Leach, R.R.; Schultz, C.; Dowla, F.
1997-07-15
Development of a worldwide network to monitor seismic activity requires deployment of seismic sensors in areas which have not been well studied or may have from available recordings. Development and testing of detection and discrimination algorithms requires a robust representative set of calibrated seismic events for a given region. Utilizing events with poor signal-to-noise (SNR) can add significant numbers to usable data sets, but these events must first be adequately filtered. Source and path effects can make this a difficult task as filtering demands are highly varied as a function of distance, event magnitude, bearing, depth etc. For a given region, conventional methods of filter selection can be quite subjective and may require intensive analysis of many events. In addition, filter parameters are often overly generalized or contain complicated switching. We have developed a method to provide an optimized filter for any regional or teleseismically recorded event. Recorded seismic signals contain arrival energy which is localized in frequency and time. Localized temporal signals whose frequency content is different from the frequency content of the pre-arrival record are identified using rms power measurements. The method is based on the decomposition of a time series into a set of time series signals or scales. Each scale represents a time-frequency band with a constant Q. SNR is calculated for a pre-event noise window and for a window estimated to contain the arrival. Scales with high SNR are used to indicate the band pass limits for the optimized filter.The results offer a significant improvement in SNR particularly for low SNR events. Our method provides a straightforward, optimized filter which can be immediately applied to unknown regions as knowledge of the geophysical characteristics is not required. The filtered signals can be used to map the seismic frequency response of a region and may provide improvements in travel-time picking, bearing estimation
WAVELET RATIONAL FILTERS AND REGULARITY ANALYSIS
Zheng Kuang; Ming-gen Cui
2000-01-01
In this paper, we choose the trigonometric rational functions as wavelet filters and use them to derive various wavelets. Especially for a certain family of wavelets generated by the rational filters, the better smoothness results than Daubechies' are obtained.
Linear Phase Perfect Reconstruction Filters and Wavelets with Even Symmetry
Monzon, Lucas
2011-01-01
Perfect reconstruction filter banks can be used to generate a variety of wavelet bases. Using IIR linear phase filters one can obtain symmetry properties for the wavelet and scaling functions. In this paper we describe all possible IIR linear phase filters generating symmetric wavelets with any prescribed number of vanishing moments. In analogy with the well known FIR case, we construct and study a new family of wavelets obtained by considering maximal number of vanishing moments for each fixed order of the IIR filter. Explicit expressions for the coefficients of numerator, denominator, zeroes, and poles are presented. This new parameterization allows one to design linear phase quadrature mirror filters with many other properties of interest such as filters that have any preassigned set of zeroes in the stopband or that satisfy an almost interpolating property. Using Beylkin's approach, it is indicated how to implement these IIR filters not as recursive filters but as FIR filters.
Wavelet filtering of chaotic data
M. Grzesiak
2000-01-01
Full Text Available Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD and finite impulse response (FIR filter methods.
Wavelet filtering of chaotic data
Grzesiak, M.
Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.
Applications of Multidimensional Wavelet Filtering in Geosciences
Yuen, D. A.; Vincent, A. P.; Kido, M.
2001-12-01
Today we are facing a severe crisis of being flooded with huge amounts of data being generated by higher-resolution numerical simulations , laboratory instrumentions and satellite observations. Since there is no way one can visualize the full data set, we must extract essential features from the data-set. One way of addressing this problem is to use mathematical filters , such as multidimensional wavelets. We present imaging results in the geosciences based on using multidimensional Gaussian wavelets as a filter. This approach has been applied to a wide-range of problems, which span from the nanoscale in mineral surfaces imaged by atomic force microscopy to hundreds of kilometers in geoidal undulations determined from satellite orbits or small-scale plumes in high Rayleigh number convection. Besides decomposing the field under consideration into various scales , called a scalogram, we have also constructed two-dimensional maps, delineating the spatial distributions of the maximum of the wavelet transformed quantity E-max and the associated local wave-number. We have generalized the application of multidimensional wavelets to quantify in terms of a two-dimensional map the correlation C for two multidimensional fields A and B. We will show a simple 2D isotropic wavelet-like transform for a spherical surface. We have analyzed the transformed geoid data with a band-pass filter in the spherical harmonic domain and have shown the equivalency of the two representations. This spherical wavelet-like filter can be applied also to problems in planetary science, such as the surface topography and geoid of other planetary bodies, like Mars.
FPGA Implementations of Bireciprocal Lattice Wave Discrete Wavelet Filter Banks
Jassim M. Abdul-Jabbar
2012-06-01
Full Text Available In this paper, a special type of IIR filter banks; that is the bireciprocal lattice wave digital filter (BLWDF bank, is presented to simulate scaling and wavelet functions of six-level wavelet transform. 1st order all-pass sections are utilized for the realization of such filter banks in wave lattice structures. The resulting structures are a bireciprocal lattice wave discrete wavelet filter banks (BLW-DWFBs. Implementation of these BLW-DWFBs are accomplished on Spartan-3E FPGA kit. Implementation complexity and operating frequency characteristics of such discrete wavelet 5th order filter bank is proved to be comparable to the corresponding characteristics of the lifting scheme implementation of Bio. 5/3 wavelet filter bank. On the other hand, such IIR filter banks possess superior band discriminations and perfect roll-off frequency characteristics when compared to their Bio. 5/3 wavelet FIR counterparts.
Long memory analysis by using maximal overlapping discrete wavelet transform
Shafie, Nur Amalina binti; Ismail, Mohd Tahir; Isa, Zaidi
2015-05-01
Long memory process is the asymptotic decay of the autocorrelation or spectral density around zero. The main objective of this paper is to do a long memory analysis by using the Maximal Overlapping Discrete Wavelet Transform (MODWT) based on wavelet variance. In doing so, stock market of Malaysia, China, Singapore, Japan and United States of America are used. The risk of long term and short term investment are also being looked into. MODWT can be analyzed with time domain and frequency domain simultaneously and decomposing wavelet variance to different scales without loss any information. All countries under studied show that they have long memory. Subprime mortgage crisis in 2007 is occurred in the United States of America are possible affect to the major trading countries. Short term investment is more risky than long term investment.
Multidimensional filter banks and wavelets research developments and applications
Levy, Bernard
1997-01-01
Multidimensional Filter Banks and Wavelets: Reserach Developments and Applications brings together in one place important contributions and up-to-date research results in this important area. Multidimensional Filter Banks and Wavelets: Research Developments and Applications serves as an excellent reference, providing insight into some of the most important research issues in the field.
Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction.
Zitong Zhang
Full Text Available Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite their common use, however, practical guidelines for the choice of wavelet method, filter, and length have remained largely undelineated. Here, we explicitly explore the effects of wavelet method (MODWT vs. DWT, wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families, and wavelet length (2 to 24-each essential parameters in wavelet-based methods-on the estimated values of graph metrics and in their sensitivity to alterations in psychiatric disease. We observe that the MODWT method produces less variable estimates than the DWT method. We also observe that the length of the wavelet filter chosen has a greater impact on the estimated values of graph metrics than the type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of the method to detect differences between health and disease and tunes classification accuracy. Collectively, our results suggest that the choice of wavelet method and length significantly alters the reliability and sensitivity of these methods in estimating values of metrics drawn from graph theory. They furthermore demonstrate the importance of reporting the choices utilized in neuroimaging studies and support the utility of exploring wavelet parameters to maximize classification accuracy in the development of biomarkers of psychiatric disease and neurological disorders.
A wavelet phase filter for emission tomography
Olsen, E.T.; Lin, B. [Illinois Inst. of Tech., Chicago, IL (United States). Dept. of Mathematics
1995-07-01
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.
Understanding wavelet analysis and filters for engineering applications
Parameswariah, Chethan Bangalore
Wavelets are signal-processing tools that have been of interest due to their characteristics and properties. Clear understanding of wavelets and their properties are a key to successful applications. Many theoretical and application-oriented papers have been written. Yet the choice of a right wavelet for a given application is an ongoing quest that has not been satisfactorily answered. This research has successfully identified certain issues, and an effort has been made to provide an understanding of wavelets by studying the wavelet filters in terms of their pole-zero and magnitude-phase characteristics. The magnitude characteristics of these filters have flat responses in both the pass band and stop band. The phase characteristics are almost linear. It is interesting to observe that some wavelets have the exact same magnitude characteristics but their phase responses vary in the linear slopes. An application of wavelets for fast detection of the fault current in a transformer and distinguishing from the inrush current clearly shows the advantages of the lower slope and fewer coefficients---Daubechies wavelet D4 over D20. This research has been published in the IEEE transactions on Power systems and is also proposed as an innovative method for protective relaying techniques. For detecting the frequency composition of the signal being analyzed, an understanding of the energy distribution in the output wavelet decompositions is presented for different wavelet families. The wavelets with fewer coefficients in their filters have more energy leakage into adjacent bands. The frequency bandwidth characteristics display flatness in the middle of the pass band confirming that the frequency of interest should be in the middle of the frequency band when performing a wavelet transform. Symlets exhibit good flatness with minimum ripple but the transition regions do not have sharper cut off. The number of wavelet levels and their frequency ranges are dependent on the two
V. Elamaran
2012-12-01
Full Text Available In this study, we present Embedded Zerotree Wavelet (EZW algorithm to compress the image using different wavelet filters such as Biorthogonal, Coiflets, Daubechies, Symlets and Reverse Biorthogonal and to remove noise by setting appropriate threshold value while decoding. Compression methods are important in telemedicine applications by reducing number of bits per pixel to adequately represent the image. Data storage requirements are reduced and transmission efficiency is improved because of compressing the image. The EZW algorithm is an effective and computationally efficient technique in image coding. Obtaining the best image quality for a given bit rate and accomplishing this task in an embedded fashion are the two problems addressed by the EZW algorithm. A technique to decompose the image using wavelets has gained a great deal of popularity in recent years. Apart from very good compression performance, EZW algorithm has the property that the bitstream can be truncated at any point and still be decoded with a good quality image. All the standard wavelet filters are used and the results are compared with different thresholds in the encoding section. Bit rate versus PSNR simulation results are obtained for the image 256x256 barbara with different wavelet filters. It shows that the computational overhead involved with Daubechies wavelet filters but are produced better results. Like even missing details i.e., higher frequency components are picked by them which are missed by other family of wavelet filters.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-05-01
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
3D Wavelet-Based Filter and Method
Moss, William C.; Haase, Sebastian; Sedat, John W.
2008-08-12
A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.
On robust kalman filtering with using wavelet analysis
Lobach, V. I.
2013-01-01
One presents a nonlinear filtering algorithm that propagates the entire condi- tional probability density functions. These functions are recursively computed in efficient manner using the discrete wavelet transform. With the multiresolution analysis we can speed up the computation by ignoring the high-frequency details of the probability density function up to a certain level. The level of the wavelet decomposition can be determined at each time step adaptively.
Option pricing from wavelet-filtered financial series
de Almeida, V. T. X.; Moriconi, L.
2012-10-01
We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most (≃99.6%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day.
Filtering, Coding, and Compression with Malvar Wavelets
1993-12-01
2-10 2.4. The Malvar Wavelet Represented in Polyphase Form ...................... 2-11 3.1. (a) Real Part and (b) Imaginary Part of the Complex... Sleeping Pill", Using (a) 1 Point Overlap and (b) 50% (128 Point) Overlap ...... ............... 5-8 5.8. Reconstruction of the Same Sentence (From Sample...For example, if M=2 then 2-10 LICOMP_ U-Cc LCC-N SX,8) Y() Figure 2.4. The Malvar Wavelet Represented in Polyphase Form the signal would be broken
李建平; 唐远炎; 严中洪; 张万萍
2001-01-01
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When/N = 2k- 1 and N = 2k , the unified analytic constructions of orthogonal wavelet filters are put forward,respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
Detecting surface geostrophic currents using wavelet filter from satellite geodesy
HSU; HouTse
2007-01-01
According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.
Detecting surface geostrophic currents using wavelet filter from satellite geodesy
ZHANG ZiZhan; LU Yang; HSU HouTse
2007-01-01
According to the features of spatial spectrum of the dynamic ocean topography (DOT), wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96), combining an altimetry-derived mean sea surface height model (KMSS04), two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter, and the DOT models associated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global, Kuroshio and equatorial Pacific regions with that from oceanography, and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale, the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography, which indicates that ocean currents detected by satellite measurement have reached relatively high precision.
Improved Performance by Parametrizing Wavelet Filters for Digital Image Watermarking
Mangaiyarkarasi Palanivel
2012-03-01
Full Text Available In recent years, watermarking has become an attractive field in areas like copyright protection, imageauthentication and biomedical engineering. Many literatures have reported about discrete wavelet transform (DWT watermarking techniques for data security. However, DWT based watermarking schemes are found to be less robust against image processing attacks. In this paper, an attempt is made to develop a scheme based on Redundant Discrete Wavelet Transform (RDWT. The robustness and security of the proposed RDWT scheme is improved by parametrizing the scaling and wavelet filters by Pollen’s parametrizing technique. An Independent Component Analysis (ICA based detector is also applied, whichextracts watermark directly in spatial domain rather than in transform domain. The unique feature of ICA is that it does not require any transformation during extraction. The results reveal that the proposedscheme produces high peak signal to noise ratio (PSNR values and similarity measure under various image processing attacks.
Optical image segmentation using wavelet filtering techniques
Veronin, Christopher P.
1990-12-01
This research effort successfully implemented an automatic, optically based image segmentation scheme for locating potential targets in a cluttered FLIR image. Such a design is critical to achieve real-time segmentation and classification for machine vision applications. The segmentation scheme used in this research was based on texture discrimination and employs orientation specific, bandpass spatial filters as its main component. The orientation specific, bandpass spatial filters designed during this research include symmetrically located circular apertures implemented on heavy, black aluminum foil; cosine and sine Gabor filters implemented with detour-phase computer generated holography photoreduced onto glass slides; and symmetrically located circular apertures implemented on a liquid crystal television (LCTV) for real-time filter selection. The most successful design was the circular aperture pairs implemented on the aluminum foil. Segmentation was illustrated for simple and complex texture slides, glass template slides, and static and real-time FLIR imagery displayed on an LCTV.
A Speckle Reduction Filter Using Wavelet-Based Methods for Medical Imaging Application
2001-10-25
A Speckle Reduction Filter using Wavelet-Based Methods for Medical Imaging Application Su...Wavelet-Based Methods for Medical Imaging Application Contract Number Grant Number Program Element Number Author(s) Project Number Task Number Work
Diffusion filtering in image processing based on wavelet transform
LIU Feng
2006-01-01
The nonlinear diffusion filtering in image processing bases on the heat diffusion equations. Its key is the control of diffusion amount. In the previous models, the diffusivity depends on the gradients of images. So it is easily affected by noises. This paper first gives a new multiscale computational technique for diffusivity. Then we proposed a class of nonlinear wavelet diffusion (NWD) models that are used to restore images. The NWD model has strong ability to resist noise.But it, like the previous models, requires higher computational effort. Thus, by simplifying the NWD, we establish linear wavelet diffusion (LWD) models that consist of advection and diffusion. Since there exists the advection, the LWD filter is anisotropic, and hence can well preserve edges although the diffusion at edges is isotropic. The advantage is that the LWD model is easy to be analyzed and has lesser computational load. Finally, a variety of numerical experiments compared with the previous model are shown.
Wavelet transform based ECG signal filtering implemented on FPGA
Germán-Salló Zoltán
2011-12-01
Full Text Available Filtering electrocardiographic (ECG signals is always a challenge because the accuracy of their interpretation depends strongly on filtering results. The Discrete Wavelet Transform (DWT is an efficient, new and useful tool for signal processing applications and it’s adopted in many domains as biomedical signal filtering. This transform came about from different fields, including mathematics, physics and signal processing, it has a growing applicability due to its so-called multiresolution analyzing capabilities. FPGAs are reconfigurable logic devices made up of arrays of logic cells and routing channels having some specific characteristics which allow to use them in signal processing applications. This paper presents a DWT based ECG signal denoising method implemented on FPGA, using Matlab specific Xilinx tool, as System Generator, the procedure is simulated and evaluated through filtering specific parameters.
Do wavelet filters provide more accurate estimates of reverberation times at low frequencies
Sobreira Seoane, Manuel A.; Pérez Cabo, David; Agerkvist, Finn T.
2016-01-01
the continuous wavelet transform (CTW) has been implemented using a Morlet mother function. Although in general, the wavelet filter bank performs better than the usual filters, the influence of decaying modes outside the filter bandwidth on the measurements has been detected, leading to a biased estimation...
NOVEL FIBER GRATING SENSOR DEMODULATION TECHNIQUE BASED ON OPTICAL WAVELET FILTERING
无
2006-01-01
The optical wavelet filter is designed. It can filter and choose frequency swiftly. It can realize demodulation of distributed fiber Bragg grating(FBG) measurement system. Its scanning resolution and scanning period depend on wavelet function. Wavelet function is controlled by computer. Compared to conventional scan filter, optical wavelet filtering has some advantages such as simple structure, high scan frequency, high resolution and good linearity. At last, the error of optical wavelet filter scanning procedure is analyzed. Scanning step length refers to the shifting of optical wavelet window's central frequency. It affects system precision directly. If scanning step length is different, the measured signal is different. The methods of reducing step length guarantee scanning periodic time are presented.
Wang, Zhengzi; Ren, Zhong; Liu, Guodong
2016-10-01
In this paper, the wavelet threshold denoising method was used into the filtered back-projection algorithm of imaging reconstruction. To overcome the drawbacks of the traditional soft- and hard-threshold functions, a modified wavelet threshold function was proposed. The modified wavelet threshold function has two threshold values and two variants. To verify the feasibility of the modified wavelet threshold function, the standard test experiments were performed by using the software platform of MATLAB. Experimental results show that the filtered back-projection reconstruction algorithm based on the modified wavelet threshold function has better reconstruction effect because of more flexible advantage.
Chaotic Synchronization with Filter Based on Wavelet Transformation
XiaoanZHOU; JunfengLAN; 等
1999-01-01
A kind of chaotic synchronization method is presented in the paper,In the transmitter,part signals are transformed by wavelet and the detail information is removed.In the receiver.the component with low frequency is reconstructed and discrete feedback is used,we show that synchronization of two identical structure chaotic systems is attained.The effect of feedback on chaotic synchronization is discussed.Using the synchronous method,the transmitting signal is transported in compressible way system resource is saved,the component with high frequency is filtered and the effect of disturbance on synchronization is reduced.The synchronization method is illustrated by numerical simulation experiment.
A Comparison of IIR and Wavelet Filtering for Noise Reduction of the ECG.
Sørensen, Js; Johannesen, L; Grove, Usl; Lundhus, K; Couderc, J-P; Graff, C
2010-09-26
This study compares the ability to preserve information and reduce noise contaminants on the ECG for five wavelet filters and three IIR filters. Two 3-lead Holter ECGs were used. White Gaussian Noise was added to the first ECG in increments of 10% coverage. The second ECG contained alternating muscle transients and noise-free segments. Computation times and SNR improvements for different noise coverages were calculated and compared. RMS errors were calculated from noise-free segments on the ECG with transient muscle noise. Wavelet filters improved SNR more than IIR filters when the signal coverage was more than 50% noise. In contrast, the computation times were shorter for IIR filters (6 s) than for wavelet filters (88 s). On the ECG with transient muscle noise there was a trade-off in performance between wavelet and IIR filtering. In a clinical setting where the amount of noise is unknown, using IIR filters appears to be preferred for consistent performance.
A Multiresolution Ensemble Kalman Filter using Wavelet Decomposition
Hickmann, Kyle S
2015-01-01
We present a method of using classical wavelet based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales. Our method uses a transformation of the observation operator in order to separate the information from different scales of the observations. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale's effect on the forecast. To demonstrate feasibility we present applications to a one dimensional Kuramoto-Sivashinsky (...
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.
A blind watermarking scheme using new nontensor product wavelet filter banks.
You, Xinge; Du, Liang; Cheung, Yiu-Ming; Chen, Qiuhui
2010-12-01
As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual system (HVS). Usually, human eyes are insensitive to image singularities revealed by different high frequency subbands of wavelet decomposed images. Hence, adding watermarks into these singularities will improve the imperceptibility that is a desired property of a watermarking scheme. That is, the capability for revealing singularities of images plays a key role in designing wavelet-based watermarking algorithms. Unfortunately, the existing wavelets have a limited ability in revealing singularities in different directions. This motivates us to construct new wavelet filter banks that can reveal singularities in all directions. In this paper, we utilize special symmetric matrices to construct the new nontensor product wavelet filter banks, which can capture the singularities in all directions. Empirical studies will show their advantages of revealing singularities in comparison with the existing wavelets. Based upon these new wavelet filter banks, we, therefore, propose a modified significant difference watermarking algorithm. Experimental results show its promising results.
Video Denoising based on Stationary Wavelet Transform and Center Weighted Median Filter
Soundarya K
2014-01-01
Full Text Available Noise removal using wavelet has the characteristic of preserving signal uniqueness even if noise is going to be minimized. Images are getting corrupted by impulse noise during image acquisition and transmission. A new median filter termed as the center weighted median filter (CWMF in the wavelet coefficient domain combined with stationary wavelet transform (SWT is proposed for video denoising. This filter iteratively smoothes the noisy wavelet coefficients variances preserving the edge information contained in the large magnitude wavelet coefficients. This Paper deals with uncompressed video of .avi format. The proposed algorithm works well for suppressing Gaussian noise with noise density from 10 to 70% while preserving image details. Simulation results show that higher peak signal to noise ratio can be obtained as compared to other recent image denoising methods.
Construction of Two-Dimensional Compactly Supported Orthogonal Wavelets Filters with Linear Phase
Si Long PENG
2002-01-01
In this paper, a large class of two-dimensional orthogonal wavelet filters, (lowpass andhighpass), are presented in explicit expression. We also characterize the filters with linear phase in thiscase. Some examples are also given, including non-separable filters with linear phase.
Iris image recognition wavelet filter-banks based iris feature extraction schemes
Rahulkar, Amol D
2014-01-01
This book provides the new results in wavelet filter banks based feature extraction, and the classifier in the field of iris image recognition. It provides the broad treatment on the design of separable, non-separable wavelets filter banks, and the classifier. The design techniques presented in the book are applied on iris image analysis for person authentication. This book also brings together the three strands of research (wavelets, iris image analysis, and classifier). It compares the performance of the presented techniques with state-of-the-art available schemes. This book contains the compilation of basic material on the design of wavelets that avoids reading many different books. Therefore, it provide an easier path for the new-comers, researchers to master the contents. In addition, the designed filter banks and classifier can also be effectively used than existing filter-banks in many signal processing applications like pattern classification, data-compression, watermarking, denoising etc. that will...
Medical image denoising using dual tree complex thresholding wavelet transform and Wiener filter
Hilal Naimi
2015-01-01
Full Text Available Image denoising is the process to remove the noise from the image naturally corrupted by the noise. The wavelet method is one among various methods for recovering infinite dimensional objects like curves, densities, images, etc. The wavelet techniques are very effective to remove the noise because of their ability to capture the energy of a signal in few energy transform values. The wavelet methods are based on shrinking the wavelet coefficients in the wavelet domain. We propose in this paper, a denoising approach basing on dual tree complex wavelet and shrinkage with the Wiener filter technique (where either hard or soft thresholding operators of dual tree complex wavelet transform for the denoising of medical images are used. The results proved that the denoised images using DTCWT (Dual Tree Complex Wavelet Transform with Wiener filter have a better balance between smoothness and accuracy than the DWT and are less redundant than SWT (StationaryWavelet Transform. We used the SSIM (Structural Similarity Index Measure along with PSNR (Peak Signal to Noise Ratio and SSIM map to assess the quality of denoised images.
Image denoising algorithm of refuge chamber by combining wavelet transform and bilateral filtering
Zhang Weipeng
2013-01-01
In order to preferably identify infrared image of refuge chamber,reduce image noises of refuge chamber and retain more image details,we propose the method of combining two-dimensional discrete wavelet transform and bilateral denoising.First,the wavelet transform is adopted to decompose the image of refuge chamber,of which low frequency component remains unchanged.Then,three high-frequency components are treated by bilateral filtering,and the image is reconstructed.The result shows that the combination of bilateral filtering and wavelet transform for image denoising can better retain the details which are included in the image,while providing better visual effect.This is superior to using either bilateral filtering or wavelet transform alone.It is useful for perfecting emergency refuge system of coal.
