisting of structure and damage features could be recovered via a limited number of measurements. Subsequently, a mode sweeping process based on theoretical dispersion curves has been designed for mode characterization and direction of arrival estimation. Moreover, 2D f-k filtering and inverse transforms are applied to the reconstructed f-k distribution in order to extract the purified mode of interest. As a result, overlapping waveforms can be separated and the direction of defects can be estimated. A uniform linear sensor array consisting of 16 laser excitations is finally employed for experimental investigations and the results demonstrate the efficiency of the proposed method.
Huang, Wei; Xiao, Liang; Liu, Hongyi; Wei, Zhihui
2015-01-19
Due to the instrumental and imaging optics limitations, it is difficult to acquire high spatial resolution hyperspectral imagery (HSI). Super-resolution (SR) imagery aims at inferring high quality images of a given scene from degraded versions of the same scene. This paper proposes a novel hyperspectral imagery super-resolution (HSI-SR) method via dictionary learning and spatial-spectral regularization. The main contributions of this paper are twofold. First, inspired by the compressive sensing (CS) framework, for learning the high resolution dictionary, we encourage stronger sparsity on image patches and promote smaller coherence between the learned dictionary and sensing matrix. Thus, a sparsity and incoherence restricted dictionary learning method is proposed to achieve higher efficiency sparse representation. Second, a variational regularization model combing a spatial sparsity regularization term and a new local spectral similarity preserving term is proposed to integrate the spectral and spatial-contextual information of the HSI. Experimental results show that the proposed method can effectively recover spatial information and better preserve spectral information. The high spatial resolution HSI reconstructed by the proposed method outperforms reconstructed results by other well-known methods in terms of both objective measurements and visual evaluation.