Image restoration using regularized inverse filtering and adaptive threshold wavelet denoising
Mr. Firas Ali
2007-01-01
Full Text Available Although the Wiener filtering is the optimal tradeoff of inverse filtering and noise smoothing, in the case when the blurring filter is singular, the Wiener filtering actually amplify the noise. This suggests that a denoising step is needed to remove the amplified noise .Wavelet-based denoising scheme provides a natural technique for this purpose .In this paper a new image restoration scheme is proposed, the scheme contains two separate steps : Fourier-domain inverse filtering and wavelet-domain image denoising. The first stage is Wiener filtering of the input image , the filtered image is inputted to adaptive threshold wavelet denoising stage . The choice of the threshold estimation is carried out by analyzing the statistical parameters of the wavelet sub band coefficients like standard deviation, arithmetic mean and geometrical mean . The noisy image is first decomposed into many levels to obtain different frequency bands. Then soft thresholding method is used to remove the noisy coefficients, by fixing the optimum thresholding value by this method .Experimental results on test image by using this method show that this method yields significantly superior image quality and better Peak Signal to Noise Ratio (PSNR. Here, to prove the efficiency of this method in image restoration , we have compared this with various restoration methods like Wiener filter alone and inverse filter.
Are the Wavelet Transforms the Best Filter Banks for Image Compression?
Tor A. Ramstad
2008-03-01
Full Text Available Maximum regular wavelet filter banks have received much attention in the literature, and it is a general conception that they enjoy some type of optimality for image coding purposes. To investigate this claim, this article focuses on one particular biorthogonal wavelet filter bank, namely, the 2-channel 9/7. As a comparison, we generate all possible 9/7 filter banks with perfect reconstruction and linear phase while having a different number of zeros at z=Ã¢ÂˆÂ’1 for both analysis and synthesis lowpass filters. The best performance is obtained when the filter bank has 2/2 zeros at z=Ã¢ÂˆÂ’1 for the analysis and synthesis lowpass filters, respectively. The competing wavelet 9/7 filter bank, which has 4/4 zeros at z=Ã¢ÂˆÂ’1, is thus judged inferior both in terms of objective error measurements and informal visual inspections. It is further shown that the 9/7 wavelet filter bank can be obtained using gain-optimized 9/7 filter bank.
Are the Wavelet Transforms the Best Filter Banks for Image Compression?
Ramstad TorA
2008-01-01
Full Text Available Abstract Maximum regular wavelet filter banks have received much attention in the literature, and it is a general conception that they enjoy some type of optimality for image coding purposes. To investigate this claim, this article focuses on one particular biorthogonal wavelet filter bank, namely, the 2-channel 9/7. As a comparison, we generate all possible 9/7 filter banks with perfect reconstruction and linear phase while having a different number of zeros at for both analysis and synthesis lowpass filters. The best performance is obtained when the filter bank has 2/2 zeros at for the analysis and synthesis lowpass filters, respectively. The competing wavelet 9/7 filter bank, which has 4/4 zeros at , is thus judged inferior both in terms of objective error measurements and informal visual inspections. It is further shown that the 9/7 wavelet filter bank can be obtained using gain-optimized 9/7 filter bank.
Fourier and wavelet spectral analysis of EMG signals in maximal constant load dynamic exercise.
Costa, Marcelo V; Pereira, Lucas A; Oliveira, Ricardo S; Pedro, Rafael E; Camata, Thiago V; Abrao, Taufik; Brunetto, Maria A C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in maximal constant load dynamic exercise (100% W(max)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in maximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P〈0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Noise Reduction in Breath Sound Files Using Wavelet Transform Based Filter
Syahputra, M. F.; Situmeang, S. I. G.; Rahmat, R. F.; Budiarto, R.
2017-04-01
The development of science and technology in the field of healthcare increasingly provides convenience in diagnosing respiratory system problem. Recording the breath sounds is one example of these developments. Breath sounds are recorded using a digital stethoscope, and then stored in a file with sound format. This breath sounds will be analyzed by health practitioners to diagnose the symptoms of disease or illness. However, the breath sounds is not free from interference signals. Therefore, noise filter or signal interference reduction system is required so that breath sounds component which contains information signal can be clarified. In this study, we designed a filter called a wavelet transform based filter. The filter that is designed in this study is using Daubechies wavelet with four wavelet transform coefficients. Based on the testing of the ten types of breath sounds data, the data is obtained in the largest SNRdB bronchial for 74.3685 decibels.
Application of Wavelet-based Active Power Filter in Accelerator Magnet Power Supply
Xiaoling, Guo
2013-01-01
As modern accelerators demand excellent stability to magnet power supply (PS), it is necessary to decrease harmonic currents passing magnets. Aim at depressing rappel current from PS in Beijing electron-positron collider II, a wavelet-based active power filter (APF) is proposed in this paper. APF is an effective device to improve the quality of currents. As a countermeasure to these harmonic currents, the APF circuit generates a harmonic current, countervailing harmonic current from PS. An active power filter based on wavelet transform is proposed in this paper. Discrete wavelet transform is used to analyze the harmonic components in supply current, and active power filter circuit works according to the analysis results. At end of this paper, the simulation and experiment results are given to prove the effect of the mentioned Active power filter.
A simple structure wavelet transform circuit employing function link neural networks and SI filters
Mu, Li; Yigang, He
2016-12-01
Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. Implementing wavelet transform (WT) using analog circuits is of great interest when low-power consumption becomes an important issue. In this article, a novel simple structure WT circuit in analog domain is presented by employing functional link neural network (FLNN) and switched-current (SI) filters. First, the wavelet base is approximated using FLNN algorithms for giving a filter transfer function that is suitable for simple structure WT circuit implementation. Next, the WT circuit is constructed with the wavelet filter bank, whose impulse response is the approximated wavelet and its dilations. The filter design that follows is based on a follow-the-leader feedback (FLF) structure with multiple output bilinear SI integrators and current mirrors as the main building blocks. SI filter is well suited for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by the clock frequency of the circuit with the same system architecture. Finally, to illustrate the design procedure, a seventh-order FLNN-approximated Gaussian wavelet is implemented as an example. Simulations have successfully verified that the designed simple structure WT circuit has low sensitivity, low-power consumption and litter effect to the imperfections.
A Novel 9/7 Wavelet Filter banks For Texture Image Coding
Songjun Zhang
2012-09-01
Full Text Available This paper proposes a novel 9/7 wavelet filter bank for texture image coding applications based on lifting a 5/3 filter to a 7/5 filter, and then to a 9/7 filter. Moreover, a one-dimensional optimization problem for the above 9/7 filter family is carried out according to the perfect reconstruction (PR condition of wavelet transforms and wavelet properties. Finally, the optimal control parameter of the 9/7 filter family for image coding applications is determined by statistical analysis of compressibility tests applied on all the images in the Brodatz standard texture image database. Thus, a new 9/7 filter with only rational coefficients is determined. Compared to the design method of Cohen, Daubechies, and Feauveau, the design approach proposed in this paper is simpler and easier to implement. The experimental results show that the overall coding performances of the new 9/7 filter are superior to those of the CDF 9/7 filter banks in the JPEG2000 standard, with a maximum increase of 0.185315 dB at compression ratio 32:1. Therefore, this new 9/7 filter bank can be applied in image coding for texture images as the transform coding kernel.
Pattern discrimination of joint transform correlator based on wavelet subband filtering
Lin, Li-Chien; Cheng, Chau-Jern
2004-04-01
We propose and demonstrate a Gabor wavelet prefiltering prior to classical and binarized joint transform correlator implementation to enhance texture features of fingerprints. The frequency- and orientation-selective properties of the wavelet subband filter are utilized to extract important textural features for optimal correlation recognition. A selection criterion for wavelet subbands is derived, and it is shown that the maximum signal-to-noise ratio of the correlator is achieved by optimizing the threshold level. Simulation results show that the proposed method increases the discrimination power of the correlator, especially under noisy environments.
Sikora, Andrzej; Rodak, Aleksander; Unold, Olgierd; Klapetek, Petr
2016-12-01
In this paper a novel approach for the practical utilization of the 2D wavelet filter in terms of the artifacts removal from atomic force microscopy measurements results is presented. The utilization of additional data such as summary photodiode signal map is implemented in terms of the identification of the areas requiring the data processing, filtering settings optimization and the verification of the process performance. Such an approach allows to perform the filtering parameters adjustment by average user, while the straightforward method requires an expertise in this field. The procedure was developed as the function of the Gwyddion software. The examples of filtering the phase imaging and Electrostatic Force Microscopy measurement result are presented. As the wavelet filtering feature may remove a local artifacts, its superior efficiency over similar approach with 2D Fast Fourier Transformate based filter (2D FFT) can be noticed. Copyright © 2016 Elsevier B.V. All rights reserved.
Use of switched capacitor filters to implement the discrete wavelet transform
Kaiser, Kraig E.; Peterson, James N.
1993-01-01
This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.
Filtering of the Radon transform to enhance linear signal features via wavelet pyramid decomposition
Meckley, John R.
1995-09-01
The information content in many signal processing applications can be reduced to a set of linear features in a 2D signal transform. Examples include the narrowband lines in a spectrogram, ship wakes in a synthetic aperture radar image, and blood vessels in a medical computer-aided tomography scan. The line integrals that generate the values of the projections of the Radon transform can be characterized as a bank of matched filters for linear features. This localization of energy in the Radon transform for linear features can be exploited to enhance these features and to reduce noise by filtering the Radon transform with a filter explicitly designed to pass only linear features, and then reconstructing a new 2D signal by inverting the new filtered Radon transform (i.e., via filtered backprojection). Previously used methods for filtering the Radon transform include Fourier based filtering (a 2D elliptical Gaussian linear filter) and a nonlinear filter ((Radon xfrm)**y with y >= 2.0). Both of these techniques suffer from the mismatch of the filter response to the true functional form of the Radon transform of a line. The Radon transform of a line is not a point but is a function of the Radon variables (rho, theta) and the total line energy. This mismatch leads to artifacts in the reconstructed image and a reduction in achievable processing gain. The Radon transform for a line is computed as a function of angle and offset (rho, theta) and the line length. The 2D wavelet coefficients are then compared for the Haar wavelets and the Daubechies wavelets. These filter responses are used as frequency filters for the Radon transform. The filtering is performed on the wavelet pyramid decomposition of the Radon transform by detecting the most likely positions of lines in the transform and then by convolving the local area with the appropriate response and zeroing the pyramid coefficients outside of the response area. The response area is defined to contain 95% of the total
Constructions of Vector-Valued Filters and Vector-Valued Wavelets
Jianxun He
2012-01-01
Full Text Available Let a =(a1,a2,…,am∈ℂm be an m-dimensional vector. Then, it can be identified with an m×m circulant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002, we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.
[Detection of R-wave in Fetal EGG Based on Wavelet Transform and Matched Filtering].
Yan, Wenhong; Jiang, Ning
2015-09-01
By analyzing the characteristics of maternal abdominal ECG (Electrocardiogram), a method based on wavelet transform and matched filtering is proposed to detect the R-wave in fetal EGG (FECG). In this method, the high-frequency coefficients are calculated by using wavelet transform. First, the maternal QRS template is obtained by using the arithmetic mean scheme. Finally, the R-wave of FECG is detected based on matched filtering. The experimental results show that this method can effectively eliminate the noises, such as the maternal ECG signal and baseline drift, enhancing the accuracy of the detection of fetal ECG.
Nonstationary Dynamics Data Analysis with Wavelet-SVD Filtering
Brenner, Marty; Groutage, Dale; Bessette, Denis (Technical Monitor)
2001-01-01
Nonstationary time-frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time-frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied.
Denoising lidar signal by combining wavelet improved threshold with wavelet domain spatial filtering
Shirong Yin; Weiran Wang
2006-01-01
Lidar is an effective tool for remotely monitoring target or object, but the lidar signal is often affected by various noises or interferences. Therefore, detecting the weak signals buried in noises is a fundamental and important problem in the lidar systems. In this paper, an effective noise reduction method combining wavelet improved threshold with wavelet domain spatial filtration is presented to denoise pulse lidar signal and is investigated by detecting the simulating pulse lidar signals in noise. The simulation results show that this method can effectively identify the edge of signal and detect the weak lidar signal buried in noises.
Identification of linear continuous-time system using wavelet modulating filters
贺尚红; 钟掘
2004-01-01
An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable(V) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.
Galiana-Merino, J. J.; Rosa-Herranz, J. L.; Rosa-Cintas, S.; Martinez-Espla, J. J.
2013-01-01
A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of multichannel seismic data. The considered time-frequency transforms include the continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform. The developed approaches provide a fast and precise time-frequency examination of the seismograms at different frequency bands. Moreover, filtering methods for noise, transients or even baseline removal, are implemented. The primary motivation is to support seismologists with a user-friendly and fast program for the wavelet analysis, providing practical and understandable results. Program summaryProgram title: SeismicWaveTool Catalogue identifier: AENG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 611072 No. of bytes in distributed program, including test data, etc.: 14688355 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.8.0.347 (R2009a) or higher. Wavelet Toolbox is required. Computer: Developed on a MacBook Pro. Tested on Mac and PC. No computer-specific optimization was performed. Operating system: Any supporting MATLAB (MathWorks Inc.) v7.8.0.347 (R2009a) or higher. Tested on Mac OS X 10.6.8, Windows XP and Vista. Classification: 13. Nature of problem: Numerous research works have developed a great number of free or commercial wavelet based software, which provide specific solutions for the analysis of seismic data. On the other hand, standard toolboxes, packages or libraries, such as the MathWorks' Wavelet Toolbox for MATLAB, offer command line functions and interfaces for the wavelet analysis of one-component signals. Thus, software usually is focused on very specific problems
An Applied Method for Designing Maximally Decimating Non-uniform Filter Banks
无
2003-01-01
Assembling individual line phase filters to form a multi-channel filter bank allows the synthesis filter to be similar to corresponding analysis filters, and the design calculation can be simple. The appropriate relations between synthesis filters and analysis filters eliminate most aliasing resulting from decimation in non-uniform maximally decimating filter banks, and LS algorithm and Remez algorithm are used to optimize the composite character. This design method can achieve approximate Perfect-Reconstruction. An example is given in which the general parameter filters with approximate line phase are used as units of a filter bank.
The use of wavelet filters for reducing noise in posterior fossa Computed Tomography images
Pita-Machado, Reinado [Centro de Ingeniería Clínica. Guacalote y Circunvalación, Santa Clara 50200 (Cuba); Perez-Diaz, Marlen, E-mail: mperez@uclv.edu.cu; Lorenzo-Ginori, Juan V., E-mail: mperez@uclv.edu.cu; Bravo-Pino, Rolando, E-mail: mperez@uclv.edu.cu [Centro de Estudios de Electrónica y Tecnologías de la Información (CEETI), Universidad Central Marta Abreu de las Villas, Carretera a Camajuaní, km. 5 1/2 Santa Clara 54830 (Cuba)
2014-11-07
Wavelet transform based de-noising like wavelet shrinkage, gives the good results in CT. This procedure affects very little the spatial resolution. Some applications are reconstruction methods, while others are a posteriori de-noising methods. De-noising after reconstruction is very difficult because the noise is non-stationary and has unknown distribution. Therefore, methods which work on the sinogram-space don’t have this problem, because they always work over a known noise distribution at this point. On the other hand, the posterior fossa in a head CT is a very complex region for physicians, because it is commonly affected by artifacts and noise which are not eliminated during the reconstruction procedure. This can leads to some false positive evaluations. The purpose of our present work is to compare different wavelet shrinkage de-noising filters to reduce noise, particularly in images of the posterior fossa within CT scans in the sinogram-space. This work describes an experimental search for the best wavelets, to reduce Poisson noise in Computed Tomography (CT) scans. Results showed that de-noising with wavelet filters improved the quality of posterior fossa region in terms of an increased CNR, without noticeable structural distortions.
Color Image Denoising Using Stationary Wavelet Transform and Adaptive Wiener Filter
Iman M.G. Alwan
2012-01-01
Full Text Available The denoising of a natural image corrupted by Gaussian noise is a problem in signal or image processing. Much work has been done in the field of wavelet thresholding but most of it was focused on statistical modeling of wavelet coefficients and the optimal choice of thresholds. This paper describes a new method for the suppression of noise in image by fusing the stationary wavelet denoising technique with adaptive wiener filter. The wiener filter is applied to the reconstructed image for the approximation coefficients only, while the thresholding technique is applied to the details coefficients of the transform, then get the final denoised image is obtained by combining the two results. The proposed method was applied by using MATLAB R2010a with color images contaminated by white Gaussian noise. Compared with stationary wavelet and wiener filter algorithms, the experimental results show that the proposed method provides better subjective and objective quality, and obtain up to 3.5 dB PSNR improvement.
Wavelet-filtering of symbolic music representations for folk tune segmentation and classification
Velarde, Gissel; Weyde, Tillman; Meredith, David
2013-01-01
The aim of this study is to evaluate a machine-learning method in which symbolic representations of folk songs are segmented and classified into tune families with Haar-wavelet filtering. The method is compared with previously proposed Gestalt based method. Melodies are represented as discrete...... coefficients’ local maxima to indicate local boundaries and classify segments by means of k-nearest neighbours based on standard vector-metrics (Euclidean, cityblock), and compare the results to a Gestalt-based segmentation method and metrics applied directly to the pitch signal. We found that the wavelet...
Wavelet Kernels on a DSP: A Comparison between Lifting and Filter Banks for Image Coding
Gnavi, Stefano; Penna, Barbara; Grangetto, Marco; Magli, Enrico; Olmo, Gabriella
2002-12-01
We develop wavelet engines on a digital signal processors (DSP) platform, the target application being image and intraframe video compression by means of the forthcoming JPEG2000 and Motion-JPEG2000 standards. We describe two implementations, based on the lifting scheme and the filter bank scheme, respectively, and we present experimental results on code profiling. In particular, we address the following problems: (1) evaluating the execution speed of a wavelet engine on a modern DSP; (2) comparing the actual execution speed of the lifting scheme and the filter bank scheme with the theoretical results; (3) using the on-board direct memory access (DMA) to possibly optimize the execution speed. The results allow to assess the performance of a modern DSP in the image coding task, as well as to compare the lifting and filter bank performance in a realistic application scenario. Finally, guidelines for optimizing the code efficiency are provided by investigating the possible use of the on-board DMA.
Wavelet-based method for image filtering using scale-space continuity
Jung, Claudio R.; Scharcanski, Jacob
2001-04-01
This paper proposes a novel technique to reduce noise while preserving edge sharpness during image filtering. This method is based on the image multiresolution decomposition by a discrete wavelet transform, given a proper wavelet basis. In the transform spaces, edges are implicitly located and preserved, at the same time that image noise is filtered out. At each resolution level, geometric continuity is used to preserve edges that are not isolated. Finally, we compare consecutive levels to preserve edges having continuity along scales. As a result, the proposed technique produces a filtered version of the original image, where homogeneous regions appear segmented by well-defined edges. Possible applications include image presegmentation and image denoising.
A novel 3D wavelet based filter for visualizing features in noisy biological data
Moss, W C; Haase, S; Lyle, J M; Agard, D A; Sedat, J W
2005-01-05
We have developed a 3D wavelet-based filter for visualizing structural features in volumetric data. The only variable parameter is a characteristic linear size of the feature of interest. The filtered output contains only those regions that are correlated with the characteristic size, thus denoising the image. We demonstrate the use of the filter by applying it to 3D data from a variety of electron microscopy samples including low contrast vitreous ice cryogenic preparations, as well as 3D optical microscopy specimens.
Wavelet filtered shifted phase-encoded joint transform correlation for face recognition
Moniruzzaman, Md.; Alam, Mohammad S.
2017-05-01
A new wavelet-filtered-based Shifted- phase-encoded Joint Transform Correlation (WPJTC) technique has been proposed for efficient face recognition. The proposed technique uses discrete wavelet decomposition for preprocessing and can effectively accommodate various 3D facial distortions, effects of noise, and illumination variations. After analyzing different forms of wavelet basis functions, an optimal method has been proposed by considering the discrimination capability and processing speed as performance trade-offs. The proposed technique yields better correlation discrimination compared to alternate pattern recognition techniques such as phase-shifted phase-encoded fringe-adjusted joint transform correlator. The performance of the proposed WPJTC has been tested using the Yale facial database and extended Yale facial database under different environments such as illumination variation, noise, and 3D changes in facial expressions. Test results show that the proposed WPJTC yields better performance compared to alternate JTC based face recognition techniques.
Yaseen, Alauldeen S.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-03-01
Speech signal processing is widely used to reduce noise impact in acquired data. During the last decades, wavelet-based filtering techniques are often applied in communication systems due to their advantages in signal denoising as compared with Fourier-based methods. In this study we consider applications of a 1-D double density complex wavelet transform (1D-DDCWT) and compare the results with the standard 1-D discrete wavelet-transform (1DDWT). The performances of the considered techniques are compared using the mean opinion score (MOS) being the primary metric for the quality of the processed signals. A two-dimensional extension of this approach can be used for effective image denoising.
Adaptive wavelet packet-based de-speckling of ultrasound images with bilateral filter.
Esakkirajan, Sankaralingam; Vimalraj, Chinna Thambi; Muhammed, Rashad; Subramanian, Ganapathi
2013-12-01
A new adaptive wavelet packet-based approach to minimize speckle noise in ultrasound images is proposed. This method combines wavelet packet thresholding with a bilateral filter. Here, the best bases after wavelet packet decomposition are selected by comparing the first singular value of all sub-bands, and the noisy coefficients are thresholded using a modified NeighShrink technique. The algorithm is tested with various ultrasound images, and the results, in terms of peak signal-to-noise ratio and mean structural similarity values, are compared with those for some well-known de-speckling techniques. The simulation results indicate that the proposed method has better potential to minimize speckle noise and retain fine details of the ultrasound image. Copyright © 2013 World Federation for Ultrasound in Medicine & Biology. All rights reserved.
Zhang, Yan; Tang, Baoping; Liu, Ziran; Chen, Rengxiang
2016-02-01
Fault diagnosis of rolling element bearings is important for improving mechanical system reliability and performance. Vibration signals contain a wealth of complex information useful for state monitoring and fault diagnosis. However, any fault-related impulses in the original signal are often severely tainted by various noises and the interfering vibrations caused by other machine elements. Narrow-band amplitude demodulation has been an effective technique to detect bearing faults by identifying bearing fault characteristic frequencies. To achieve this, the key step is to remove the corrupting noise and interference, and to enhance the weak signatures of the bearing fault. In this paper, a new method based on adaptive wavelet filtering and spectral subtraction is proposed for fault diagnosis in bearings. First, to eliminate the frequency associated with interfering vibrations, the vibration signal is bandpass filtered with a Morlet wavelet filter whose parameters (i.e. center frequency and bandwidth) are selected in separate steps. An alternative and efficient method of determining the center frequency is proposed that utilizes the statistical information contained in the production functions (PFs). The bandwidth parameter is optimized using a local ‘greedy’ scheme along with Shannon wavelet entropy criterion. Then, to further reduce the residual in-band noise in the filtered signal, a spectral subtraction procedure is elaborated after wavelet filtering. Instead of resorting to a reference signal as in the majority of papers in the literature, the new method estimates the power spectral density of the in-band noise from the associated PF. The effectiveness of the proposed method is validated using simulated data, test rig data, and vibration data recorded from the transmission system of a helicopter. The experimental results and comparisons with other methods indicate that the proposed method is an effective approach to detecting the fault-related impulses
Design of optimal binary phase and amplitude filters for maximization of correlation peak sharpness
Downie, John D.
1991-01-01
Current binary-phase filters used for optical correlation are usually assumed to have uniform amplitude transmission. Here, a new type of filter is studied, the binary-phase-and-amplitude filter. If binary phase values of 0 and pi are assumed, the amplitude transmittance values of this type of filter can be optimized to maximize the peak sharpness. For a polarization-encoded binary-phase filter this can be translated into optimization of the rotation angle of the output polarizer following the filter-spatial-light modulator. An analytic expression is presented for the optimum polarizer angle and thus for the optimum binary-phase-and-amplitude filter design.
Zielinski, B.; Patorski, K.
2010-06-01
The aim of this paper is to analyze 2D fringe pattern denoising performed by two chosen methods based on quasi-1D two-arm spin filter and 2D discrete wavelet transform (DWT) signal decomposition and thresholding. The ultimate aim of this comparison is to estimate which algorithm is better suited for high-accuracy measurements by phase shifting interferometry (PSI) with the phase step evaluation using the lattice site approach. The spin filtering method proposed by Yu et al. (1994) was designed to minimize possible fringe blur and distortion. The 2D DWT also presents such features due to a lossless nature of the signal wavelet decomposition. To compare both methods, a special 2D histogram introduced by Gutman and Weber (1998) is used to evaluate intensity errors introduced by each of the presented algorithms.
ZHOU Fu-chang; CHEN Jin; HE Jun; BI Guo; LI Fu-cai; ZHANG Gui-cai
2005-01-01
The vibration signals of rolling element bearing are produced by a combination of periodic and random processes due to the machine's rotation cycle and interaction with the real world. The combination of such components can give rise to signals, which have periodically time-varying ensemble statistical and are best considered as cyclostationary. When the early fault occurs, the background noise is very heavy, it is difficult to disclose the latent periodic components successfully using cyclostationary analysis alone. In this paper the degree of cyclostationarity is combined with wavelet filtering for detection of rolling element bearing early faults. Using the proposed entropy minimization rule. The parameters of the wavelet filter are optimized. This method is shown to be effective in detecting rolling element bearing early fault when cyclostationary analysis by itself fails.
Acharya, U Rajendra; Sree, S Vinitha; Swapna, G; Gupta, Savita; Molinari, Filippo; Garberoglio, R; Witkowska, Agnieszka; Suri, Jasjit S
2013-03-01
Ultrasonography has great potential in differentiating malignant thyroid nodules from the benign ones. However, visual interpretation is limited by interobserver variability, and further, the speckle distribution poses a challenge during the classification process. This article thus presents an automated system for tumor classification in three-dimensional contrast-enhanced ultrasonography data sets. The system first processes the contrast-enhanced ultrasonography images using complex wavelet transform-based filter to mitigate the effect of speckle noise. The higher order spectra features are then extracted and used as input for training and testing a fuzzy classifier. In the off-line training system, higher order spectra features are extracted from a set of images known as the training images. These higher order spectra features along with the clinically assigned ground truth are used to train the classifier and obtain an estimate of the classifier or training parameters. The ground truth tells the class label of the image (i.e. whether the image belongs to a benign or malignant nodule). During the online testing phase, the estimated classifier parameters are applied on the higher order spectra features that are extracted from the testing images to predict their class labels. The predicted class labels are compared with their corresponding original ground truth to evaluate the performance of the classifier. Without utilizing the complex wavelet transform filter, the fuzzy classifier demonstrated an accuracy of 91.6%, while utilizing the complex wavelet transform filter, the accuracy significantly boosted to 99.1%.
Improving the performance of the prony method using a wavelet domain filter for MRI denoising.
Jaramillo, Rodney; Lentini, Marianela; Paluszny, Marco
2014-01-01
The Prony methods are used for exponential fitting. We use a variant of the Prony method for abnormal brain tissue detection in sequences of T 2 weighted magnetic resonance images. Here, MR images are considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process is implemented to reduce the noise in the images. This filter is a modification of Kazubek's algorithm and we use synthetic images to show the ability of the new procedure to suppress noise and compare its performance with respect to the original filter, using quantitative and qualitative criteria. The tissue classification process is illustrated using a real sequence of T 2 MR images, and the filter is applied to each image before using the variant of the Prony method.
Improving the Performance of the Prony Method Using a Wavelet Domain Filter for MRI Denoising
Rodney Jaramillo
2014-01-01
Full Text Available The Prony methods are used for exponential fitting. We use a variant of the Prony method for abnormal brain tissue detection in sequences of T2 weighted magnetic resonance images. Here, MR images are considered to be affected only by Rician noise, and a new wavelet domain bilateral filtering process is implemented to reduce the noise in the images. This filter is a modification of Kazubek’s algorithm and we use synthetic images to show the ability of the new procedure to suppress noise and compare its performance with respect to the original filter, using quantitative and qualitative criteria. The tissue classification process is illustrated using a real sequence of T2 MR images, and the filter is applied to each image before using the variant of the Prony method.
Mahavir Dhoka
2014-06-01
Full Text Available In recent years, data protection is one of important aspect because of cases like piracy, copyright and ownership issues. Digital watermark seems to be solution to the problem. In our paper, we proposed a method of invisible watermark to medical image using Biorthogonal wavelet filter and transformed domain watermark embedding. Generally watermark is embedded in original image either directly or in transform of original image. In our method, we transformed both original image and watermark using discrete wavelet transform and Biorthogonal wavelet filter coefficients. We specifically follow this method considering the case of medical images. As medical images are low contrast images and are taken at high precision with special equipment, so it is not expected that any one will claim for its ownership. Hence we tried to develop a method which will recover watermark through medical image considering any kind of attacks. We tested our method on multiple medical images and listed down results and comparison is made on basis of PSNR and normalised correlation (NC. From the values of NC, we concluded that our method gives better recovery of watermark from watermarked image.
Export-led growth in Tunisia: A wavelet filtering based analysis
Hamrita Mohamed Essaied
2013-10-01
Full Text Available In this paper, we use a wavelet filtering based approach to study the econometric relationship between exports, imports, and economic growth for Tunisia, using quarterly data for the period 1961:1-2007:4. GDP is used as a proxy for economic growth. We explore the interactions between these primary macroeconomic inputs in a co-integrating framework. We also study the direction of causality between the three variables, based on the more robust Toda-Yamamoto modified Wald (MWALD test. The much-studied relationship between these three primary indicators of the economy is explored with the help of the wavelet multi-resolution filtering technique. Instead of an analysis at the original series level, as is usually done, we first decompose the variables using wavelet decomposition technique at various scales of resolution and obtain relationship among components of the decomposed series matched to its scale. The analysis reveals interesting aspects of the interrelationship among the three fundamental macroeconomic variables.
Improved Wavelet-based Spatial Filter of Damage Imaging Method on Composite Structures
WANG Yu; YUAN Shenfang; QIU Lei
2011-01-01
Piezoelectric sensor array-based spatial filter technology is a new promising method presented in research area of structural health monitoring(SHM)in the recent years.To apply this method to composite structures and give the actual position of damage,this paper proposes a spatial filter-based damage imaging method improved by complex Shannon wavelet transform.The basic principle of spatial filter is analyzed first.Then,this paper proposes a method of using complex Shannon wavelet transform to construct analytic signals of time domain signals of PZT sensors array.The analytic signals are synthesized depending on the principle of the spatial filter to give a damage imaging in the form of angle-time.A method of converting the damage imaging to the form of angle-distance is discussed.Finally,an aircraft composite oil tank is adopted to validate the damage imaging method.The validating results show that this method can recognize angle and distance of damage successfully.
Weld Defect Extraction Based on Adaptive Morphology Filtering and Edge Detection by Wavelet Analysis
WANGDonghua; ZHOUYuanhua; GANGTie
2003-01-01
One of the most key steps in X-ray au-tomatic inspection and intelligent recognition systems is how to extract defects and detect their edges effectively.In this paper, a novel method of defect extraction based on the adaptive morphology filtering (DEAMF) is pro-posed, whose structuring elements can be changed with the sizes of defects adaptively. By this method, defects in X-ray weld inspection images are extracted with well-kept shapes and high speeds. Then according to the theory of edge detection based on wavelet transform modulus max-ima, a locally supported wavelet with good antisymmetry is developed to extract edges of defects and the results are satisfying.
Drift Removal in Plant Electrical Signals via IIR Filtering Using Wavelet Energy
Das, Saptarshi; Chatterjee, Shre Kumar; Ghosh, Sanmitra; Maharatna, Koushik; Dasmahapatra, Srinandan; Vitaletti, Andrea; Masi, Elisa; Mancuso, Stefano
2016-01-01
Plant electrical signals often contains low frequency drifts with or without the application of external stimuli. Quantification of the randomness in plant signals in a stimulus-specific way is hindered because the knowledge of vital frequency information in the actual biological response is not known yet. Here we design an optimum Infinite Impulse Response (IIR) filter which removes the low frequency drifts and preserves the frequency spectrum corresponding to the random component of the unstimulated plant signals by bringing the bias due to unknown artifacts and drifts to a minimum. We use energy criteria of wavelet packet transform (WPT) for optimization based tuning of the IIR filter parameters. Such an optimum filter enforces that the energy distribution of the pre-stimulus parts in different experiments are almost overlapped but under different stimuli the distributions of the energy get changed. The reported research may popularize plant signal processing, as a separate field, besides other conventiona...
Speckle Filtering in PolSAR Images by Enhanced Wavelet Thresholding
Boutarfa, Souhila; Bouchemakh, Lynda; Smara, Youcef
2016-08-01
The PolSAR images are affected by a noise called speckle, which deteriorates image quality and complicates image interpretation. The polarimetric filtering is a necessary treatment prior to analysis that allows to reduce speckle and to obtain an improved image quality.In this paper, we present a polarimetric speckle filtering method based on enhancement of wavelet thresholding, hard and soft thresholding using directional coefficients improvement to reduce speckle without destroying the information. This algorithm is based on the classification of significant coefficients and applying the thresholding to obtain a better image quality.The methods are applied to the three polarimetric E-SAR images acquired on Oberpfaffenhofen area located in Munich, Germany, in P-band and the fully polarimetric RADARSAT-2 images acquired on Algiers, Algeria, in C-band.To evaluate the performance of each filter, we based it on the following criteria: smoothing homogeneous areas, preserving structural characteristics of objects and maintaining the information.
Stripe and ring artifact removal with combined wavelet--Fourier filtering.
Münch, Beat; Trtik, Pavel; Marone, Federica; Stampanoni, Marco
2009-05-11
A fast, powerful and stable filter based on combined wavelet and Fourier analysis for the elimination of horizontal or vertical stripes in images is presented and compared with other types of destriping filters. Strict separation between artifacts and original features allowing both, suppression of the unwanted structures and high degree of preservation of the original image information is endeavoured. The results are validated by visual assessments, as well as by quantitative estimation of the image energy loss. The capabilities and the performance of the filter are tested on a number of case studies related to applications in tomographic imaging. The case studies include (i) suppression of waterfall artifacts in electron microscopy images based on focussed ion beam nanotomography, (ii) removal of different types of ring artifacts in synchrotron based X-ray microtomography and (iii) suppression of horizontal stripe artifacts from phase projections in grating interferometry.
Adaptive multiple subtraction with wavelet-based complex unary Wiener filters
Ventosa, Sergi; Huard, Irène; Pica, Antonio; Rabeson, Hérald; Ricarte, Patrice; Duval, Laurent
2011-01-01
Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between actual multiples and their prediction, and thus to minimize multiples in the input dataset after the subtraction. In this work we focus on the subtraction element. We propose an adaptive multiple removal technique in a 1-D complex wavelet frame combined with a non-stationary adaptation performed via single-sample (unary) Wiener filters, consistently estimated on overlapping windows in the transformed domain. This approach greatly simplifies the matching filter estimation and, despite its simplicity, compares promisingly with standard adaptive 2-D methods, both in terms of results and retained speed a...
A Wavelet Phase Filtering Algorithm for Image Noise Reduction%图像噪声去除的小波相位滤波算法
赵瑞珍; 徐龙; 宋国乡
2001-01-01
Most of the wavelet denoising methods available are based on magnitudes. However,for the images with low SNR.the edges of the image m the wavelet domain are hidden in the noise. A wavelet phase filtering algorithm is presented in this paper, which is insensitive to the magnitude of image.
ZENG Qing-hu; QIU Jing; LIU Guan-jun
2007-01-01
Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.
Bijan Rahmani
2016-08-01
Full Text Available Available photovoltaic (PV systems show a prolonged transient response, when integrated into the power grid via active filters. On one hand, the conventional low-pass filter, employed within the integrated PV system, works with a large delay, particularly in the presence of system’s low-order harmonics. On the other hand, the switching of the DC (direct current–DC converters within PV units also prolongs the transient response of an integrated system, injecting harmonics and distortion through the PV-end current. This paper initially develops a wavelet-based low-pass filter to improve the transient response of the interconnected PV systems to grid lines. Further, a damped input filter is proposed within the PV system to address the raised converter’s switching issue. Finally, Matlab/Simulink simulations validate the effectiveness of the proposed wavelet-based low-pass filter and damped input filter within an integrated PV system.
Wavelet Kernels on a DSP: A Comparison between Lifting and Filter Banks for Image Coding
Gnavi Stefano
2002-01-01
Full Text Available We develop wavelet engines on a digital signal processors (DSP platform, the target application being image and intraframe video compression by means of the forthcoming JPEG2000 and Motion-JPEG2000 standards. We describe two implementations, based on the lifting scheme and the filter bank scheme, respectively, and we present experimental results on code profiling. In particular, we address the following problems: (1 evaluating the execution speed of a wavelet engine on a modern DSP; (2 comparing the actual execution speed of the lifting scheme and the filter bank scheme with the theoretical results; (3 using the on-board direct memory access (DMA to possibly optimize the execution speed. The results allow to assess the performance of a modern DSP in the image coding task, as well as to compare the lifting and filter bank performance in a realistic application scenario. Finally, guidelines for optimizing the code efficiency are provided by investigating the possible use of the on-board DMA.
Zielinski, B.; Patorski, K.
2008-12-01
The aim of this paper is to analyze the accuracy of 2D fringe pattern denoising performed by two chosen methods using quasi-1D two-arm spin filter and 2D Discrete Wavelet Transform (DWT) signal decomposition and thresholding. The ultimate aim of this comparison is to estimate which algorithm is better suited for high-accuracy interferometric measurements. In spite of the fact that both algorithms are designed to minimize possible fringe blur and distortion, the evaluation of errors introduced by each algorithm is essential for proper estimation of their performance.
Dantas, José L; Camata, Thiago V; Brunetto, Maria A C; Moraes, Antonio C; Abrão, Taufik; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in isometric and dynamic exercise. The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in isometric and dynamic exercise (P>0.05). However, the results of the variance was lower for both types of exercise in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Wiaux, Y.; Jacques, L.; Vandergheynst, P.
2005-12-01
Wavelets on the sphere are reintroduced and further developed on both the theoretical and the algorithmic grounds. A specific application to cosmology is also discussed. First, a new practical approach to the wavelet filtering of signals on the sphere is developed. Translations and rotations of the filters are naturally implemented through three-dimensional rotations of the group SO(3), and a unitary, radial, and conformal dilation operator is required. The resulting formalism is unique. A correspondence principle is also established, stating that the inverse stereographic projection of a wavelet on the plane (i.e., Euclidean wavelet) also uniquely leads to a wavelet on the sphere (i.e., spherical wavelet). It simplifies the construction of wavelets on the sphere and allows the transfer onto the sphere of properties of wavelets on the plane, such as directionality and steerability. Second, an exact fast algorithm is developed for the directional correlation on the sphere of band-limited signals of band limit L and steerable (wavelet) filters, on 2L×2L equi-angular grids in the coordinates (θ,φ). On the one hand, the algorithm is based on a technique of separation of variables in the Wigner D-functions, basis functions for the harmonic analysis on the rotation group SO(3). The asymptotic complexity of the algorithm is correspondingly reduced from O(L5) to O(L4). On the other hand, the filter steerability and the use of the Driscoll and Healy fast scalar spherical harmonics transform further reduce the algorithm complexity to a simple O(L2log22L). Finally, we consider the perspective of the wavelet analysis of the cosmic microwave background (CMB) temperature and polarization anisotropies on the sphere of the sky. The notions of directionality and steerability are important tools for the identification of local directional features in the wavelet coefficients of the signal, and for their interpretation in cosmology. In this context, computation times for the exact
Optimal IIR filter design using Gravitational Search Algorithm with Wavelet Mutation
S.K. Saha
2015-01-01
Full Text Available This paper presents a global heuristic search optimization technique, which is a hybridized version of the Gravitational Search Algorithm (GSA and Wavelet Mutation (WM strategy. Thus, the Gravitational Search Algorithm with Wavelet Mutation (GSAWM was adopted for the design of an 8th-order infinite impulse response (IIR filter. GSA is based on the interaction of masses situated in a small isolated world guided by the approximation of Newtonian’s laws of gravity and motion. Each mass is represented by four parameters, namely, position, active, passive and inertia mass. The position of the heaviest mass gives the near optimal solution. For better exploitation in multidimensional search spaces, the WM strategy is applied to randomly selected particles that enhance the capability of GSA for finding better near optimal solutions. An extensive simulation study of low-pass (LP, high-pass (HP, band-pass (BP and band-stop (BS IIR filters unleashes the potential of GSAWM in achieving better cut-off frequency sharpness, smaller pass band and stop band ripples, smaller transition width and higher stop band attenuation with assured stability.
Tankanag, Arina V; Chemeris, Nikolay K
2009-10-01
The paper describes an original method for analysis of the peripheral blood flow oscillations measured with the laser Doppler flowmetry (LDF) technique. The method is based on the continuous wavelet transform and adaptive wavelet theory and applies an adaptive wavelet filtering to the LDF data. The method developed allows one to examine the dynamics of amplitude oscillations in a wide frequency range (from 0.007 to 2 Hz) and to process both stationary and non-stationary short (6 min) signals. The capabilities of the method have been demonstrated by analyzing LDF signals registered in the state of rest and upon humeral occlusion. The paper shows the main advantage of the method proposed, which is the significant reduction of 'border effects', as compared to the traditional wavelet analysis. It was found that the low-frequency amplitudes obtained by adaptive wavelets are significantly higher than those obtained by non-adaptive ones. The method suggested would be useful for the analysis of low-frequency components of the short-living transitional processes under the conditions of functional tests. The method of adaptive wavelet filtering can be used to process stationary and non-stationary biomedical signals (cardiograms, encephalograms, myograms, etc), as well as signals studied in the other fields of science and engineering.
Tzanis, A.
2012-04-01
GPR is an invaluable tool for civil and geotechnical engineering applications. One of the most significant objectives of such applications is the detection of fractures, inclined interfaces, empty or filled cavities frequently associated with jointing/faulting and a host of other oriented features. These types of target, especially fractures, are usually not good reflectors and are spatially localized. Their scale is therefore a factor significantly affecting their detectability. Quite frequently, systemic or extraneous noise, or other significant structural characteristics swamp the data with information which blurs, or even masks reflections from such targets, rendering their recognition difficult. This paper reports a method of extracting information (isolating) oriented and scale-dependent structural characteristics, based on oriented two-dimensional B-spline wavelet filters and Gabor wavelet filters. In addition to their advantageous properties (e.g. compact support, orthogonality etc), B-spline wavelets comprise a family with a broad spectrum of frequency localization properties and frequency responses that mimic, more or less, the shape of the radar source wavelet. For instance, the Ricker wavelet is also approximated by derivatives of Cardinal B-splines. An oriented two-dimensional B-spline filter is built by sidewise arranging a number of identical one-dimensional wavelets to create a matrix, tapering the edge-parallel direction with an orthogonal window function and rotating the resulting matrix to the desired orientation. The length of the one-dimensional wavelet (edge-normal direction) determines the width of the topographic features to be isolated. The number of parallel wavelets (edge-parallel direction) determines the feature length over which to smooth. The Gabor wavelets were produced by a Gabor kernel that is a product of an elliptical Gaussian and a complex plane wave: it is two-dimensional by definition. Their applications have hitherto focused
Ellmauthaler, Andreas; Pagliari, Carla L; da Silva, Eduardo A B
2013-03-01
Multiscale transforms are among the most popular techniques in the field of pixel-level image fusion. However, the fusion performance of these methods often deteriorates for images derived from different sensor modalities. In this paper, we demonstrate that for such images, results can be improved using a novel undecimated wavelet transform (UWT)-based fusion scheme, which splits the image decomposition process into two successive filtering operations using spectral factorization of the analysis filters. The actual fusion takes place after convolution with the first filter pair. Its significantly smaller support size leads to the minimization of the unwanted spreading of coefficient values around overlapping image singularities. This usually complicates the feature selection process and may lead to the introduction of reconstruction errors in the fused image. Moreover, we will show that the nonsubsampled nature of the UWT allows the design of nonorthogonal filter banks, which are more robust to artifacts introduced during fusion, additionally improving the obtained results. The combination of these techniques leads to a fusion framework, which provides clear advantages over traditional multiscale fusion approaches, independent of the underlying fusion rule, and reduces unwanted side effects such as ringing artifacts in the fused reconstruction.
WaVPeak: Picking NMR peaks through wavelet-based smoothing and volume-based filtering
Liu, Zhi
2012-02-10
Motivation: Nuclear magnetic resonance (NMR) has been widely used as a powerful tool to determine the 3D structures of proteins in vivo. However, the post-spectra processing stage of NMR structure determination usually involves a tremendous amount of time and expert knowledge, which includes peak picking, chemical shift assignment and structure calculation steps. Detecting accurate peaks from the NMR spectra is a prerequisite for all following steps, and thus remains a key problem in automatic NMR structure determination. Results: We introduce WaVPeak, a fully automatic peak detection method. WaVPeak first smoothes the given NMR spectrum by wavelets. The peaks are then identified as the local maxima. The false positive peaks are filtered out efficiently by considering the volume of the peaks. WaVPeak has two major advantages over the state-of-the-art peak-picking methods. First, through wavelet-based smoothing, WaVPeak does not eliminate any data point in the spectra. Therefore, WaVPeak is able to detect weak peaks that are embedded in the noise level. NMR spectroscopists need the most help isolating these weak peaks. Second, WaVPeak estimates the volume of the peaks to filter the false positives. This is more reliable than intensity-based filters that are widely used in existing methods. We evaluate the performance of WaVPeak on the benchmark set proposed by PICKY (Alipanahi et al., 2009), one of the most accurate methods in the literature. The dataset comprises 32 2D and 3D spectra from eight different proteins. Experimental results demonstrate that WaVPeak achieves an average of 96%, 91%, 88%, 76% and 85% recall on 15N-HSQC, HNCO, HNCA, HNCACB and CBCA(CO)NH, respectively. When the same number of peaks are considered, WaVPeak significantly outperforms PICKY. The Author(s) 2012. Published by Oxford University Press.
无
2010-01-01
The research purpose of this paper is to show the limitations of the existing radiometric normalization approaches and their disadvantages in change detection of artificial objects by comparing the existing approaches,on the basis of which a preprocessing approach to radiometric consistency,based on wavelet transform and a spatial low-pass filter,has been devised.This approach first separates the high frequency information and low frequency information by wavelet transform.Then,the processing of relative radiometric consistency based on a low-pass filter is conducted on the low frequency parts.After processing,an inverse wavelet transform is conducted to obtain the results image.The experimental results show that this approach can substantially reduce the influence on change detection of linear or nonlinear radiometric differences in multi-temporal images.
Non-separable 2D wavelets with two-row filters
Y. Zhan; H.J.A.M. Heijmans (Henk)
2003-01-01
textabstractIn the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we
Singh, Omkar; Sunkaria, Ramesh Kumar
2015-01-01
Separating an information-bearing signal from the background noise is a general problem in signal processing. In a clinical environment during acquisition of an electrocardiogram (ECG) signal, The ECG signal is corrupted by various noise sources such as powerline interference (PLI), baseline wander and muscle artifacts. This paper presents novel methods for reduction of powerline interference in ECG signals using empirical wavelet transform (EWT) and adaptive filtering. The proposed methods are compared with the empirical mode decomposition (EMD) based PLI cancellation methods. A total of six methods for PLI reduction based on EMD and EWT are analysed and their results are presented in this paper. The EWT-based de-noising methods have less computational complexity and are more efficient as compared with the EMD-based de-noising methods.
Shristi Jha
2016-01-01
Full Text Available Iris pattern Recognition is an automated method of biometric identification that uses mathematical pattern-Recognition techniques on images of one or both of the irises of an individual’s eyes, whose complex random patterns are unique, stable, and can be seen from some distance. Iris recognition uses video camera technology with subtle near infrared illumination to acquire images of the detail-rich, intricate structures of the iris which are visible externally. In this narrative research paper the input image is captured and the success of the iris recognition depends on the quality of the image so the captured image is subjected to the preliminary image preprocessing techniques like localization, segmentation, normalization and noise detection followed by texture and edge feature extraction by using Gabor filters and wavelets then the processed image is matched with templates stored in the database to detect the Iris Patterns.
Spatial resolution enhancement residual coding using hybrid wavelets and directional filter banks
Ankit Ashokrao Bhurane; Prateek Chaplot; Dushyanth Nutulapati; Vikram M Gadre
2015-10-01
Traditional video coding uses classical predictive coding techniques, where a signal is initially approximated by taking advantage of the various redundancies present. Most of the video coding standards, including the latest HEVC, use the well-accepted procedure of applying transform coding on self-contained (intra) and inter-predicted frame residuals. Nevertheless, it has been shown in the literature that, a normal video frames possess distinct characteristics compared to a residual frame. In this paper, we have made use of hybrid wavelet transforms and directional filter banks (HWD) to encode resolution enhancement residuals in the context of scalable video coding. The results are presented for the use of HWD in the framework of the Dirac video codec. The experiments are carried out on a variety of test frames. Our experiments on residue coding using HWD show better performance compared to the conventional DWT, when tested on the same platform of the well-known SPIHT algorithm.
Non-separable 2D wavelets with two-row filters
Zhan, Y; Heijmans, Henk
2003-01-01
textabstractIn the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang [2]. A characteristic feature of this class of wavelets is that the support of the corresponding f...
Weighted-Sum-Rate-Maximizing Linear Transceiver Filters for the K-User MIMO Interference Channel
Shin, Joonwoo
2012-01-01
This letter is concerned with transmit and receive filter optimization for the K-user MIMO interference channel. Specifically, linear transmit and receive filter sets are designed which maximize the weighted sum rate while allowing each transmitter to utilize only the local channel state information. Our approach is based on extending the existing method of minimizing the weighted mean squared error (MSE) for the MIMO broadcast channel to the K-user interference channel at hand. For the case of the individual transmitter power constraint, however, a straightforward generalization of the existing method does not reveal a viable solution. It is in fact shown that there exists no closed-form solution for the transmit filter but simple one-dimensional parameter search yields the desired solution. Compared to the direct filter optimization using gradient-based search, our solution requires considerably less computational complexity and a smaller amount of feedback resources while achieving essentially the same lev...
Design of Maximally Flat FIR Filters Based on Explicit Formulas Combined with Optimization
无
2006-01-01
A maximally flat FIR filter design method based on explicit formulas combined with simulated annealing and random search was presented. Utilizing the explicit formulas to calculate the initial values, the finite-word-length FIR filter design problem was converted into optimization of the filter coefficients. An optimization method combined with local discrete random search and simulated annealing was proposed, with the result of optimum solution in the sense of Chebyshev approximation. The proposed method can simplify the design process of FIR filter and reduce the calculation burden. The simulation result indicates that the proposed method is superior to the traditional round off method and can reduce the value of the objective function to 41%-74%.
Optimization of wavelet decomposition for image compression and feature preservation.
Lo, Shih-Chung B; Li, Huai; Freedman, Matthew T
2003-09-01
A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.
Zhou, Zhenggan; Ma, Baoquan; Jiang, Jingtao; Yu, Guang; Liu, Kui; Zhang, Dongmei; Liu, Weiping
2014-10-01
Air-coupled ultrasonic testing (ACUT) technique has been viewed as a viable solution in defect detection of advanced composites used in aerospace and aviation industries. However, the giant mismatch of acoustic impedance in air-solid interface makes the transmission efficiency of ultrasound low, and leads to poor signal-to-noise (SNR) ratio of received signal. The utilisation of signal-processing techniques in non-destructive testing is highly appreciated. This paper presents a wavelet filtering and phase-coded pulse compression hybrid method to improve the SNR and output power of received signal. The wavelet transform is utilised to filter insignificant components from noisy ultrasonic signal, and pulse compression process is used to improve the power of correlated signal based on cross-correction algorithm. For the purpose of reasonable parameter selection, different families of wavelets (Daubechies, Symlet and Coiflet) and decomposition level in discrete wavelet transform are analysed, different Barker codes (5-13 bits) are also analysed to acquire higher main-to-side lobe ratio. The performance of the hybrid method was verified in a honeycomb composite sample. Experimental results demonstrated that the proposed method is very efficient in improving the SNR and signal strength. The applicability of the proposed method seems to be a very promising tool to evaluate the integrity of high ultrasound attenuation composite materials using the ACUT.
Directional Filtering Using Wavelet Transform%基于小波变换的方向滤波
耿茵茵; 蔡安妮; 孙景鳌
2001-01-01
In the images with local strong direction, there is often noise in other directions. To elimi-nate the noise, we propose a novel directional filtering method which takes advantage of directional se-lection ability of wavelet transform skillfully through rotating the image to be filtered and controls the times of rotation through direction quantization. This method employs only directional characteristics for denoising and there is no need to evaluate the frequency characteristics or statistical characteristics of signals and noise, which makes this method easy to implement. The experimental results on finger-print image enhancement show good ability of this method.
Multi-resolutional brain network filtering and analysis via wavelets on non-Euclidean space.
Kim, Won Hwa; Adluru, Nagesh; Chung, Moo K; Charchut, Sylvia; GadElkarim, Johnson J; Altshuler, Lori; Moody, Teena; Kumar, Anand; Singh, Vikas; Leow, Alex D
2013-01-01
Advances in resting state fMRI and diffusion weighted imaging (DWI) have led to much interest in studies that evaluate hypotheses focused on how brain connectivity networks show variations across clinically disparate groups. However, various sources of error (e.g., tractography errors, magnetic field distortion, and motion artifacts) leak into the data, and make downstream statistical analysis problematic. In small sample size studies, such noise have an unfortunate effect that the differential signal may not be identifiable and so the null hypothesis cannot be rejected. Traditionally, smoothing is often used to filter out noise. But the construction of convolving with a Gaussian kernel is not well understood on arbitrarily connected graphs. Furthermore, there are no direct analogues of scale-space theory for graphs--ones which allow to view the signal at multiple resolutions. We provide rigorous frameworks for performing 'multi-resolutional' analysis on brain connectivity graphs. These are based on the recent theory of non-Euclidean wavelets. We provide strong evidence, on brain connectivity data from a network analysis study (structural connectivity differences in adult euthymic bipolar subjects), that the proposed algorithm allows identifying statistically significant network variations, which are clinically meaningful, where classical statistical tests, if applied directly, fail.
Wavelet-based information filtering for fault diagnosis of electric drive systems in electric ships.
Silva, Andre A; Gupta, Shalabh; Bazzi, Ali M; Ulatowski, Arthur
2017-09-21
Electric machines and drives have enjoyed extensive applications in the field of electric vehicles (e.g., electric ships, boats, cars, and underwater vessels) due to their ease of scalability and wide range of operating conditions. This stems from their ability to generate the desired torque and power levels for propulsion under various external load conditions. However, as with the most electrical systems, the electric drives are prone to component failures that can degrade their performance, reduce the efficiency, and require expensive maintenance. Therefore, for safe and reliable operation of electric vehicles, there is a need for automated early diagnostics of critical failures such as broken rotor bars and electrical phase failures. In this regard, this paper presents a fault diagnosis methodology for electric drives in electric ships. This methodology utilizes the two-dimensional, i.e. scale-shift, wavelet transform of the sensor data to filter optimal information-rich regions which can enhance the diagnosis accuracy as well as reduce the computational complexity of the classifier. The methodology was tested on sensor data generated from an experimentally validated simulation model of electric drives under various cruising speed conditions. The results in comparison with other existing techniques show a high correct classification rate with low false alarm and miss detection rates. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Van Dijck, Gert; Van Hulle, Marc M.
2011-01-01
The damage caused by corrosion in chemical process installations can lead to unexpected plant shutdowns and the leakage of potentially toxic chemicals into the environment. When subjected to corrosion, structural changes in the material occur, leading to energy releases as acoustic waves. This acoustic activity can in turn be used for corrosion monitoring, and even for predicting the type of corrosion. Here we apply wavelet packet decomposition to extract features from acoustic emission signals. We then use the extracted wavelet packet coefficients for distinguishing between the most important types of corrosion processes in the chemical process industry: uniform corrosion, pitting and stress corrosion cracking. The local discriminant basis selection algorithm can be considered as a standard for the selection of the most discriminative wavelet coefficients. However, it does not take the statistical dependencies between wavelet coefficients into account. We show that, when these dependencies are ignored, a lower accuracy is obtained in predicting the corrosion type. We compare several mutual information filters to take these dependencies into account in order to arrive at a more accurate prediction. PMID:22163921
High-order wavelet reconstruction/differentiation filters and Gibbs phenomena
Lombardini, Richard; Acevedo, Ramiro; Kuczala, Alexander; Keys, Kerry; Goodrich, Carl; Johnson, Bruce
2016-03-01
We have developed an efficient method to accurately represent 1D or 2D, smooth or discontinuous, solutions to partial differential equations (PDE's), such as Schrodinger or Maxwell's equations, in an orthogonal Daubechies wavelet basis. This is a crucial step in the future development of a wavelet method that solves these PDE's. There are two main developments from this research. First, a reconstruction transform for smooth functions, discovered in previous works [Keinert and Kwon (1997) and Neelov and Goedecker (2006)], is generalized in order to develop a systematic way of tuning its error. This transform converts the wavelet basis representation back to the actual point values of the function. Since this reconstruction can far exceed the wavelet approximation order, it is shown that shorter wavelets can be used while maintaining a high-order accuracy resulting in an increase of computational efficiency. Second, a new ``truncated'' reconstruction transform is developed, using pieces of wavelets, or ``tail functions'', which can be applied to discontinuous functions. Not only does it avoid the wavelet Gibbs phenomenon, but also maintains a tunable accuracy similar to the smooth function case.
[The noise filtering and baseline correction for harmonic spectrum based on wavelet transform].
Guo, Yuan; Zhao, Xue-Hong; Zhang, Rui; Hu, Ya-Jun; Wang, Yan
2013-08-01
The problem of noise and baseline drift is a hot topic in infrared spectral harmonic detection system. This paper presents a new algorithm based on wavelet transform Mallet decomposition to solve the problem of eliminating a variety of complex noise and baseline drift in the harmonic detection. In the algorithm, the appropriate wavelet function and decomposition level were selected to decomposed the noise, baseline drift and useful signal in the harmonic curve into different frequency bands. the bands' information was analysed and a detecting band was set, then the information in useful frequency was reserved by zeroing method of treatment and the coefficient of the threshold. We can just use once transform and reconstruction to remove interference noise and baseline from double-harmonic signal by applying the wavelet transform technique to the harmonic detection spectrum pretreatment. Experiments show that the wavelet transform method can be used to different harmonic detection systems and has universal applicability.
Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena
Lombardini, Richard; Acevedo, Ramiro; Kuczala, Alexander; Keys, Kerry P.; Goodrich, Carl P.; Johnson, Bruce R.
2016-01-01
An orthogonal wavelet basis is characterized by its approximation order, which relates to the ability of the basis to represent general smooth functions on a given scale. It is known, though perhaps not widely known, that there are ways of exceeding the approximation order, i.e., achieving higher-order error in the discretized wavelet transform and its inverse. The focus here is on the development of a practical formulation to accomplish this first for 1D smooth functions, then for 1D functions with discontinuities and then for multidimensional (here 2D) functions with discontinuities. It is shown how to transcend both the wavelet approximation order and the 2D Gibbs phenomenon in representing electromagnetic fields at discontinuous dielectric interfaces that do not simply follow the wavelet-basis grid.
Chan, Y T
1995-01-01
Since the study of wavelets is a relatively new area, much of the research coming from mathematicians, most of the literature uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. Wavelet Basics has therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in elaborate detail in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multiresolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest: wave...
SU-C-207B-02: Maximal Noise Reduction Filter with Anatomical Structures Preservation
Maitree, R; Guzman, G; Chundury, A; Roach, M; Yang, D [Washington University School of Medicine, St Louis, MO (United States)
2016-06-15
Purpose: All medical images contain noise, which can result in an undesirable appearance and can reduce the visibility of anatomical details. There are varieties of techniques utilized to reduce noise such as increasing the image acquisition time and using post-processing noise reduction algorithms. However, these techniques are increasing the imaging time and cost or reducing tissue contrast and effective spatial resolution which are useful diagnosis information. The three main focuses in this study are: 1) to develop a novel approach that can adaptively and maximally reduce noise while preserving valuable details of anatomical structures, 2) to evaluate the effectiveness of available noise reduction algorithms in comparison to the proposed algorithm, and 3) to demonstrate that the proposed noise reduction approach can be used clinically. Methods: To achieve a maximal noise reduction without destroying the anatomical details, the proposed approach automatically estimated the local image noise strength levels and detected the anatomical structures, i.e. tissue boundaries. Such information was used to adaptively adjust strength of the noise reduction filter. The proposed algorithm was tested on 34 repeating swine head datasets and 54 patients MRI and CT images. The performance was quantitatively evaluated by image quality metrics and manually validated for clinical usages by two radiation oncologists and one radiologist. Results: Qualitative measurements on repeated swine head images demonstrated that the proposed algorithm efficiently removed noise while preserving the structures and tissues boundaries. In comparisons, the proposed algorithm obtained competitive noise reduction performance and outperformed other filters in preserving anatomical structures. Assessments from the manual validation indicate that the proposed noise reduction algorithm is quite adequate for some clinical usages. Conclusion: According to both clinical evaluation (human expert ranking) and
Luengo Hendriks, Cris. L.; David W Knowles
2006-01-01
Moss et al.(2005) describe, in a recent paper, a filter that they use to detect lines. We noticed that the wavelet on which this filter is based is a difference of uniform filters. This filter is an approximation to the second derivative operator, which is commonly implemented as the Laplace of Gaussian (or Marr-Hildreth) operator (Marr & Hildreth, 1980; Jahne, 2002), Figure 1. We have compared Moss' filter with 1) the Laplace of Gaussian operator, 2) an approximation of the Laplace of G...
Tu, Yiheng; Huang, Gan; Hung, Yeung Sam; Hu, Li; Hu, Yong; Zhang, Zhiguo
2013-01-01
Event-related potentials (ERPs) are widely used in brain-computer interface (BCI) systems as input signals conveying a subject's intention. A fast and reliable single-trial ERP detection method can be used to develop a BCI system with both high speed and high accuracy. However, most of single-trial ERP detection methods are developed for offline EEG analysis and thus have a high computational complexity and need manual operations. Therefore, they are not applicable to practical BCI systems, which require a low-complexity and automatic ERP detection method. This work presents a joint spatial-time-frequency filter that combines common spatial patterns (CSP) and wavelet filtering (WF) for improving the signal-to-noise (SNR) of visual evoked potentials (VEP), which can lead to a single-trial ERP-based BCI.
Restrepo-Agudelo, Sebastian; Roldan-Vasco, Sebastian; Ramirez-Arbelaez, Lina; Cadavid-Arboleda, Santiago; Perez-Giraldo, Estefania; Orozco-Duque, Andres
2017-08-01
The visual inspection is a widely used method for evaluating the surface electromyographic signal (sEMG) during deglutition, a process highly dependent of the examiners expertise. It is desirable to have a less subjective and automated technique to improve the onset detection in swallowing related muscles, which have a low signal-to-noise ratio. In this work, we acquired sEMG measured in infrahyoid muscles with high baseline noise of ten healthy adults during water swallowing tasks. Two methods were applied to find the combination of cutoff frequencies that achieve the most accurate onset detection: discrete wavelet decomposition based method and fixed steps variations of low and high cutoff frequencies of a digital bandpass filter. Teager-Kaiser Energy operator, root mean square and simple threshold method were applied for both techniques. Results show a narrowing of the effective bandwidth vs. the literature recommended parameters for sEMG acquisition. Both level 3 decomposition with mother wavelet db4 and bandpass filter with cutoff frequencies between 130 and 180Hz were optimal for onset detection in infrahyoid muscles. The proposed methodologies recognized the onset time with predictive power above 0.95, that is similar to previous findings but in larger and more superficial muscles in limbs. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mosbeh R. Kaloop
2015-10-01
Full Text Available This study describes the performance assessment of the Huangpu Bridge in Guangzhou, China based on long-term monitoring in real-time by the kinematic global positioning system (RTK-GPS technique. Wavelet transformde-noising is applied to filter the GPS measurements, while the adaptive neuro-fuzzy inference system (ANFIS time series output-only model is used to predict the deformations of GPS-bridge monitoring points. In addition, GPS and accelerometer monitoring systems are used to evaluate the bridge oscillation performance. The conclusions drawn from investigating the numerical results show that: (1the wavelet de-noising of the GPS measurements of the different recording points on the bridge is a suitable tool to efficiently eliminate the signal noise and extract the different deformation components such as: semi-static and dynamic displacements; (2 the ANFIS method with two multi-input single output model is revealed to powerfully predict GPS movement measurements and assess the bridge deformations; and (3 The installed structural health monitoring system and the applied ANFIS movement prediction performance model are solely sufficient to assure bridge safety based on the analyses of the different filtered movement components.
Han Wenhua; Que Peiwen
2006-01-01
With the widespread application and fast development of gas and oil pipeline network in China, the pipeline inspection technology has been used more extensively. The magnetic flux leakage (MFL) method has established itself as the most widely used in-line inspection technique for the evaluation of gas and oil pipelines. The MFL data obtained from seamless pipeline inspection is usually contaminated by the seamless pipe noise (SPN). SPN can in some cases completely mask MFL signals from certain type of defects,and therefore considerably reduces the detectability of the defect signals. In this paper, a new de-noising algorithm called wavelet domain adaptive filtering is proposed for removing the SPN contained in the MFL data. The new algorithm results from combining the wavelet transform with the adaptive filtering technique. Results from application of the proposed algorithm to the MFL data from field tests show that the proposed algorithm has good performance and considerably improves the detectability of the defect signals in the MFL data.
Improving the quality of the ECG signal by filtering in wavelet transform domain
DzierŻak, RóŻa; Surtel, Wojciech; Dzida, Grzegorz; Maciejewski, Marcin
2016-09-01
The article concerns the research methods of noise reduction occurring in the ECG signals. The method is based on the use of filtration in wavelet transform domain. The study was conducted on two types of signal - received during the rest of the patient and obtained during physical activity. For each of the signals 3 types of filtration were used. The study was designed to determine the effectiveness of various wavelets for de-noising signals obtained in both cases. The results confirm the suitability of the method for improving the quality of the electrocardiogram in case of both types of signals.
An approach to melodic segmentation and classification based on filtering with the Haar-wavelet
Velarde, Gissel; Weyde, Tillman; Meredith, David
2013-01-01
Haar wavelet transform. The melodies are first segmented using local maxima or zero-crossings of ws. The segments of ws are then classified using the k–nearest neighbour algorithm with Euclidian and city-block distances. The method proves more effective than using unfiltered pitch signals and Gestalt...
Wavelet entropy filter and cross-correlation of gravitational wave data
Terenziand, R
2009-01-01
We present a method for enhancing the cross-correlation of gravitational wave signals eventually present in data streams containing otherwise uncorrelated noise. Such method makes use of the wavelet decomposition to cast the cross-correlation time series in time-frequency space. Then an entropy criterion is applied to identify the best time frequency resolution, i.e. the resolution allowing to concentrate the signal in the smallest number of wavelet coefficients. By keeping only the coefficients above a certain threshold, it is possible to reconstruct a cross-correlation time series where the effect of common signal is stronger. We tested our method against signals injected over two data streams of uncorrelated white noise.
Implementation of a Two-Channel Maximally Decimated Filter Bank using Switched Capacitor Circuits
Nahlik, J.; Hospodka, J.; P. Sovka; B. Psenicka
2013-01-01
The aim of this paper is to describe the implementation of a two-channel filter bank (FB) using the switched capacitor (SC) technique considering real properties of operational amplifiers (OpAmps). The design procedure is presented and key recommendations for the implementation are given. The implementation procedure describes the design of two-channel filter bank using an IIR Cauer filter, conversion of IIR into the SC filters and the final implementation of the SC filters. The whole design ...
Luengo Hendriks, Cris L.; Knowles, David W.
2006-02-04
Moss et al.(2005) describe, in a recent paper, a filter thatthey use to detect lines. We noticed that the wavelet on which thisfilter is based is a difference of uniform filters. This filter is anapproximation to the second derivative operator, which is commonlyimplemented as the Laplace of Gaussian (or Marr-Hildreth) operator (Marr&Hildreth, 1980; Jahne, 2002), Figure 1. We have compared Moss'filter with 1) the Laplace of Gaussian operator, 2) an approximation ofthe Laplace of Gaussian using uniform filters, and 3) a few common noisereduction filters. The Laplace-like operators detect lines by suppressingimage features both larger and smaller than the filter size. The noisereduction filters only suppress image features smaller than the filtersize. By estimating the signal to noise ratio (SNR) and mean squaredifference (MSD) of the filtered results, we found that the filterproposed by Moss et al. does not outperform the Laplace of Gaussianoperator. We also found that for images with extreme noise content, linedetection filters perform better than the noise reduction filters whentrying to enhance line structures. In less extreme cases of noise, thestandard noise reduction filters perform significantly better than boththe Laplace of Gaussian and Moss' filter.
Grziwa, Sascha; Korth, Judith; Paetzold, Martin; KEST
2016-10-01
The Rheinisches Institut für Umweltforschung (RIU-PF) has developed the software package EXOTRANS for the detection of transits of exoplanets in stellar light curves. This software package was in use during the CoRoT space mission (2006-2013). EXOTRANS was improved by different wavelet-based filter methods during the following years to separate stellar variation, orbital disturbances and instrumental effects from stellar light curves taken by space telescopes (Kepler, K2, TESS and PLATO). The VARLET filter separates faint transit signals from stellar variations without using a-priori information about the target star. VARLET considers variations by frequency, amplitude and shape simultaneously. VARLET is also able to extract most instrumental jumps and glitches. The PHALET filter separates periodic features independent of their shape and is used with the intention to separate diluting stellar binaries. It is also applied for the multi transit search. Stellar light curves of the K2 mission are constructed from the processing of target pixel files which corrects disturbances caused by the reduced pointing precision of the Kepler telescope after the failure of two gyroscopes. The combination of target pixel file processing with both filter techniques and the proven detection pipeline EXOTRANS lowers the detection limit, reduces false alarms and simplifies the detection of faint transits in light curves of the K2 mission. Using EXOTRANS many new candidates were detected in K2 light curves by using EXOTRANS which were successfully confirmed by ground-based follow-up observation of the KEST collaboration. New candidates and confirmed planets are presented.
Non-Stationary Dynamics Data Analysis with Wavelet-Svd Filtering
Brenner, M. J.
2003-07-01
Non-stationary time-frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time-frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular-value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied. The primary objective is the automation of time-frequency analysis with modal system identification. The contribution is a more general approach in which distinct analysis tools are merged into a unified procedure for linear and non-linear data analysis. This method is first applied to aeroelastic pitch-plunge wing section models. Instability is detected in the linear system, and non-linear dynamics are observed from the time-frequency map and parameter estimates of the non-linear system. Aeroelastic and aeroservoelastic flight data from the drone for aerodynamic and structural testing and F18 aircraft are also investigated and comparisons made between the SVD and TSVD results. Input-output data are used to show that this process is an efficient and reliable tool for automated on-line analysis. Published by Elsevier Science Ltd.
P.B. Chopade
2014-05-01
Full Text Available This paper presents image super-resolution scheme based on sub-pixel image registration by the design of a specific class of dyadic-integer-coefficient based wavelet filters derived from the construction of a half-band polynomial. First, the integer-coefficient based half-band polynomial is designed by the splitting approach. Next, this designed half-band polynomial is factorized and assigned specific number of vanishing moments and roots to obtain the dyadic-integer coefficients low-pass analysis and synthesis filters. The possibility of these dyadic-integer coefficients based wavelet filters is explored in the field of image super-resolution using sub-pixel image registration. The two-resolution frames are registered at a specific shift from one another to restore the resolution lost by CCD array of camera. The discrete wavelet transform (DWT obtained from the designed coefficients is applied on these two low-resolution images to obtain the high resolution image. The developed approach is validated by comparing the quality metrics with existing filter banks.
Implementation of a Two-Channel Maximally Decimated Filter Bank using Switched Capacitor Circuits
J. Nahlik
2013-04-01
Full Text Available The aim of this paper is to describe the implementation of a two-channel filter bank (FB using the switched capacitor (SC technique considering real properties of operational amplifiers (OpAmps. The design procedure is presented and key recommendations for the implementation are given. The implementation procedure describes the design of two-channel filter bank using an IIR Cauer filter, conversion of IIR into the SC filters and the final implementation of the SC filters. The whole design and an SC circuit implementation is performed by a PraCAn package in Maple. To verify the whole filter bank, resulting real property circuit structures are completely simulated by WinSpice and ELDO simulators. The results confirm that perfect reconstruction conditions can be almost accepted for the filter bank implemented by the SC circuits. The phase response of the SC filter bank is not strictly linear due to the IIR filters. However, the final ripple of a magnitude frequency response in the passband is almost constant, app. 0.5 dB for a real circuit analysis.
Kang, Wonseok; Yu, Soohwan; Seo, Doochun; Jeong, Jaeheon; Paik, Joonki
2015-09-10
In very high-resolution (VHR) push-broom-type satellite sensor data, both destriping and denoising methods have become chronic problems and attracted major research advances in the remote sensing fields. Since the estimation of the original image from a noisy input is an ill-posed problem, a simple noise removal algorithm cannot preserve the radiometric integrity of satellite data. To solve these problems, we present a novel method to correct VHR data acquired by a push-broom-type sensor by combining wavelet-Fourier and multiscale non-local means (NLM) filters. After the wavelet-Fourier filter separates the stripe noise from the mixed noise in the wavelet low- and selected high-frequency sub-bands, random noise is removed using the multiscale NLM filter in both low- and high-frequency sub-bands without loss of image detail. The performance of the proposed method is compared to various existing methods on a set of push-broom-type sensor data acquired by Korean Multi-Purpose Satellite 3 (KOMPSAT-3) with severe stripe and random noise, and the results of the proposed method show significantly improved enhancement results over existing state-of-the-art methods in terms of both qualitative and quantitative assessments.
Two-band hybrid FIR-IIR filters for image compression.
Lin, Jianyu; Smith, Mark J T
2011-11-01
Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity.
Sánchez-Úbeda, Juan Pedro; Calvache, María Luisa; Duque, Carlos; López-Chicano, Manuel
2016-11-01
A new methodology has been developed to obtain tidal-filtered time series of groundwater levels in coastal aquifers. Two methods used for oceanography processing and forecasting of sea level data were adapted for this purpose and compared: HA (Harmonic Analysis) and CWT (Continuous Wavelet Transform). The filtering process is generally comprised of two main steps: the detection and fitting of the major tide constituents through the decomposition of the original signal and the subsequent extraction of the complete tidal oscillations. The abilities of the optional HA and CWT methods to decompose and extract the tidal oscillations were assessed by applying them to the data from two piezometers at different depths close to the shoreline of a Mediterranean coastal aquifer (Motril-Salobreña, SE Spain). These methods were applied to three time series of different lengths (one month, one year, and 3.7 years of hourly data) to determine the range of detected frequencies. The different lengths of time series were also used to determine the fit accuracies of the tidal constituents for both the sea level and groundwater heads measurements. The detected tidal constituents were better resolved with increasing depth in the aquifer. The application of these methods yielded a detailed resolution of the tidal components, which enabled the extraction of the major tidal constituents of the sea level measurements from the groundwater heads (e.g., semi-diurnal, diurnal, fortnightly, monthly, semi-annual and annual). In the two wells studied, the CWT method was shown to be a more effective method than HA for extracting the tidal constituents of highest and lowest frequencies from groundwater head measurements.
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Logging Signals Filter Based on Wavelet Modulus Maximum%基于小波模极大值的测井信号滤波
董璐璐; 房文静; 徐静
2012-01-01
On the basis of thermal neutron count curve filter in Pulsed Neutron-Neutron (PNN) logging, the effective formation macroscopic capture cross section can be obtained. Because the interference of statistic fluctuation on PNN logging signals; the spread characteristics of wavelet transform modulus maximum of the signals and noise in different scales are discussed based on the investigation of modulus maximum characteristics. Proposed is an effective PNN logging signals preprocessing method-wavelet transform modulus maximum filtering method. For case study, PNN logging SSN curves in a well are filtered by db4 wavelet. The practical application result shows that the wavelet modulus maximum effectively removes the noise and improves the signal to noise ratio of PNN logging signals.%脉冲中子-中子测井(PNN)热中子计数率曲线滤波处理是获取有效地层宏观俘获截面值的研究基础.针对PNN测井信号受到统计起伏的噪声干扰问题,在分析小波变换模极大值特性的基础上,分析PNN测井信号和干扰噪声的小波变换模极大值在不同尺度上的传播特性,建立PNN测井信号小波变换模极大值去噪算法.以油田某井为例,实现对PNN测井短源距计数率曲线的滤波处理.结果表明,基于小波变换模极大值的滤波方法能够有效去除PNN测井信号噪声干扰,提高测井信号的信噪比.
Hu, Ye; Lounkine, Eugen; Bajorath, Jürgen
2009-07-01
Extended connectivity fingerprints produce variable numbers of structural features for molecules and quantitative comparison of feature ensembles is typically carried out as a measure of molecular similarity. As an alternative way to utilize the information content of extended connectivity fingerprint features, we have introduced a compound class-directed feature filtering technique. In combination with a simple feature counting protocol, feature filtering significantly improves the performance of extended connectivity fingerprint similarity searching compared with state-of-the-art fingerprint search methods. Subsets of extended connectivity fingerprint features that are unique to active compounds are found to be responsible for high compound recall. Moreover, feature filtering and counting is shown to result in significantly higher scaffold hopping potential than data fusion or fingerprint averaging methods. Extended connectivity fingerprint feature filtering and counting represents one of the simplest similarity search methods introduced to date, yet it produces top compound recall and maximizes the scaffold diversity of hits, which is a longstanding goal of similarity searching.
Krishnaveni, M; Subashini, P
2009-01-01
A new fangled method for ship wake detection in synthetic aperture radar (SAR) images is explored here. Most of the detection procedure applies the Radon transform as its properties outfit more than any other transformation for the detection purpose. But still it holds problems when the transform is applied to an image with a high level of noise. Here this paper articulates the combination between the radon transformation and the shrinkage methods which increase the mode of wake detection process. The latter shrinkage method with RT maximize the signal to noise ratio hence it leads to most optimal detection of lines in the SAR images. The originality mainly works on the denoising segment of the proposed algorithm. Experimental work outs are carried over both in simulated and real SAR images. The detection process is more adequate with the proposed method and improves better than the conventional methods.
Health assessment of cooling fan bearings using wavelet-based filtering.
Miao, Qiang; Tang, Chao; Liang, Wei; Pecht, Michael
2012-12-24
As commonly used forced convection air cooling devices in electronics, cooling fans are crucial for guaranteeing the reliability of electronic systems. In a cooling fan assembly, fan bearing failure is a major failure mode that causes excessive vibration, noise, reduction in rotation speed, locked rotor, failure to start, and other problems; therefore, it is necessary to conduct research on the health assessment of cooling fan bearings. This paper presents a vibration-based fan bearing health evaluation method using comblet filtering and exponentially weighted moving average. A new health condition indicator (HCI) for fan bearing degradation assessment is proposed. In order to collect the vibration data for validation of the proposed method, a cooling fan accelerated life test was conducted to simulate the lubricant starvation of fan bearings. A comparison between the proposed method and methods in previous studies (i.e., root mean square, kurtosis, and fault growth parameter) was carried out to assess the performance of the HCI. The analysis results suggest that the HCI can identify incipient fan bearing failures and describe the bearing degradation process. Overall, the work presented in this paper provides a promising method for fan bearing health evaluation and prognosis.
Health Assessment of Cooling Fan Bearings Using Wavelet-Based Filtering
Qiang Miao
2012-12-01
Full Text Available As commonly used forced convection air cooling devices in electronics, cooling fans are crucial for guaranteeing the reliability of electronic systems. In a cooling fan assembly, fan bearing failure is a major failure mode that causes excessive vibration, noise, reduction in rotation speed, locked rotor, failure to start, and other problems; therefore, it is necessary to conduct research on the health assessment of cooling fan bearings. This paper presents a vibration-based fan bearing health evaluation method using comblet filtering and exponentially weighted moving average. A new health condition indicator (HCI for fan bearing degradation assessment is proposed. In order to collect the vibration data for validation of the proposed method, a cooling fan accelerated life test was conducted to simulate the lubricant starvation of fan bearings. A comparison between the proposed method and methods in previous studies (i.e., root mean square, kurtosis, and fault growth parameter was carried out to assess the performance of the HCI. The analysis results suggest that the HCI can identify incipient fan bearing failures and describe the bearing degradation process. Overall, the work presented in this paper provides a promising method for fan bearing health evaluation and prognosis.
Burge, Johannes
2017-01-01
Accuracy Maximization Analysis (AMA) is a recently developed Bayesian ideal observer method for task-specific dimensionality reduction. Given a training set of proximal stimuli (e.g. retinal images), a response noise model, and a cost function, AMA returns the filters (i.e. receptive fields) that extract the most useful stimulus features for estimating a user-specified latent variable from those stimuli. Here, we first contribute two technical advances that significantly reduce AMA’s compute time: we derive gradients of cost functions for which two popular estimators are appropriate, and we implement a stochastic gradient descent (AMA-SGD) routine for filter learning. Next, we show how the method can be used to simultaneously probe the impact on neural encoding of natural stimulus variability, the prior over the latent variable, noise power, and the choice of cost function. Then, we examine the geometry of AMA’s unique combination of properties that distinguish it from better-known statistical methods. Using binocular disparity estimation as a concrete test case, we develop insights that have general implications for understanding neural encoding and decoding in a broad class of fundamental sensory-perceptual tasks connected to the energy model. Specifically, we find that non-orthogonal (partially redundant) filters with scaled additive noise tend to outperform orthogonal filters with constant additive noise; non-orthogonal filters and scaled additive noise can interact to sculpt noise-induced stimulus encoding uncertainty to match task-irrelevant stimulus variability. Thus, we show that some properties of neural response thought to be biophysical nuisances can confer coding advantages to neural systems. Finally, we speculate that, if repurposed for the problem of neural systems identification, AMA may be able to overcome a fundamental limitation of standard subunit model estimation. As natural stimuli become more widely used in the study of psychophysical and
Tzanis, Andreas
2013-02-01
The Ground Probing Radar (GPR) is a valuable tool for near surface geological, geotechnical, engineering, environmental, archaeological and other work. GPR images of the subsurface frequently contain geometric information (constant or variable-dip reflections) from various structures such as bedding, cracks, fractures, etc. Such features are frequently the target of the survey; however, they are usually not good reflectors and they are highly localized in time and in space. Their scale is therefore a factor significantly affecting their detectability. At the same time, the GPR method is very sensitive to broadband noise from buried small objects, electromagnetic anthropogenic activity and systemic factors, which frequently blurs the reflections from such targets. This paper introduces a method to de-noise GPR data and extract geometric information from scale-and-dip dependent structural features, based on one-dimensional B-Spline Wavelets, two-dimensional directional B-Spline Wavelet (BSW) Filters and two-dimensional Gabor Filters. A directional BSW Filter is built by sidewise arranging s identical one-dimensional wavelets of length L, tapering the s-parallel direction (span) with a suitable window function and rotating the resulting matrix to the desired orientation. The length L of the wavelet defines the temporal and spatial scale to be isolated and the span determines the length over which to smooth (spatial resolution). The Gabor Filter is generated by multiplying an elliptical Gaussian by a complex plane wave; at any orientation the temporal or spatial scale(s) to be isolated are determined by the wavelength. λ of the plane wave and the spatial resolution by the spatial aspect ratio γ, which specifies the ellipticity of the support of the Gabor function. At any orientation, both types of filter may be tuned at any frequency or spatial wavenumber by varying the length or the wavelength respectively. The filters can be applied directly to two
The EM Method in a Probabilistic Wavelet-Based MRI Denoising
Marcos Martin-Fernandez
2015-01-01
Full Text Available Human body heat emission and others external causes can interfere in magnetic resonance image acquisition and produce noise. In this kind of images, the noise, when no signal is present, is Rayleigh distributed and its wavelet coefficients can be approximately modeled by a Gaussian distribution. Noiseless magnetic resonance images can be modeled by a Laplacian distribution in the wavelet domain. This paper proposes a new magnetic resonance image denoising method to solve this fact. This method performs shrinkage of wavelet coefficients based on the conditioned probability of being noise or detail. The parameters involved in this filtering approach are calculated by means of the expectation maximization (EM method, which avoids the need to use an estimator of noise variance. The efficiency of the proposed filter is studied and compared with other important filtering techniques, such as Nowak’s, Donoho-Johnstone’s, Awate-Whitaker’s, and nonlocal means filters, in different 2D and 3D images.
Dwi Nugroho, Kreshna; Pebrianto, Singgih; Arif Fatoni, Muhammad; Fatikhunnada, Alvin; Liyantono; Setiawan, Yudi
2017-01-01
Information on the area and spatial distribution of paddy field are needed to support sustainable agricultural and food security program. Mapping or distribution of cropping pattern paddy field is important to obtain sustainability paddy field area. It can be done by direct observation and remote sensing method. This paper discusses remote sensing for paddy field monitoring based on MODIS time series data. In time series MODIS data, difficult to direct classified of data, because of temporal noise. Therefore wavelet transform and moving average are needed as filter methods. The Objective of this study is to recognize paddy cropping pattern with wavelet transform and moving average in West Java using MODIS imagery (MOD13Q1) from 2001 to 2015 then compared between both of methods. The result showed the spatial distribution almost have the same cropping pattern. The accuracy of wavelet transform (75.5%) is higher than moving average (70.5%). Both methods showed that the majority of the cropping pattern in West Java have pattern paddy-fallow-paddy-fallow with various time planting. The difference of the planting schedule was occurs caused by the availability of irrigation water.
Efficient Rectangular Maximal-Volume Algorithm for Rating Elicitation in Collaborative Filtering
Fonarev, Alexander
2017-02-07
Cold start problem in Collaborative Filtering can be solved by asking new users to rate a small seed set of representative items or by asking representative users to rate a new item. The question is how to build a seed set that can give enough preference information for making good recommendations. One of the most successful approaches, called Representative Based Matrix Factorization, is based on Maxvol algorithm. Unfortunately, this approach has one important limitation - a seed set of a particular size requires a rating matrix factorization of fixed rank that should coincide with that size. This is not necessarily optimal in the general case. In the current paper, we introduce a fast algorithm for an analytical generalization of this approach that we call Rectangular Maxvol. It allows the rank of factorization to be lower than the required size of the seed set. Moreover, the paper includes the theoretical analysis of the method\\'s error, the complexity analysis of the existing methods and the comparison to the state-of-the-art approaches.
MAO Yibo
2003-01-01
The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-0rder and 2-0rder balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesn't increase the length of filters, which suggests that a relatively short balanced multiwavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.
Dolabdjian, Ch.; Fadili, J.; Huertas Leyva, E.
2002-11-01
We have implemented a real-time numerical denoising algorithm, using the Discrete Wavelet Transform (DWT), on a TMS320C3x Digital Signal Processor (DSP). We also compared from a theoretical and practical viewpoints this post-processing approach to a more classical low-pass filter. This comparison was carried out using an ECG-type signal (ElectroCardiogram). The denoising approach is an elegant and extremely fast alternative to the classical linear filters class. It is particularly adapted to non-stationary signals such as those encountered in biological applications. The denoising allows to substantially improve detection of such signals over Fourier-based techniques. This processing step is a vital element in our acquisition chain using high sensitivity magnetic sensors. It should enhance detection of cardiac-type magnetic signals or magnetic particles in movement.
吉书鹏; 丁小青
2003-01-01
Image enhancement methods are typically aimed at improvement of the overall visibility of features. Though histogram equalization can enhance the contrast by redistributing the gray levels, it has the drawback that it reduces the information in the processed image. In this paper, we present a new image enhancement algorithm. After histogram equalization is carried out, morphological filters and wavelet-based enhancement algorithm is used to clean out the unwanted details and further enhance the image and compensate for the information loss during histogram equalization. Experimental results show that the morphological filters and wavelet-based histogram equalization algorithm can significantly enhance the contrast and increase the information entropy of the image.
A Failure Prognosis Method Based on Wavelet-Kalman Filtering with Missing Data%含缺失数据的小波-卡尔曼滤波故障预测方法
杜党波; 张伟; 胡昌华; 周志杰; 司小胜; 张建勋
2014-01-01
研究了复杂系统存在缺失数据时的故障预测问题。首先，针对测试数据的非平稳性，在小波-卡尔曼滤波预测模型的基础上进行了改进，并利用期望最大化算法对模型参数进行了在线更新，提高其对非平稳时间序列的预测能力；其次，将数据缺失通过一个满足伯努利分布的随机变量描述，实现了缺失数据情况下小波-卡尔曼滤波状态估计。基于此，提出了缺失数据下的故障预测算法；最后，通过数值仿真和实例验证，说明了所提算法的有效性和可行性。%This paper concerns the problem of failure prediction for complex systems in the presence of missing data. First, an improved wavelet-Kalman filtering based prediction method is presented to incorporate non-stationary charac-teristics of the measured data. In the presented method, to improve its predictive capacity, the expectation maximization (EM) algorithm is applied to online updating the parameters of the filtering model. Secondly, the data missing mechanism is described by a Bernoulli distributed random variable. In this case, the state of the system can be estimated through the presented wavelet-Kalman filter with the EM-based parameters updating mechanism. Together with the above devel-opments, an algorithm is presented for failure prediction in presence of missing data. Finally, the results of a numerical example and case study validate the effectiveness and feasibility of the developed method.
王小兵; 孙久运; 汤海燕
2012-01-01
为了有效滤除图像高斯噪声,将数学形态学与小波域增强相结合,提出了一种高斯噪声新型滤波算法.该算法首先将噪声图像进行二维小波分解,得到低频和高频子图像;然后保留低频子图像不变,对各高频子图像根据其噪声分布特点分别设计出多角度、多结构逐级形态学滤波器进行滤波处理,并进行小波分解系数重构;最后对经过形态学滤波后的图像进行2层小波分解,通过设计出一种新型小波增强函数对不同幅值的小波系数进行不同程度的收缩处理,在此基础上进行分解系数重构.将自适应中值滤波与数学形态学滤波与本文算法进行比较,实验证明本文滤波算法其去噪效果优于前两种算法.%In order to filter the Gaussian noise in digital image,combining the Mathematical morphology and Wavelet domain enhancement,a new filter algorithm is put forward.Firstly,the noise image is conducted two-dimensional wavelet decomposition,obtaining high-frequency and low-frequency sub image.Then keep the low-frequency sub image unchanged,according to the characteristics of the Gaussian noise distribution in each high-frequency sub image,the multi-angles,multi-structure mathematical morphology filters are designed to filter out the Gaussian noise,then the wavelet coefficient are reconstructed.Finally,the image after mathematical morphology filtering are conducted two layer wavelet decomposition,a new wavelet domain enhancement function is designed so as to contract the different amplitude wavelet coefficients in different degree,then the wavelet coefficient are reconstructed.The adaptive average filter and mathematical morphology and the new filter algorithm in this paper are applied to denoising the Gaussian noise in digital image respectively,the experiment results show that the new filter algorithm in this paper is better than the others.
McDonald, Alison C; Sanei, Kia; Keir, Peter J
2013-06-01
Muscle force estimates are important for full understanding of the musculoskeletal system and EMG is a modeling method used to estimate muscle force. The purpose of this investigation was to examine the effect of high pass filtering and non-linear normalization on the EMG-force relationship of sub-maximal finger exertions. Sub-maximal isometric ramp exertions were performed under three conditions (i) extension with restraint at the mid-proximal phalanx, (ii) flexion at the proximal phalanx and (iii) flexion at the distal phalanx. Thirty high pass filter designs were compared to a standardized processing procedure and an exponential fit equation was used for non-linear normalization. High pass filtering significantly reduced the %RMS error and increased the peak cross correlation between EMG and force in the distal flexion condition and in the other two conditions there was a trend towards improving force predictions with high pass filtering. The degree of linearity differed between the three contraction conditions and high pass filtering improved the linearity in all conditions. Non-linear normalization had greater impact on the EMG-force relationship than high pass filtering. The difference in optimal processing parameters suggests that high pass filtering and linearity are dependent on contraction mode as well as the muscle analyzed.
Yan, Xin-Guo; Xie, Chi; Wang, Gang-Jin
2015-08-01
We study the topological stability of stock market network by investigating the topological robustness, namely the ability of the network to resist structural or topological changes. The stock market network is extracted by minimal spanning tree (MST) and planar maximally filtered graph (PMFG). We find that the specific delisting thresholds of the listed companies exist in both MST and PMFG networks. In comparison with MST, PMFG provides more information and is better for the aim of exploring stock market network’s robustness. The PMFG before the US sub-prime crisis (i.e., from June 2005 to May 2007) has a stronger robustness against the intentional topological damage than the other two sub-periods (i.e., from June 2007 to May 2009 and from June 2009 to May 2011). We also find that the nonfractal property exists in MSTs of S&P 500, i.e., the highly connected nodes link with each other directly, which indicates that the MSTs are vulnerable to the removal of such important nodes. Moreover, the financial institutions and high technology companies are important in maintaining the stability of S&P 500 network.
Aboufadel, Edward
1999-01-01
An accessible and practical introduction to wavelets. With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets
Tests for Wavelets as a Basis Set
Baker, Thomas; Evenbly, Glen; White, Steven
A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We develop metrics to evaluate wavelets for general problems on test one-dimensional systems. The goal is to eventually use a wavelet basis in electronic structure calculations. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets. We also evaluate a new type of orthogonal wavelet with dilation factor three which is both symmetric and compact in real space. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC008696.
小波滤波程序设计中三种BASIC语言的比较%Programming Compare of Three Basic Languages in Wavelet Filtering
无
2001-01-01
比较了True Basic (TB)、Quick Basic (QB)和Visual Basic (VB)三种编程语言在正交小波滤波程序设计中程序代码的输入、运算速度、图形输出等方面的差异。结果表明VB中输入代码最为容易，程序的可读性最强；运算速度最快，比QB快了7倍多、比TB快了一半；输出的图形最光滑、漂亮，其界面最为美观；而且最易于操作。VB明显优于QB和TB。%The differences among True Basic (TB), Quick Basic (QB) and Visual Basic (VB), which are structured programming language, in wavelet filtering are analyzed from three aspects, i.e. codes input, run-speed and graph output. The filtering arithmetic of orthogonal wavelet adopts Mallat's decomposition and reconstruction algorithm. The processed data (1024 points, S/N = 4) are from simulated electroanalysis signal. And the filtering parameters are same: 8th-Daubechies Wavelet and truncation frequency 4. First, inputting or editing codes in VB, the initials of key words can automatically change to capital letters. In addition, the variables defined by progranmers also can keep consistent with ones in Dim sentence. The codes input in QB is basically the same to that in VB. But then, there is nuance between the both, which is the variables defined by programmers accord to ones of the programmer's latest inputting or editing. Whereas, the capitals and lowercases of codes including key words in TB must be changed artificially; therefore, it is troublesome. The results show that the code-input is most convenient and easy in VB. Secondly, TB and QB base on 16bit DOS, whose conventional memory is confined to 640KB, thus some complicated operation such as iterative one time after time can not run. And VB bases on 32bit Windows operating system. Since there is a three nested repetition in decomposition subprogram and reconstruction subprogram respectively, the run-speed in QB and TB is apparently slower than that in VB. The run-speed in VB is more than
魏文斌; 杨力华; 蔡建宏
2005-01-01
本文研究了一类与多通道正交小波滤波器相关的矩阵方程.运用多相位分解的方法,获得了这类矩阵方程的通解.借助于该结果,可以从一组多通道正交小波能够产生许多组多通道正交小波.%In this paper, we study a certain class of the matrix equations associated with multiple channel orthonormal wavelet filters. By polyphase factorization, we obtain the general solutions of this class of matrix equations, by which we can produce a great number of groups of multiple channel orthonormal wavelets from one group of multiple channel orthonormal wavelets.
Adaptive boxcar/wavelet transform
Sezer, Osman G.; Altunbasak, Yucel
2009-01-01
This paper presents a new adaptive Boxcar/Wavelet transform for image compression. Boxcar/Wavelet decomposition emphasizes the idea of average-interpolation representation which uses dyadic averages and their interpolation to explain a special case of biorthogonal wavelet transforms (BWT). This perspective for image compression together with lifting scheme offers the ability to train an optimum 2-D filter set for nonlinear prediction (interpolation) that will adapt to the context around the low-pass wavelet coefficients for reducing energy in the high-pass bands. Moreover, the filters obtained after training is observed to posses directional information with some textural clues that can provide better prediction performance. This work addresses a firrst step towards obtaining this new set of training-based fillters in the context of Boxcar/Wavelet transform. Initial experimental results show better subjective quality performance compared to popular 9/7-tap and 5/3-tap BWTs with comparable results in objective quality.
Wavelet Transform and its Application to CBIR
Mr. V. K. Magar
2013-07-01
Full Text Available Wavelet filter bank, based on the lifting scheme framework. The lifting scheme there are two linear filters denoted Adapt a multidimensional P (prediction and U (update are defined as Neville filters of order N and Ñ, respectively. We are applying the Haar wavelet transform {&} wavelet decomposition of the image then we enter the Neville filter order {&} optimization the Neville filter. Lifting scheme on quincunx grids perform wavelet decomposition of 2-D signal (image and corresponding reconstruction tools for image as well as a function for computation of moments. The wavelet schemes rely on the lifting scheme use the splitting of rectangular grid into quincunx grid. The proposed methods apply the genetic algorithm wide range of problems, from optimization problem inductive concept learning, scheduling, and layout problem. In this project we did comparison between separable wavelet and nonseparable wavelet. We calculate the retrieval rate of separable and nonseparable.Retrieval rate is more means maximum features can be extracted. This method is applied to content-based image retrieval (CBIR an image signature is derived from this new adaptive non-separable wavelet transform. In CBIR we are used Texture feature for retrieving the image. We used 260 image databases. There are 5 classes. Images are scanned through its particular characteristics now some degree of freedom is given to the algorithm to find the image from its weight so term non-separable lifting is used and through the wavelet transformation Image primal and dual wavelet is taken into consideration for the application
A modified OSEM algorithm for PET reconstruction using wavelet processing.
Lee, Nam-Yong; Choi, Yong
2005-12-01
Ordered subset expectation-maximization (OSEM) method in positron emission tomography (PET) has been very popular recently. It is an iterative algorithm and provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. Due to the lack of smoothness in images in OSEM iterations, however, some type of inter-smoothing is required. For this purpose, the smoothing based on the convolution with the Gaussian kernel has been used in clinical PET practices. In this paper, we incorporated a robust wavelet de-noising method into OSEM iterations as an inter-smoothing tool. The proposed wavelet method is based on a hybrid use of the standard wavelet shrinkage and the robust wavelet shrinkage to have edge preserving and robust de-noising simultaneously. The performances of the proposed method were compared with those of the smoothing methods based on the convolution with Gaussian kernel using software phantoms, physical phantoms, and human PET studies. The results demonstrated that the proposed wavelet method provided better spatial resolution characteristic than the smoothing methods based on the Gaussian convolution, while having comparable performance in noise removal.
Wavelets and multiscale signal processing
Cohen, Albert
1995-01-01
Since their appearance in mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in mathematical analysis and in applications to numerical analysis and signal processing. This book is based on "Ondelettes et Traitement Numerique du Signal" by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing. Throughout, the book concentrates on the fundamentals. It begins with a chapter on the concept of multiresolution analysis, which contains complete proofs of the basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case (Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of the filters and the importance of regularity for t...
Image Denoising Based on Wavelet Transform and Median Filter%一种基于中值滤波和小波变换的图像去噪算法研究
万小红
2012-01-01
针对同时含有脉冲噪声和高斯噪声的混合含噪图像特点,结合自适应中值滤波和小波变换的阈值滤波的各自优点,提出了一种基于中值滤波和小波变换阈值去噪相结合的图像去噪方法,即先对图像进行自适应中值滤波去除脉冲噪声,然后利用小波变换去除剩余的高斯噪声.实验表明：该方法能在有效去除混合噪声的同时,较好地保持边缘和细节信息.%As for the features of the noise image mixed with the impulse noise and the Gaussian noise, combined with the respective merits of the adaptive median filter and wavelet transform threshold denoising, a kind of denoising method based on the combination of the median filter and wavelet threshold denoising is put forward. Firstly,remove the impulsive noise in the adaptive median filter, and then removes the Gaussian noise by using wavelet transform. Experiments show that this method can effectively remove the mixture noise. At the same time, it also can maintain the edge details of the information.
小波滤波与AR模型在脑电信号处理的应用%Application of Wavelet Filter and AR Model in EEG Signal Processing
王力; 张雄
2012-01-01
针对脑-计算机接口技术中的脑电信号处理、事件相关同步和事件相关去同步的特点,提出了一种基于离散小波滤波和AR模型来提取脑电信号特征向量的方法.利用 Daubechies类小波函数对脑电信号进行4层分解,然后使用Burg算法提取脑电信号8阶AR模型系数,最后用BP神经网络进行分类和比较.得到最优的正确率为71.64％,小波滤波的效果要优于FIR滤波器.%Due to the feature of event related synchronization and event related desynchronization, identification and classification technology of electroencephalography ( EEG) plays an important role in the study of brain-computer interface ( BCI) system. A novel method of extracting feature vector of EEG based on discrete wavelet filter and au-toregressive(AR) model was proposed. First, the KEG signal was decomposed to four levels by Daubechies wavelet function and then its eight order AR coefficients were estimated by Burg's algorithm. At last, the features were classified by BP neural network, the best accuracy is 71. 64% , and the effect of wavelet filter is better than FIR filter's.
Cheng, Lizhi; Luo, Yong; Chen, Bo
2014-01-01
This book could be divided into two parts i.e. fundamental wavelet transform theory and method and some important applications of wavelet transform. In the first part, as preliminary knowledge, the Fourier analysis, inner product space, the characteristics of Haar functions, and concepts of multi-resolution analysis, are introduced followed by a description on how to construct wavelet functions both multi-band and multi wavelets, and finally introduces the design of integer wavelets via lifting schemes and its application to integer transform algorithm. In the second part, many applications are discussed in the field of image and signal processing by introducing other wavelet variants such as complex wavelets, ridgelets, and curvelets. Important application examples include image compression, image denoising/restoration, image enhancement, digital watermarking, numerical solution of partial differential equations, and solving ill-conditioned Toeplitz system. The book is intended for senior undergraduate stude...
OPTICAL REALIZATION OF WAVELET TRANSFORM WITH A SINGLE LENS
王取泉; 熊贵光; 李承芳; 张苏淮; 王琳
2001-01-01
Two optical set-ups to implement wavelet transform with a single lens have been proposed, in which the wavelet filter was placed in front of the imaging lens or on the frequency plane. The general formula of the complex field distribution of the output plane has been deduced. The analysing wavelet functions of the band-pass wavelet filters with double and circular slits have been discussed.
路倩倩; 王友仁; 罗慧
2012-01-01
图像形成与传输过程中,常受到复杂混合噪声的干扰.本文结合二维分数阶小波变换与中值滤波,提出一种新的混合未知图像噪声滤除方法.该方法先通过噪声检测将脉冲噪声标识出来,并利用中值滤波方法滤除,然后计算剩余噪声,进一步得到二维分数阶小波变换的最优阶次,在二维分数阶小波时频域,将剩余的高斯白噪声用阈值去噪方法滤除.经实验证明,该方法在有效去除混合噪声时具有优势.%In the forming and transporting process,images are often disturbed by complicated mixed noises.Combined the 2-D fractional wavelet transform with median filtering,a new image filtering method for filtering mixed and unknown noise was proposed.First,impulse noise was detected and marked up by the impulse noise detection,and filtered by median filtering in this method.Then the residual noise was calculated,further the optimal fractional order of the 2-D fractional wavelet transform can be got,and the residual Gaussian noise can be removed by using the threshold shrinking method in 2-D fractional wavelet time-frequency domain.The experiments show that the proposed method can remove the mixed noise effectively.
On optimisation of wavelet algorithms for non-perfect wavelet compression of digital medical images
Ricke, J
2001-01-01
Aim: Optimisation of medical image compression. Evaluation of wavelet-filters for wavelet-compression. Results: Application of filters with different complexity results in significant variations in the quality of image reconstruction after compression specifically in low frequency information. Filters of high complexity proved to be advantageous despite of heterogenous results during visual analysis. For high frequency details, complexity of filters did not prove to be of significant impact on image after reconstruction.
无
2007-01-01
In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.
Construction of compactly supported orthonormal wavelets with beautiful structure
PENG Lizhong; WANG Yongge
2004-01-01
In this paper, a new method of constructing symmetric (antisymmetric) scaling and wavelet filters is introduced, and we get a new type of wavelet system that has very beautiful structure. Using this kind of wavelet system, we can achieve filters with the properties: rational, symmetric or antisymmetric, the lengths of the filters are shorter and the corresponding functions have higher smoothness, so they have good prospect in applications.
Hu, L; Liang, M; Mouraux, A; Wise, R G; Hu, Y; Iannetti, G D
2011-12-01
Across-trial averaging is a widely used approach to enhance the signal-to-noise ratio (SNR) of event-related potentials (ERPs). However, across-trial variability of ERP latency and amplitude may contain physiologically relevant information that is lost by across-trial averaging. Hence, we aimed to develop a novel method that uses 1) wavelet filtering (WF) to enhance the SNR of ERPs and 2) a multiple linear regression with a dispersion term (MLR(d)) that takes into account shape distortions to estimate the single-trial latency and amplitude of ERP peaks. Using simulated ERP data sets containing different levels of noise, we provide evidence that, compared with other approaches, the proposed WF+MLR(d) method yields the most accurate estimate of single-trial ERP features. When applied to a real laser-evoked potential data set, the WF+MLR(d) approach provides reliable estimation of single-trial latency, amplitude, and morphology of ERPs and thereby allows performing meaningful correlations at single-trial level. We obtained three main findings. First, WF significantly enhances the SNR of single-trial ERPs. Second, MLR(d) effectively captures and measures the variability in the morphology of single-trial ERPs, thus providing an accurate and unbiased estimate of their peak latency and amplitude. Third, intensity of pain perception significantly correlates with the single-trial estimates of N2 and P2 amplitude. These results indicate that WF+MLR(d) can be used to explore the dynamics between different ERP features, behavioral variables, and other neuroimaging measures of brain activity, thus providing new insights into the functional significance of the different brain processes underlying the brain responses to sensory stimuli.
Hu, L.; Liang, M.; Mouraux, A.; Wise, R. G.; Hu, Y.
2011-01-01
Across-trial averaging is a widely used approach to enhance the signal-to-noise ratio (SNR) of event-related potentials (ERPs). However, across-trial variability of ERP latency and amplitude may contain physiologically relevant information that is lost by across-trial averaging. Hence, we aimed to develop a novel method that uses 1) wavelet filtering (WF) to enhance the SNR of ERPs and 2) a multiple linear regression with a dispersion term (MLRd) that takes into account shape distortions to estimate the single-trial latency and amplitude of ERP peaks. Using simulated ERP data sets containing different levels of noise, we provide evidence that, compared with other approaches, the proposed WF+MLRd method yields the most accurate estimate of single-trial ERP features. When applied to a real laser-evoked potential data set, the WF+MLRd approach provides reliable estimation of single-trial latency, amplitude, and morphology of ERPs and thereby allows performing meaningful correlations at single-trial level. We obtained three main findings. First, WF significantly enhances the SNR of single-trial ERPs. Second, MLRd effectively captures and measures the variability in the morphology of single-trial ERPs, thus providing an accurate and unbiased estimate of their peak latency and amplitude. Third, intensity of pain perception significantly correlates with the single-trial estimates of N2 and P2 amplitude. These results indicate that WF+MLRd can be used to explore the dynamics between different ERP features, behavioral variables, and other neuroimaging measures of brain activity, thus providing new insights into the functional significance of the different brain processes underlying the brain responses to sensory stimuli. PMID:21880936
Ranganadh Narayanam
2015-10-01
Full Text Available The objective of this project is to discuss a versatile speech enhancement method based on the human auditory model. In this project a speech enhancement scheme is being described which meets the demand for quality noise reduction algorithms which are capable of operating at a very low signal to noise ratio. We will be discussing how proposed speech enhancement system is capable of reducing noise with little speech degradation in diverse noise environments. In this model to reduce the residual noise and improve the intelligibility of speech a psychoacoustic model is incorporated into the generalized perceptual wavelet denoising method to reduce the residual noise. This is a generalized time frequency subtraction algorithm which advantageously exploits the wavelet multirate signal representation to preserve the critical transient information. Simultaneous masking and temporal masking of the human auditory system are modeled by the perceptual wavelet packet transform via the frequency and temporal localization of speech components. To calculate the bark spreading energy and temporal spreading energy the wavelet coefficients are used from which a time frequency masking threshold is deduced to adaptively adjust the subtraction parameters of the discussed method. To increase the intelligibility of speech an unvoiced speech enhancement algorithm also integrated into the system.
Low-power Analog VLSI Implementation of Wavelet Transform
ZHANG Jiang-hong
2009-01-01
For applications requiring low-power, low-voltage and real-time, a novel analog VLSI implementation of continuous Marr wavelet transform based on CMOS log-domain integrator is proposed.Mart wavelet is approximated by a parameterized class of function and with Levenbery-Marquardt nonlinear least square method,the optimum parameters of this function are obtained.The circuits of implementating Mart wavelet transform are composed of analog filter whose impulse response is the required wavelet.The filter design is based on IFLF structure with CMOS log-domain integrators as the main building blocks.SPICE simulations indicate an excellent approximations of ideal wavelet.
Kong, Yun; Wang, Tianyang; Li, Zheng; Chu, Fulei
2017-01-01
Planetary transmission plays a vital role in wind turbine drivetrains, and its fault diagnosis has been an important and challenging issue. Owing to the complicated and coupled vibration source, time-variant vibration transfer path, and heavy background noise masking effect, the vibration signal of planet gear in wind turbine gearboxes exhibits several unique characteristics: Complex frequency components, low signal-to-noise ratio, and weak fault feature. In this sense, the periodic impulsive components induced by a localized defect are hard to extract, and the fault detection of planet gear in wind turbines remains to be a challenging research work. Aiming to extract the fault feature of planet gear effectively, we propose a novel feature extraction method based on spectral kurtosis and time wavelet energy spectrum (SK-TWES) in the paper. Firstly, the spectral kurtosis (SK) and kurtogram of raw vibration signals are computed and exploited to select the optimal filtering parameter for the subsequent band-pass filtering. Then, the band-pass filtering is applied to extrude periodic transient impulses using the optimal frequency band in which the corresponding SK value is maximal. Finally, the time wavelet energy spectrum analysis is performed on the filtered signal, selecting Morlet wavelet as the mother wavelet which possesses a high similarity to the impulsive components. The experimental signals collected from the wind turbine gearbox test rig demonstrate that the proposed method is effective at the feature extraction and fault diagnosis for the planet gear with a localized defect.
Kong, Yun; Wang, Tianyang; Li, Zheng; Chu, Fulei
2017-09-01
Planetary transmission plays a vital role in wind turbine drivetrains, and its fault diagnosis has been an important and challenging issue. Owing to the complicated and coupled vibration source, time-variant vibration transfer path, and heavy background noise masking effect, the vibration signal of planet gear in wind turbine gearboxes exhibits several unique characteristics: Complex frequency components, low signal-to-noise ratio, and weak fault feature. In this sense, the periodic impulsive components induced by a localized defect are hard to extract, and the fault detection of planet gear in wind turbines remains to be a challenging research work. Aiming to extract the fault feature of planet gear effectively, we propose a novel feature extraction method based on spectral kurtosis and time wavelet energy spectrum (SK-TWES) in the paper. Firstly, the spectral kurtosis (SK) and kurtogram of raw vibration signals are computed and exploited to select the optimal filtering parameter for the subsequent band-pass filtering. Then, the band-pass filtering is applied to extrude periodic transient impulses using the optimal frequency band in which the corresponding SK value is maximal. Finally, the time wavelet energy spectrum analysis is performed on the filtered signal, selecting Morlet wavelet as the mother wavelet which possesses a high similarity to the impulsive components. The experimental signals collected from the wind turbine gearbox test rig demonstrate that the proposed method is effective at the feature extraction and fault diagnosis for the planet gear with a localized defect.
Wavelet-Based Denoising Attack on Image Watermarking
XUAN Jian-hui; WANG Li-na; ZHANG Huan-guo
2005-01-01
In this paper, we propose wavelet-based denoising attack methods on image watermarking in discrete cosine transform (DCT) or discrete Fourier transform (DFT) domain or discrete wavelet transform (DWT) domain. Wiener filtering based on wavelet transform is performed in approximation subband to remove DCT or DFT domain watermark,and adaptive wavelet soft thresholding is employed to remove the watermark resided in detail subbands of DWT domain.
Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
Kensuke Fujinoki
2009-01-01
Full Text Available This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.
Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
Fujinoki Kensuke
2009-01-01
Full Text Available Abstract This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.
Optical Wavelet Signals Processing and Multiplexing
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2005-12-01
We present compact integrable architectures to perform the discrete wavelet transform (DWT) and the wavelet packet (WP) decomposition of an optical digital signal, and we show that the combined use of planar lightwave circuits (PLC) technology and multiresolution analysis (MRA) can add flexibility to current multiple access optical networks. We furnish the design guidelines to synthesize wavelet filters as two-port lattice-form planar devices, and we give some examples of optical signal denoising and compression/decompression techniques in the wavelet domain. Finally, we present a fully optical wavelet packet division multiplexing (WPDM) scheme where data signals are waveform-coded onto wavelet atom functions for transmission, and numerically evaluate its performances.
Adapted wavelet analysis from theory to software
Wickerhauser, Mladen Victor
1994-01-01
This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients
Optical Planar Discrete Fourier and Wavelet Transforms
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2007-10-01
We present all-optical architectures to perform discrete wavelet transform (DWT), wavelet packet (WP) decomposition and discrete Fourier transform (DFT) using planar lightwave circuits (PLC) technology. Any compact-support wavelet filter can be implemented as an optical planar two-port lattice-form device, and different subband filtering schemes are possible to denoise, or multiplex optical signals. We consider both parallel and serial input cases. We design a multiport decoder/decoder that is able to generate/process optical codes simultaneously and a flexible logarithmic wavelength multiplexer, with flat top profile and reduced crosstalk.
An Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization
2013-01-01
applications. We view the rows of a discrete cosine transform matrix as the filters associated with a multiresolution analysis. Non-decimated wavelet ...a redundant system which is formed by a set of transforms such as the discrete cosine transform, wavelets , framelets, and curvelets. The missing...vol. 93, pp. 273–299, 1965. [33] Q. Lian, L. Shen, Y. Xu, and L. Yang, “Filters of wavelets on invariant sets for image denoising ,” Applicable
郑明言
2014-01-01
为了有效地滤除红外图像中的噪声，提出了一种小波域多方向自适应加权伪中值滤波算法。该算法首先对红外噪声图像的各高频分解子图像分别进行噪声点检测和标记；然后根据各子图像中像素点分布特征分别设计出4类具有多方向性的滤波模板进行自适应加权滤波；最后将低频分解子图像与滤波后的各小波高频分解子图像进行重构。分别将中值滤波（MF）、伪中值滤波（PMF）、极值中值滤波（EMF）、加权中值滤波（WMF）、以及本文算法应用于标准测试图像以及红外图像去噪，并引入峰值信噪比（PSNR）、平均绝对误差（MAE）进行去噪效果评定。标准测试图像和红外图像仿真结果表明，该算法性能明显优于PMF，且相对于与其余几类同类型算法而言，也具有一定的优势。%In order to filter the noise in infrared image, a multi-direction adaptive weighted pseudo median filtering algorithm is proposed based on wavelet transform. Firstly, the salt & pepper noise image is conducted by wavelet transform, and the high-frequency sub-images and low-frequency sub-image are obtained. The noise distribution areas of the high-frequency sub-images are detected and labeled effectively. Then, according to the characteristics of the ground objects and the features of the directionality of the high frequency wavelet decomposition sub-images, four kinds of directional filtering templates are respectively designed so as to deal with the noise through adaptive weighted filtering. Finally, low-frequency sub-image and high-frequency sub-images are reconstructed. The median filtering(MF), pseudo median filtering(PMF), extreme median filtering(EMF), weighted median filtering(WMF) and the algorithm in this paper are used to filter the salt & pepper noise in standard test image and infrared image. Peak signal to noise ratio(PSNR) and mean absolute error (MAE)are adopted to evaluate the
Wavelet-based SAR images despeckling using joint hidden Markov model
Li, Qiaoliang; Wang, Guoyou; Liu, Jianguo; Chen, Shaobo
2007-11-01
In the past few years, wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the deficiency for taking account of intrascale correlations that exist among neighboring wavelet coefficients. In this paper, we propose to develop a joint hidden Markov model by fusing the wavelet Bayesian denoising technique with an image regularization procedure based on HMT and Markov random field (MRF). The Expectation Maximization algorithm is used to estimate hyperparameters and specify the mixture model. The noise-free wavelet coefficients are finally estimated by a shrinkage function based on local weighted averaging of the Bayesian estimator. It is shown that the joint method outperforms lee filter and standard HMT techniques in terms of the integrative measure of the equivalent number of looks (ENL) and Pratt's figure of merit(FOM), especially when dealing with speckle noise in large variance.
Lifting scheme of symmetric tight wavelets frames
ZHUANG BoJin; YUAN WeiTao; PENG LiZhong
2008-01-01
This paper proposes a method to realize the lifting scheme of tight frame wavelet filters. As for 4-channel tight frame wavelet filter, the tight frame transforms' ma-trix is 2×4, but the lifting scheme transforms' matrix must be 4×4. And in the case of 3-channel tight frame wavelet filter, the transforms' matrix is 2×3, but the lifting scheme transforms' matrix must be 3×3. In order to solve this problem, we intro-duce two concepts: transferred polyphase matrix for 4-channel filters and trans-ferred unitary matrix for 3-channel filters. The transferred polyphase matrix is sym-metric/antisymmetric. Thus, we use this advantage to realize the lifting scheme.
Harikumar, Rajaguru; Vijayakumar, Thangavel
2014-12-01
The objective of this paper is to compare the performance of singular value decomposition (SVD), expectation maximization (EM), and modified expectation maximization (MEM) as the postclassifiers for classifications of the epilepsy risk levels obtained from extracted features through wavelet transforms and morphological filters from electroencephalogram (EEG) signals. The code converter acts as a level one classifier. The seven features such as energy, variance, positive and negative peaks, spike and sharp waves, events, average duration, and covariance are extracted from EEG signals. Out of which four parameters like positive and negative peaksand spike and sharp waves, events and average duration are extracted using Haar, dB2, dB4, and Sym 8 wavelet transforms with hard and soft thresholding methods. The above said four features are also extracted through morphological filters. Then, the performance of the code converter and classifiers are compared based on the parameters such as performance index (PI) and quality value (QV).The performance index and quality value of code converters are at low value of 33.26% and 12.74, respectively. The highest PI of 98.03% and QV of 23.82 are attained at dB2 wavelet with hard thresholding method for SVD classifier. All the postclassifiers are settled at PI value of more than 90% at QV of 20.
Application of wavelet transform in active power filter harmonic analysis%小波变换在有源电力滤波器谐波分析中的应用
梁东莺; 毛蔚
2009-01-01
In order to effectively analyze and resolve Active impedance transform, wavelet transform on the use of harmonic and inter harmonic detection methods are studied, and on this basis to explore the use of wavelet analysis to study the control of time-frequency characteristics of impedance and frequency characteristics of the basic principles of analysis of the use of wavelet transform to separate harmonic inter-harmonic wave with the algorithm, taking into account time and frequency domain resolution. The simulation results show that the method not only has the characteristics of high-resolution, but also can identify the APF time-frequency impedance chara-cteristics, it is very useful for harmonic analysis, in the active power filter harmonic inhibitory aspects, and it has providing a feasible solution.%为有效分析和解决有源阻抗变换,对使用小波变换检测谐波与间谐波的方法进行了研究,并在此基础上探讨了利用小波分析、研究时频阻抗的控制特性和频率特性的基本原理,提出了利用小波变换来分离谐波与间谐波的算法,并兼顾时域和频域的分辨率.仿真结果表明,该方法不仅具有高分辨率特性,能较好地找出APF的时频阻抗特性,可以较好地分析谐波,以使其跟踪特性最优,为有源电力滤波器谐波抑制提供了可行的解决途径.
Image denoising using least squares wavelet support vector machines
Guoping Zeng; Ruizhen Zhao
2007-01-01
We propose a new method for image denoising combining wavelet transform and support vector machines (SVMs). A new image filter operator based on the least squares wavelet support vector machines (LSWSVMs) is presented. Noisy image can be denoised through this filter operator and wavelet thresholding technique. Experimental results show that the proposed method is better than the existing SVM regression with the Gaussian radial basis function (RBF) and polynomial RBF. Meanwhile, it can achieve better performance than other traditional methods such as the average filter and median filter.
Shukla, K K
2013-01-01
Due to its inherent time-scale locality characteristics, the discrete wavelet transform (DWT) has received considerable attention in signal/image processing. Wavelet transforms have excellent energy compaction characteristics and can provide perfect reconstruction. The shifting (translation) and scaling (dilation) are unique to wavelets. Orthogonality of wavelets with respect to dilations leads to multigrid representation. As the computation of DWT involves filtering, an efficient filtering process is essential in DWT hardware implementation. In the multistage DWT, coefficients are calculated
Perceptually Lossless Wavelet Compression
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
刘立生; 杨宇航
2012-01-01
主减速器(简称“主减”)是直升机传动系统的关键部件,它常处于高转速高负荷的恶劣环境下,对其运行状态进行预测,于直升机的安全性来说至关重要.鉴于此,提出了一种离散小波变换(DWT)、Kalman滤波以及Elman神经网络相结合的直升机主减智能状态预测系统:DWT使用“db44”母小波对振动信号进行分解提取特征向量,Kalman滤波对未来各时刻的特征向量进行预测,Elman神经网络对预测值进行故障辨识和分类.在Kalman滤波算法中,提出了一种新的预测算法,并用实验对该算法组成的系统进行验证,结果表明:该Kalman滤波算法预测效果好,更适用于对主减的特征向量进行预测；离散小波变换(DWT)、Kalman滤波以及Elman神经网络相结合组成的智能状态预测系统是可行的,它能很好地对主减的未来状态进行预测.%Main gearbox ( MGB) is a key component of a helicopter transmission system, it often runs under atrocious conditions of high rotating speed and high burden, it is very important to perform condition prognostic for safety of a helicopter. An intelligent condition prognostic system for helicopter MGB was presented here using discrete wavelet transformation (DWT) , Kalman filtering and Elman neural network. The mother wavelet of Daubechies 44 (db44) was selected to extract feature vectors in the process of DWT. Kalman filtering was used for feature vector prognostic, and Elman neural network was taken for fault discrimination and classification. In the algorithm of Kalman filtering, a new prognostic method was proposed, and it was verified with tests. The results indicated that the prognostic outcome of Kalman filtering with this method is better, it is more applicable for prognostic of feature vectors, and the intelligent condition prognostic system composed of DWT, Kalman filtering and Elman neural network is feasible, it can predict the future condition of a helicopter MGB
Fault diagnosis of radar filter based on wavelet transform and neural network%基于小波变换和神经网络的雷达滤波器故障诊断
王翔文; 李志华
2016-01-01
由于模拟电路的非线性、容差性及元器件参数的连续可变性等特点的存在，传统的模拟电路故障诊断手段在实际运用中已经很难得到令人满意的结果。本文将小波变换与神经网络结合，对特征提取进行优化，以雷达滤波电路为研究对象，在考虑容差性的情况下对电路进行故障诊断，体现出小波神经网络在诊断正确性及时效性上所具有的优势。%With the consideration of actual analog circuit has some characteristics, such as nonlinear-ity, tolerance and the continuous variability of parameters on component, it is difficult to achieve expected results for traditional technology of analog circuit fault diagnosis in particular engineering. In this paper, wavelet transform and neural network are combined to optimization the feature extraction. Taking into account the tolerance, we researched fault diagnosis of radar filter. The result shows that wavelet neural network method reflects its adventages from both diagnosis correctness and timeliness.
OPEN-LOOP FOG SIGNAL TESTING AND WAVELET ELIMINATING NOISE
ZHUYun-zhao; WANGShun-ring; MIAOLing-juan; WANGBo
2005-01-01
An open-loop fiber optic gyro (FOG) testing system is designed. The noise characteristic of open-loop fiber optic gyro signals is analyzed. The wavelet eliminating noise method is discussed and compared with other methods, such as smoothing and low-pass filter methods. Results indicate that the wavelet eliminating noise method can satisfy the measuring demand of the FOG weak output signal with noise disturbing. The wavelet analysis method can efficiently eliminate the noise and reserve the information of the signal. The eliminating noise effect of using different wavelet base functions is compared. The effectiveness of multiresolution wavelet analyses of eliminating noise is proved by experimental results.
OU Xiaojuan; ZHOU Wei
2007-01-01
Global positioning system (GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS common-view observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0＜H＜1,the 1/f fractal characteristic of the GPS clock difference data iS a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difierence can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.
Complex Wavelet Based Modulation Analysis
Luneau, Jean-Marc; Lebrun, Jérôme; Jensen, Søren Holdt
2008-01-01
because only the magnitudes are taken into account and the phase data is often neglected. We remedy this problem with the use of a complex wavelet transform as a more appropriate envelope and phase processing tool. Complex wavelets carry both magnitude and phase explicitly with great sparsity and preserve well...... polynomial trends. Moreover an analytic Hilbert-like transform is possible with complex wavelets implemented as an orthogonal filter bank. By working in an alternative transform domain coined as “Modulation Subbands”, this transform shows very promising denoising capabilities and suggests new approaches for joint...
Wavelet-Fourier self-deconvolution
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Kaakinen, M; Huttunen, S; Paavolainen, L; Marjomäki, V; Heikkilä, J; Eklund, L
2014-01-01
Phase-contrast illumination is simple and most commonly used microscopic method to observe nonstained living cells. Automatic cell segmentation and motion analysis provide tools to analyze single cell motility in large cell populations. However, the challenge is to find a sophisticated method that is sufficiently accurate to generate reliable results, robust to function under the wide range of illumination conditions encountered in phase-contrast microscopy, and also computationally light for efficient analysis of large number of cells and image frames. To develop better automatic tools for analysis of low magnification phase-contrast images in time-lapse cell migration movies, we investigated the performance of cell segmentation method that is based on the intrinsic properties of maximally stable extremal regions (MSER). MSER was found to be reliable and effective in a wide range of experimental conditions. When compared to the commonly used segmentation approaches, MSER required negligible preoptimization steps thus dramatically reducing the computation time. To analyze cell migration characteristics in time-lapse movies, the MSER-based automatic cell detection was accompanied by a Kalman filter multiobject tracker that efficiently tracked individual cells even in confluent cell populations. This allowed quantitative cell motion analysis resulting in accurate measurements of the migration magnitude and direction of individual cells, as well as characteristics of collective migration of cell groups. Our results demonstrate that MSER accompanied by temporal data association is a powerful tool for accurate and reliable analysis of the dynamic behaviour of cells in phase-contrast image sequences. These techniques tolerate varying and nonoptimal imaging conditions and due to their relatively light computational requirements they should help to resolve problems in computationally demanding and often time-consuming large-scale dynamical analysis of cultured cells.
A Comparative Study of Wavelet Thresholding for Image Denoising
Arun Dixit
2014-11-01
Full Text Available Image denoising using wavelet transform has been successful as wavelet transform generates a large number of small coefficients and a small number of large coefficients. Basic denoising algorithm that using the wavelet transform consists of three steps – first computing the wavelet transform of the noisy image, thresholding is performed on the detail coefficients in order to remove noise and finally inverse wavelet transform of the modified coefficients is taken. This paper reviews the state of art methods of image denoising using wavelet thresholding. An Experimental analysis of wavelet based methods Visu Shrink, Sure Shrink, Bayes Shrink, Prob Shrink, Block Shrink and Neigh Shrink Sure is performed. These wavelet based methods are also compared with spatial domain methods like median filter and wiener filter. Results are evaluated on the basis of Peak Signal to Noise Ratio and visual quality of images. In the experiment, wavelet based methods perform better than spatial domain methods. In wavelet domain, recent methods like prob shrink, block shrink and neigh shrink sure performed better as compared to other wavelet based methods.
Wavelet and wavelet packet compression of electrocardiograms.
Hilton, M L
1997-05-01
Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.
Implementational Aspects of the Contourlet Filter Bank and Application in Image Coding
Truong T. Nguyen
2009-02-01
Full Text Available This paper analyzed the implementational aspects of the contourlet filter bank (or the pyramidal directional filter bank (PDFB, and considered its application in image coding. First, details of the binary tree-structured directional filter bank (DFB are presented, including a modification to minimize the phase delay factor and necessary steps for handling rectangular images. The PDFB is viewed as an overcomplete filter bank, and the directional filters are expressed in terms of polyphase components of the pyramidal filter bank and the conventional DFB. The aliasing effect of the conventional DFB and the Laplacian pyramid to the directional filters is then considered, and the conditions for reducing this effect are presented. The new filters obtained by redesigning the PDFBs satisfying these requirements have much better frequency responses. A hybrid multiscale filter bank consisting of the PDFB at higher scales and the traditional maximally decimated wavelet filter bank at lower scales is constructed to provide a sparse image representation. A novel embedded image coding system based on the image decomposition and a morphological dilation algorithm is then presented. The coding algorithm efficiently clusters the significant coefficients using progressive morphological operations. Context models for arithmetic coding are designed to exploit the intraband dependency and the correlation existing among the neighboring directional subbands. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art wavelet-based coders, such as JPEG2000, for images with directional features.
Higher-density dyadic wavelet transform and its application
Qin, Yi; Tang, Baoping; Wang, Jiaxu
2010-04-01
This paper proposes a higher-density dyadic wavelet transform with two generators, whose corresponding wavelet filters are band-pass and high-pass. The wavelet coefficients at each scale in this case have the same length as the signal. This leads to a new redundant dyadic wavelet transform, which is strictly shift invariant and further increases the sampling in the time dimension. We describe the definition of higher-density dyadic wavelet transform, and discuss the condition of perfect reconstruction of the signal from its wavelet coefficients. The fast implementation algorithm for the proposed transform is given as well. Compared with the higher-density discrete wavelet transform, the proposed transform is shift invariant. Applications into signal denoising indicate that the proposed wavelet transform has better denoising performance than other commonly used wavelet transforms. In the end, various typical wavelet transforms are applied to analyze the vibration signals of two faulty roller bearings, the results show that the proposed wavelet transform can more effectively extract the fault characteristics of the roller bearings than the other wavelet transforms.
Wavelet Based Semi-blind Channel Estimation For Multiband OFDM
Sadough, Sajad; Ichir, Mahieddine; Jaffrot, Emmanuel; Duhamel, Pierre
2007-01-01
This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response in order to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the nu...
Performance Evaluation of Wavelet Based on Human Visual System
胡海平; 莫玉龙
2002-01-01
We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function(MTF) of human visual system in the frequency domain.In this paper,we evaluate performance of the constructed wavelet,and compare it with the widely used Daubechies9-7,Daubechies 9-3 and GBCW-9-7 wavelets.The result shows that coding performance of the constructed wavelet is better than Daubechies9-3,and is competitive with Daubechies 9-7 and GBCW-9-7 wavelets.Like Dauechies 9-3 wavelet,the filter coefficients of the constructed waveklet are all dyadic fractions,and the tap is less than Daubechies 9-7 and GBOW 9-7,It has an attractive feature in the realization of discrete wavelet transform.
A comparison of wavelet analysis techniques in digital holograms
Molony, Karen M.; Maycock, Jonathan; McDonald, John B.; Hennelly, Bryan M.; Naughton, Thomas J.
2008-04-01
This study explores the effectiveness of wavelet analysis techniques on digital holograms of real-world 3D objects. Stationary and discrete wavelet transform techniques have been applied for noise reduction and compared. Noise is a common problem in image analysis and successful reduction of noise without degradation of content is difficult to achieve. These wavelet transform denoising techniques are contrasted with traditional noise reduction techniques; mean filtering, median filtering, Fourier filtering. The different approaches are compared in terms of speckle reduction, edge preservation and resolution preservation.
A Novel Digital Audio Watermarking Scheme in the Wavelet Domain
WANG Xiang-yang; YANG Hong-ying; ZHAO Hong
2005-01-01
We present a novel quantization-based digital audio watermarking scheme in wavelet domain. By quantizing a host audio's wavelet coefficients (Integer Lifting Wavelet Transform ) and utilizing the characteristics of human auditory system ( HAS), the gray image is embedded using our watermarking method. Experimental results show that the proposed watermarking scheme is inaudible and robust against various signal processing such as noising adding, lossy compression, low pass filtering, re-sampling, and re-quantifying.
武海洋; 王慧; 樊菊
2011-01-01
Filtering is one of the essential tasks in the processing and applications of remote sensing images,and image filtering based on wavelet transformation has now become the mainstream in the area.Aimed at the disadvantages in NeighShrink, the author proposed an improved strategy for threshold estimation and coefficients shrinkage, and the improved method based on DSWT was implemented.Experimentation validated the algorithm, and the PSNR was adopted to evaluate the performance of improved algorithms.%针对NeighShrink滤波算法存在的不足,提出了改进的阈值估计策略和系数收缩方案,并将改进算法与静态小波变换相结合进行图像滤波,取到了较好的滤波效果.实验验证了改进算法的有效性,以峰值信噪比PSNR作为客观评价指标,通过与经典方法的比较,对该算法的滤波性能做出了客观评价.
陈晓; 徐家品
2011-01-01
The unmanned aerial image in real-time transmission process, there may be mixed by both impulsive and Gaussian noise pollution, for the subsequent identification of the image caused great difficulties. In response, this paper based on median filter and wavelet transform for image denoising. Simulation results show that the method can effectively filter and Gaussian mixture impulsive noise, and can keep a good image detail, to improve the image of the visual effects.%在无人机航拍图像的实时传输过程中,有可能会同时受到脉冲和高斯混合噪声的污染,为后续图像的识别造成很大的困难.针对这种情况,提出了一种基于中值滤波和小波变换相结合的图像去噪方法.仿真结果表明,该方法不仅能有效地滤除脉冲和高斯的混合噪声,而且可以很好地保留图像的细节信息,改善图像的视觉效果.
Orthogonal M-band compactly supported interpolating wavelet theory
张建康; 保铮
1999-01-01
Recently, 2-band interpolating wavelet transform has attracted much attention. It has the following several features: (ⅰ)The wavelet series transform coefficients of a signal in the multiresolution subspace are exactly consistent with its discrete wavelet transform coefficints; (ⅱ)good approximation performance; (ⅲ)efficiency in computation.However orthogonal 2-band compactly supported interpolating wavelet transform is only the first order. In order to overcome this shortcoming, the orthogonal M-band compactly supported interpolating wavelet basis is established. First, the unitary interpolating scaling filters of the length L=MK are characterized. Second, a scheme is given to design highorder unitary interpolating scaling filters. Third, a parameterization of the unitary interpolating scaling filters of the length L=4M is made. Fourth, the orthogonal 2-order and 3-order three-band compactly supported interpolating scaling functions are constructed. Finally, the properties of the orthogonal M-band c
杨莉媛; 崔建明
2012-01-01
煤与瓦斯突出是煤矿开采业中最为严重的自然灾害之一。煤体的声发射信号能够反应煤体的受力情况，并通过对声发射信号的监测可以来实现煤与瓦斯突出的非接触式预测。本文将小波变换用于煤与瓦斯突出有效信号提取中，利用小波变换良好的时频特性，将采集到的声发射信号分解在不同的尺度上，从而较好的滤除噪声。这种方法的有效性在Matlab仿真软件中得到了验证了。%The coal and gas outburst is one of the worst natural disasters in the coal mining industry. The acoustic emission signals in coal can reflect the forces of the coal body, and we can monitor the acoustic emission signal to achieve the non-contact of coal and gas outburst prediction In this paper, wavelet transform is used in the extraction of coal and gas outburst effectively signal. Using the frequency characteristics of the wavelet transform, acoustic emission signal collected can decompose in a different scale, so that it can filter out the noise very well. The effectiveness of this method has been verified in Matlab simulation software.
Li Song
2010-04-01
Full Text Available Abstract Background Quantitative proteomics technologies have been developed to comprehensively identify and quantify proteins in two or more complex samples. Quantitative proteomics based on differential stable isotope labeling is one of the proteomics quantification technologies. Mass spectrometric data generated for peptide quantification are often noisy, and peak detection and definition require various smoothing filters to remove noise in order to achieve accurate peptide quantification. Many traditional smoothing filters, such as the moving average filter, Savitzky-Golay filter and Gaussian filter, have been used to reduce noise in MS peaks. However, limitations of these filtering approaches often result in inaccurate peptide quantification. Here we present the WaveletQuant program, based on wavelet theory, for better or alternative MS-based proteomic quantification. Results We developed a novel discrete wavelet transform (DWT and a 'Spatial Adaptive Algorithm' to remove noise and to identify true peaks. We programmed and compiled WaveletQuant using Visual C++ 2005 Express Edition. We then incorporated the WaveletQuant program in the Trans-Proteomic Pipeline (TPP, a commonly used open source proteomics analysis pipeline. Conclusions We showed that WaveletQuant was able to quantify more proteins and to quantify them more accurately than the ASAPRatio, a program that performs quantification in the TPP pipeline, first using known mixed ratios of yeast extracts and then using a data set from ovarian cancer cell lysates. The program and its documentation can be downloaded from our website at http://systemsbiozju.org/data/WaveletQuant.
3-D wavelet compression and progressive inverse wavelet synthesis rendering of concentric mosaic.
Luo, Lin; Wu, Yunnan; Li, Jin; Zhang, Ya-Qin
2002-01-01
Using an array of photo shots, the concentric mosaic offers a quick way to capture and model a realistic three-dimensional (3-D) environment. We compress the concentric mosaic image array with a 3-D wavelet transform and coding scheme. Our compression algorithm and bitstream syntax are designed to ensure that a local view rendering of the environment requires only a partial bitstream, thereby eliminating the need to decompress the entire compressed bitstream before rendering. By exploiting the ladder-like structure of the wavelet lifting scheme, the progressive inverse wavelet synthesis (PIWS) algorithm is proposed to maximally reduce the computational cost of selective data accesses on such wavelet compressed datasets. Experimental results show that the 3-D wavelet coder achieves high-compression performance. With the PIWS algorithm, a 3-D environment can be rendered in real time from a compressed dataset.
CLOSED FORM OF THE STEERED ELONGATED HERMITE-GAUSS WAVELETS
Papari, Giuseppe; Campisi, Patrizio; Petkov, Nicolai
2010-01-01
We provide a closed form, both in the spatial and in the frequency domain, of a family of wavelets which arise from steering elongated Hermite-Gauss filters. These wavelets have interesting mathematical properties, as they form new dyadic families of eigenfunctions of the 2D Fourier transform, and
白浪; 雷旭升; 盛蔚; 杜玉虎
2012-01-01
针对小型无人旋翼机自主飞行时高度测量信息不稳定、易受干扰的问题,提出采用基于滤波数据的自适应高度信息融合方法来提高无人旋翼机高度测量信息的精度和可信度.通过基于小波提升算法的小波分解重构方法,消除原始测量数据中的高频噪声;根据全球定位系统的测量精度受搜到卫星数目波动影响的现象,提出利用自适应卡尔曼滤波的方法实现高度信息融合.通过自主悬停和三维航迹跟踪飞行试验验证该方法的可行性和有效性.%Focusing on the low performance of the sensors for the small unmanned aerial rotorcraft,an adaptive Kalman method based on filter data was proposed to improve the accuracy and reliability of the altitude measurement information.Using the wavelet decomposition and reconstruction filter,the high frequency noise of altitude information for the small unmanned aerial rotorcraft was eliminated.Furthermore,since the global positioning system（GPS） measurement accuracy was influenced by GPS satellite-number fluctuation,an adaptive Kalman filter was used to improve altitude measurement performance.At last,hovering flight and three-dimensional track flight test were used to verify the feasibility and effectiveness of the method.
ON CONVERGENCE OF WAVELET PACKET EXPANSIONS
Morten Nielsen
2002-01-01
It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.
Multiresolution signal decomposition transforms, subbands, and wavelets
Akansu, Ali N; Haddad, Paul R
2001-01-01
The uniqueness of this book is that it covers such important aspects of modern signal processing as block transforms from subband filter banks and wavelet transforms from a common unifying standpoint, thus demonstrating the commonality among these decomposition techniques. In addition, it covers such ""hot"" areas as signal compression and coding, including particular decomposition techniques and tables listing coefficients of subband and wavelet filters and other important properties.The field of this book (Electrical Engineering/Computer Science) is currently booming, which is, of course
单昊
2015-01-01
Astronomical images have complex morphological and hierarchical structures and irregular shaped textures, and they can be represented at different scales and directions. The purpose of this paper is to represent astronomical textures, and its mechanism is assumed from the perspective of orthogonality to extract the texture information. Based on orthogonality optimization criterion( OOC) , wavelet filters, and anisotropic diffusion ( AD) , a method is presented to extract texture features for astronomical images. The theory assumes that the oscillation/texture component and the smooth piecewise/cartoon component are orthogonal to each other. The core technology is a parameter estimation method based on the orthogonality and AD. Firstly, the orthogonality measurement based wavelet thresholding scheme is adopted, and the multi-scale framework is used to extract and analyze the astronomical textures at different scales and directions. Then, the filtered smooth piecewise component is used to initialize AD. The parameter estimation is mainly applied to estimate the thresholds for multiscale wavelet filtering and AD iteration number. The images of galaxies and gravitational lensing are adopted for numerical experiments, and comparisons are implemented with 6 types of the currently used methods of image decomposition. The experimental results show that the proposed method can gain satisfying results in extracting astronomical textures, and it has advantages and advancement compared to other methods.%天文图像具有复杂的形态学层级结构和不规则的纹理形态，可在不同尺度和方向上表示。该文针对天文纹理表示，从正交性对其机理进行假设，从而提取纹理信息。基于正交优化准则( OOC)、小波以及各向异性耗散( AD)，提出一种天文图像的纹理特征提取方法。该方法的理论假设为图像纹理和分段平滑分量互相正交，核心技术是正交性参数估计。首先采用基于正交
Research on Far-Field Wavelet's Extraction and Application of Vertical Cable System
Wang, Xiangchun; Xiao, Qingsong; Xia, Changliang; Wu, Zhongliang; Xie, Chengliang
2017-03-01
In marine seismic exploration, ghost wave and bubble effect reduce the vertical resolution and interpretation accuracy seriously. Here firstly the far-field wavelet including source wavelet, ghost wave and bubble effect recorded by the vertical cable system (VCS) is extracted. Then, filters are designed using the extracted far-field wavelet to eliminate ghost wave, bubble effect and source wavelet. At last, the designed filters are applied to the seismic data of VCS. The results show that this method can eliminate ghost wave, bubble effect and source wavelet effectively and the vertical resolution of the seismic data is improved obviously.
赵静
2013-01-01
为了提高虹膜定位的准确率和速度,提出了一种基于二维小波变换及邻域均值滤波的虹膜定位算法.采用阈值法分割瞳孔,使用边缘检测算子检测瞳孔区域边缘,定位虹膜内边缘；然后对人眼图像进行二维小波处理降低虹膜图像的分辨率,以减少虹膜本身的纹理对判断外边缘点时所产生的影响；最后采用邻域均值滤波进行虹膜外边缘点提取,根据所得虹膜外边缘点确定虹膜外边界.仿真结果表明:该算法定位虹膜内外边界的平均时间为1.75s,准确卒为99.7％,其中虹膜外边缘定位误差小于4.2％,在虹膜识别系统中有较高的实际应用价值.%An iris localization algorithm based on two-dimensional wavelet transform and neighborhood average filter is proposed to improve the accuracy and the speed of the iris localization. Firstly, the algorithm segments the pupil area of the iris by the threshold. Secondly, it locates the iris inner edge by the edge detection operator in the pupil area. Thirdly, the human eye iris images is processed by the two-dimensional wavelet transform to reduce the image resolution, In order to reduce the impact of the iris texture on the judgment of the iris outer edge points. Fourthly, the algorithm extracts the iris outer edge points by the neighborhood average filter. Finally, it locates the iris outer edge by the outer edge points. The simulation results show that the algorithm locates the iris inner and outer edge with average time of 1. 75 s and accuracy of 99. 7%, the error of iris outer edge localization is less than 4. 2%, The algorithm has a higher practical value in the iris recognition system.
徐华楠; 刘哲; 刘灿
2012-01-01
This paper proposed a method of denoising the remote sensing image based on àtrous-nonsubsampled contourlet transform.The method uses the àtrous wavelet—an undecimated discrete wavelet transform algorithm to decompose the image into two parts possessing approximate part and detail parts,which are the same size as the original image.Then the nonsubsampled directional filter bank is employed to decompose the detail parts into directional subbands.The different kinds of noises of the remote sensing image can be decomposed into the wavelet coefficients in different scale and directions,with which the best method can be chosen based on the characteristics of the different noises.It is more scientific and more effective than just using one method for all kinds of noises in the past.It is proved that the method proposed in the paper is more useful in removing the noise of the image,reserving richer fine textures and edge information than other traditional filtering methods.%结合àtrous小波变换和非下采样轮廓波变换的优点,提出一种基于àtrous-非下采样轮廓波变换的遥感图像去噪方法.该方法用非抽取离散小波变换的àtrous算法对图像进行多尺度分解,然后用非下采样的多方向滤波器组对得到的细节分量进行多方向分解.对含有多种噪声的遥感图像,àtrous-非下采样轮廓波变换将图像中不同种类的噪声分解到不同的小波系数分量中,使得可以根据噪声特性选择最合适的去噪方法,比用一种方法去除所有类型的噪声更科学且去噪效果更好.
A Novel Algorithm for Robust Audio Watermarking in Wavelet Domain
FU Yu; WANG Bao-bao; LI Chun-ru; QUAN Ning-qiang
2004-01-01
A novel algorithm for digital audio watermarking in wavelet domain is proposed. First,an original audio signal is decomposed by discrete wavelet transform at three levels. Then, a discrete watermark is embedded into the coefficients of its intermediate frequencies. Finally, the watermarked audio signal is obtained by wavelet reconstruction. The proposed algorithm makes good use of the multiresolution characteristics of wavelet transform. The original audio signal is not needed when detecting the watermark correlatively. Simulation results show that the algorithm is inaudible and robust to noise, filtering and resampling.
Multiuser detector based on wavelet networks
王伶; 焦李成; 陶海红; 刘芳
2004-01-01
Multiple access interference (MAI) and near-far problem are two major obstacles in DS-CDMA systems.Combining wavelet neural networks and two matched filters, the novel multiuser detector, which is based on multiple variable function estimation wavelet networks over single path asynchronous channel and space-time channel respectively is presented. Excellent localization characteristics of wavelet functions in both time and frequency domains allowed hierarchical multiple resolution learning of input-output data mapping. The mathematic frame of the neural networks and error back ward propagation algorithm are introduced. The complexity of the multiuser detector only depends on that of wavelet networks. With numerical simulations and performance analysis, it indicates that the multiuser detector has excellent performance in eliminating MAI and near-far resistance.
Wavelet-based acoustic recognition of aircraft
Dress, W.B.; Kercel, S.W.
1994-09-01
We describe a wavelet-based technique for identifying aircraft from acoustic emissions during take-off and landing. Tests show that the sensor can be a single, inexpensive hearing-aid microphone placed close to the ground the paper describes data collection, analysis by various technique, methods of event classification, and extraction of certain physical parameters from wavelet subspace projections. The primary goal of this paper is to show that wavelet analysis can be used as a divide-and-conquer first step in signal processing, providing both simplification and noise filtering. The idea is to project the original signal onto the orthogonal wavelet subspaces, both details and approximations. Subsequent analysis, such as system identification, nonlinear systems analysis, and feature extraction, is then carried out on the various signal subspaces.
Denoising CT Images using wavelet transform
Lubna Gabralla
2015-05-01
Full Text Available Image denoising is one of the most significant tasks especially in medical image processing, where the original images are of poor quality due the noises and artifacts introduces by the acquisition systems. In this paper, we propose a new image denoising scheme by modifying the wavelet coefficients using soft-thresholding method, we present a comparative study of different wavelet denoising techniques for CT images and we discuss the obtained results. The denoising process rejects noise by thresholding in the wavelet domain. The performance is evaluated using Peak Signal-to-Noise Ratio (PSNR and Mean Squared Error (MSE. Finally, Gaussian filter provides better PSNR and lower MSE values. Hence, we conclude that this filter is an efficient one for preprocessing medical images.
Generalized Tree-Based Wavelet Transform
Ram, Idan; Cohen, Israel
2010-01-01
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in \\cite{gavish2010mwot}, and it is similarly defined via a hierarchical tree, which is assumed to capture the geometry and structure of the input data. It is applied to the data using a multiscale filtering and decimation scheme, which can employ different wavelet filters. We propose a tree construction method which results in efficient representation of the input function in the transform domain. We show that the proposed transform is more efficient than both the 1D and 2D separable wavelet transforms in representing images. We also explore the application of the proposed transform to image denoising, and show that combined with a subimage averaging scheme, it achieves denoising results which are similar to the ones obtained with the K-SVD algorithm.
A New Adaptive Mother Wavelet for Electromagnetic Transient Analysis
Guillén, Daniel; Idárraga-Ospina, Gina; Cortes, Camilo
2016-01-01
Wavelet Transform (WT) is a powerful technique of signal processing, its applications in power systems have been increasing to evaluate power system conditions, such as faults, switching transients, power quality issues, among others. Electromagnetic transients in power systems are due to changes in the network configuration, producing non-periodic signals, which have to be identified to avoid power outages in normal operation or transient conditions. In this paper a methodology to develop a new adaptive mother wavelet for electromagnetic transient analysis is proposed. Classification is carried out with an innovative technique based on adaptive wavelets, where filter bank coefficients will be adapted until a discriminant criterion is optimized. Then, its corresponding filter coefficients will be used to get the new mother wavelet, named wavelet ET, which allowed to identify and to distinguish the high frequency information produced by different electromagnetic transients.
Image coding based on energy-sorted wavelet packets
Kong, Lin-Wen; Lay, Kuen-Tsair
1995-04-01
The discrete wavelet transform performs multiresolution analysis, which effectively decomposes a digital image into components with different degrees of details. In practice, it is usually implemented in the form of filter banks. If the filter banks are cascaded and both the low-pass and the high-pass components are further decomposed, a wavelet packet is obtained. The coefficients of the wavelet packet effectively represent subimages in different resolution levels. In the energy-sorted wavelet- packet decomposition, all subimages in the packet are then sorted according to their energies. The most important subimages, as measured by the energy, are preserved and coded. By investigating the histogram of each subimage, it is found that the pixel values are well modelled by the Laplacian distribution. Therefore, the Laplacian quantization is applied to quantized the subimages. Experimental results show that the image coding scheme based on wavelet packets achieves high compression ratio while preserving satisfactory image quality.
Group-normalized processing of complex wavelet packets
石卓尔; 保铮
1997-01-01
Linear phase is not possible for real valued FIR QMF, while linear phase FIR biorthogonal wavelet filter banks make the mean squared error of the constructed signal exceed that of the quantization error. W Lawton’ s method for complex valued wavelets construction is extended to generate the complex valued compactly supported wavelet packets that are symmetrical and unitary orthogonal; then well-defined wavelet packets are chosen by the analysis remarks on their time-frequency characteristics. Since the traditional wavelel packets transform coefficients do not exactly represent the strength of signal components, a modified adaptive wavelets transform, group-normalized wavelet packet transform (GNWPT), is presented and utilized for target extraction from formidable clutter or noises with the time-frequency masking technique. The extended definition of lp-norm entropy improves the performance cf GNWPT. Similar method can also be applied to image enhancement, clutter and noise suppression, optimal detection
Brendle, Joerg
2016-01-01
We show that, consistently, there can be maximal subtrees of P (omega) and P (omega) / fin of arbitrary regular uncountable size below the size of the continuum. We also show that there are no maximal subtrees of P (omega) / fin with countable levels. Our results answer several questions of Campero, Cancino, Hrusak, and Miranda.
Szu, H.; Hsu, C. [Univ. of Southwestern Louisiana, Lafayette, LA (United States)
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Singh, Ram Chandra; Bhatla, Rajeev
2012-07-01
This paper deals with the meteorological applications of wavelets and fuzzy logics and a hybrid of wavelets and fuzzy logics. The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex non-stationary signals. It has been shown that the wavelet transform is a flexible time-frequency decomposition tool which can form the basis of useful time series analysis. It is expected to see an increased amount of research and technology development work in the coming years employing wavelets for various scientific and engineering applications.
van den Berg, J. C.
2004-03-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
New Algorithm For Calculating Wavelet Transforms
Piotr Lipinski
2009-04-01
Full Text Available In this article we introduce a new algorithm for computing Discrete Wavelet Transforms (DWT. The algorithm aims at reducing the number of multiplications, required to compute a DWT. The algorithm is general and can be used to compute a variety of wavelet transform (Daubechies and CDF. Here we focus on CDF 9/7 filters, which are used in JPEG2000 compression standard. We show that the algorithm outperforms convolution-based and lifting-based algorithms in terms of number of multiplications.
ECG signal denoising via empirical wavelet transform.
Singh, Omkar; Sunkaria, Ramesh Kumar
2016-12-29
This paper presents new methods for baseline wander correction and powerline interference reduction in electrocardiogram (ECG) signals using empirical wavelet transform (EWT). During data acquisition of ECG signal, various noise sources such as powerline interference, baseline wander and muscle artifacts contaminate the information bearing ECG signal. For better analysis and interpretation, the ECG signal must be free of noise. In the present work, a new approach is used to filter baseline wander and power line interference from the ECG signal. The technique utilized is the empirical wavelet transform, which is a new method used to compute the building modes of a given signal. Its performance as a filter is compared to the standard linear filters and empirical mode decomposition.The results show that EWT delivers a better performance.
LIDAR data compression using wavelets
Pradhan, B.; Mansor, Shattri; Ramli, Abdul Rahman; Mohamed Sharif, Abdul Rashid B.; Sandeep, K.
2005-10-01
The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. In this paper, it is extended to the LIDAR data compression. A newly developed data compression approach to approximate the LIDAR surface with a series of non-overlapping triangles has been presented. Generally a Triangulated Irregular Networks (TIN) are the most common form of digital surface model that consists of elevation values with x, y coordinates that make up triangles. But over the years the TIN data representation has become a case in point for many researchers due its large data size. Compression of TIN is needed for efficient management of large data and good surface visualization. This approach covers following steps: First, by using a Delaunay triangulation, an efficient algorithm is developed to generate TIN, which forms the terrain from an arbitrary set of data. A new interpolation wavelet filter for TIN has been applied in two steps, namely splitting and elevation. In the splitting step, a triangle has been divided into several sub-triangles and the elevation step has been used to 'modify' the point values (point coordinates for geometry) after the splitting. Then, this data set is compressed at the desired locations by using second generation wavelets. The quality of geographical surface representation after using proposed technique is compared with the original LIDAR data. The results show that this method can be used for significant reduction of data set.
K B Athreya
2009-09-01
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy $\\int fh_id_=_i$ for $i=1,2,\\ldots,\\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\\exp(\\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.
On The Harmonics Reduction Using Wavelet Based Signal Processing
Marian GAICEANU
2000-12-01
Full Text Available This paper presents a method for calculating the reference currents needed for the command of an active filter. By using the Discrete Wavelet Transform (DWT the high-frequency components of the currents are eliminated. Also, a reference is delivered to the control block of the active filter and a comparison is made between the DWT and the classical Fourier transform.
A Novel Detection and Classification Algorithm for Power Quality Disturbances using Wavelets
C. Sharmeela
2006-01-01
Full Text Available This study presents a novel method to detect and classify power quality disturbances using wavelets. The proposed algorithm uses different wavelets each for a particular class of disturbance. The method uses wavelet filter banks in an effective way and does multiple filtering to detect the disturbances. A qualitative comparison of results shows the advantages and drawbacks of each wavelet when applied to the detection of the disturbances. This method is tested for a large class of test conditions simulated in MATLAB. Power quality monitoring together with the ability of the proposed algorithm to classify the disturbances will be a powerful tool for the power system engineers.
Wavelet transform in electrocardiography--data compression.
Provazník, I; Kozumplík, J
1997-06-01
An application of the wavelet transform to electrocardiography is described in the paper. The transform is used as a first stage of a lossy compression algorithm for efficient coding of rest ECG signals. The proposed technique is based on the decomposition of the ECG signal into a set of basic functions covering the time-frequency domain. Thus, non-stationary character of ECG data is considered. Some of the time-frequency signal components are removed because of their low influence to signal characteristics. Resulting components are efficiently coded by quantization, composition into a sequence of coefficients and compression by a run-length coder and a entropic Huffman coder. The proposed wavelet-based compression algorithm can compress data to average code length about 1 bit/sample. The algorithm can be also implemented to a real-time processing system when wavelet transform is computed by fast linear filters described in the paper.
Denoising time-domain induced polarisation data using wavelet techniques
Deo, Ravin N.; Cull, James P.
2016-05-01
Time-domain induced polarisation (TDIP) methods are routinely used for near-surface evaluations in quasi-urban environments harbouring networks of buried civil infrastructure. A conventional technique for improving signal to noise ratio in such environments is by using analogue or digital low-pass filtering followed by stacking and rectification. However, this induces large distortions in the processed data. In this study, we have conducted the first application of wavelet based denoising techniques for processing raw TDIP data. Our investigation included laboratory and field measurements to better understand the advantages and limitations of this technique. It was found that distortions arising from conventional filtering can be significantly avoided with the use of wavelet based denoising techniques. With recent advances in full-waveform acquisition and analysis, incorporation of wavelet denoising techniques can further enhance surveying capabilities. In this work, we present the rationale for utilising wavelet denoising methods and discuss some important implications, which can positively influence TDIP methods.
Skopina, Maria; Protasov, Vladimir
2016-01-01
This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is ...
Hramov, Alexander E; Makarov, Valeri A; Pavlov, Alexey N; Sitnikova, Evgenia
2015-01-01
This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade. Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics. Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural ...
Wavelets, vibrations and scalings
Meyer, Yves
1997-01-01
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet "saga", Meye...
Adaptive wavelet transform algorithm for lossy image compression
Pogrebnyak, Oleksiy B.; Ramirez, Pablo M.; Acevedo Mosqueda, Marco Antonio
2004-11-01
A new algorithm of locally adaptive wavelet transform based on the modified lifting scheme is presented. It performs an adaptation of the wavelet high-pass filter at the prediction stage to the local image data activity. The proposed algorithm uses the generalized framework for the lifting scheme that permits to obtain easily different wavelet filter coefficients in the case of the (~N, N) lifting. Changing wavelet filter order and different control parameters, one can obtain the desired filter frequency response. It is proposed to perform the hard switching between different wavelet lifting filter outputs according to the local data activity estimate. The proposed adaptive transform possesses a good energy compaction. The designed algorithm was tested on different images. The obtained simulation results show that the visual and quantitative quality of the restored images is high. The distortions are less in the vicinity of high spatial activity details comparing to the non-adaptive transform, which introduces ringing artifacts. The designed algorithm can be used for lossy image compression and in the noise suppression applications.
Making electromagnetic wavelets
Kaiser, Gerald [Center for Signals and Waves, 3803 Tonkawa Trail no. 2, Austin, TX 78756-3915 (United States)
2004-06-04
Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.
Extraction of MHD Signal Based on Wavelet Transform
赵晴初; 赵彤; 李旻; 黄胜华; 徐佩霞
2002-01-01
Mirnov signals mixed with interferences are a kind of non-stationary signal. It can not obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.
Wind Speed Forecasting Using Hybrid Wavelet Transform—ARMA Techniques
Diksha Kaur; Tek Tjing Lie; Nirmal K. C. Nair; Brice Vallès
2015-01-01
The objective of this paper is to develop a novel wind speed forecasting technique, which produces more accurate prediction. The Wavelet Transform (WT) along with the Auto Regressive Moving Average (ARMA) is chosen to form a hybrid whose combination is expected to give minimum Mean Absolute Prediction Error (MAPE). A simulation study has been conducted by comparing the forecasting results using the Wavelet-ARMA with the ARMA and Artificial Neural Network (ANN)-Ensemble Kalman Filter (EnKF) hy...
Adaptive synthesis of a wavelet transform using fast neural network
J. Stolarek
2011-01-01
This paper introduces a new method for an adaptive synthesis of a wavelet transform using a fast neural network with a topology based on the lattice structure. The lattice structure and the orthogonal lattice structure are presented and their properties are discussed. A novel method for unsupervised training of the neural network is introduced. The proposed approach is tested by synthesizing new wavelets with an expected energy distribution between low- and high-pass filters. Energy compactio...
Application of wavelet transform to seismic data; Wavelet henkan no jishin tansa eno tekiyo
Nakagami, K.; Murayama, R.; Matsuoka, T. [Japan National Oil Corp., Tokyo (Japan)
1996-05-01
Introduced herein is the use of the wavelet transform in the field of seismic exploration. Among applications so far made, there are signal filtering, break point detection, data compression, and the solution of finite differential equations in the wavelet domain. In the field of data compression in particular, some examples of practical application have been introduced already. In seismic exploration, it is expected that the wavelet transform will separate signals and noises in data in a way different from the Fourier transform. The continuous wavelet transform displays time change in frequency easy to read, but is not suitable for the analysis and processing large quantities of data. On the other hand, the discrete wavelet transform, being an orthogonal transform, can handle large quantities of data. As compared with the conventional Fourier transform that handles only the frequency domain, the wavelet transform handles the time domain as well as the frequency domain, and therefore is more convenient in handling unsteady signals. 9 ref., 8 figs.
SUN Ji-ping; MA Feng-ying; WU Dong-xu; LIU Xiao-yang
2008-01-01
Underground Electro Magnetic Interference (EMI) has become so serious that there were false alarms in monitoring system, which induced troubles of coal mine safety in production. In order to overcome difficulties caused by the explosion-proof enclosure of the equipments and the limitation of multiple startup and stop in transient process during EMI measurement, a novel technique was proposed to measure underground EMI distribution indirectly and enhance Electromagnetic Campatibility(EMC) of the monitoring system. The wavelet time-frequency analysis was introduced to underground monitoring system. Therefore, the sources, the startup time, duration and waveform of EMI could be ascertained correctly based on running records of underground electric equipments. The electrical fast transient/burst (EFT/B) was studied to verify the validity of wavelet analysis.EMI filter was improved in accordance of the EMI distribution gotten from wavelet analysis.Power port immunity was developed obviously. In addition, the method of setting wavelet thresholds was amended based upon conventional thresholds in the wavelet filter design.Therefore the EFT/B of data port was restrained markedly with the wavelet filtering. Coordinative effect of EMI power and wavelet filter makes false alarms of monitoring system reduce evidently. It is concluded that wavelet analysis and the improved EMI filter have enhanced the EMC of monitoring system obviously.
Optimization technology of 9/7 wavelet lifting scheme on DSP*
Chen, Zhengzhang; Yang, Xiaoyuan; Yang, Rui
2007-12-01
Nowadays wavelet transform has been one of the most effective transform means in the realm of image processing, especially the biorthogonal 9/7 wavelet filters proposed by Daubechies, which have good performance in image compression. This paper deeply studied the implementation and optimization technologies of 9/7 wavelet lifting scheme based on the DSP platform, including carrying out the fixed-point wavelet lifting steps instead of time-consuming floating-point operation, adopting pipelining technique to improve the iteration procedure, reducing the times of multiplication calculation by simplifying the normalization operation of two-dimension wavelet transform, and improving the storage format and sequence of wavelet coefficients to reduce the memory consumption. Experiment results have shown that these implementation and optimization technologies can improve the wavelet lifting algorithm's efficiency more than 30 times, which establish a technique foundation for successfully developing real-time remote sensing image compression system in future.
The Spatial Equivalence Between Wavelet Decomposition and Phase Space Embedding of EEG
YOU Rong-yi; HUANG Xiao-jing
2008-01-01
Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.
Rotation Invariant Pattern Recognition with a Volume Holographic Wavelet Correlation Processor
Wenzhao TAN(檀文钊); Qingzeng XUE(薛庆增); Yingbai YAN(严瑛白); Guofan JIN(金国藩)
2003-01-01
A volume holographic wavelet correlation processor for performing rotation invariant pattern recognition is suggested. It uses wavelet transform to get the digital edge extraction of the original object. Simultaneously a single circular harmonic component is used as the matched filter to get good rotation invariance. The new filter used in this method is called Wavelet Circular Harmonic Component Filter (WCHCF). Simulation results validate the theory and the experiment to recognize human faces with any rotation angle shows the utility of the newly proposed method.
Wavelet Analyses and Applications
Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.
2009-01-01
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…
1994-07-29
Douglas (MDA). This has been extended to the use of local SVD methods and the use of wavelet packets to provide a controlled sparsening. The goal is to be...possibilities for segmenting, compression and denoising signals and one of us (GVW) is using these wavelets to study edge sets with Prof. B. Jawerth. The
Wavelet transform for Fresnel-transformed mother wavelets
Liu Shu-Guang; Chen Jun-Hua; Fan Hong-Yi
2011-01-01
In this paper,we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation.This motivation can let the mother-wavelet-state itself vary from |ψ〉 to Fr,s(+)｜ψ),except for variation within the family of dilations and translations.The Parseval's equality,admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed.By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform,we obtain some mother wavelets.A comparison between the newly found mother wavelets is presented.
Denoising solar radiation data using coiflet wavelets
Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my; Janier, Josefina B., E-mail: josefinajanier@petronas.com.my; Muthuvalu, Mohana Sundaram, E-mail: mohana.muthuvalu@petronas.com.my [Department of Fundamental and Applied Sciences, Faculty of Sciences and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan (Malaysia); Hasan, Mohammad Khatim, E-mail: khatim@ftsm.ukm.my [Jabatan Komputeran Industri, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Sulaiman, Jumat, E-mail: jumat@ums.edu.my [Program Matematik dengan Ekonomi, Universiti Malaysia Sabah, Beg Berkunci 2073, 88999 Kota Kinabalu, Sabah (Malaysia); Ismail, Mohd Tahir [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Minden, Penang (Malaysia)
2014-10-24
Signal denoising and smoothing plays an important role in processing the given signal either from experiment or data collection through observations. Data collection usually was mixed between true data and some error or noise. This noise might be coming from the apparatus to measure or collect the data or human error in handling the data. Normally before the data is use for further processing purposes, the unwanted noise need to be filtered out. One of the efficient methods that can be used to filter the data is wavelet transform. Due to the fact that the received solar radiation data fluctuates according to time, there exist few unwanted oscillation namely noise and it must be filtered out before the data is used for developing mathematical model. In order to apply denoising using wavelet transform (WT), the thresholding values need to be calculated. In this paper the new thresholding approach is proposed. The coiflet2 wavelet with variation diminishing 4 is utilized for our purpose. From numerical results it can be seen clearly that, the new thresholding approach give better results as compare with existing approach namely global thresholding value.
Wavelet Transform Modulus Maxima-Based Robust Digital Image Watermarking in Wavelet Domain
LUO Ting; HONG Fan
2009-01-01
A new robust watermarking approach was proposed in 2D continuous wavelet domain (CWT).The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima (WTMM) of the host image.After possible attacks,the watermark is then detected and extracted by correlation analysis.Compared with other wavelet domain watermarking approaches,the WTMM approach can endow the image with both rotation and shift invariant properties.On the other hand,scale invariance is achieved with the geometric normalization during watermark detection.Case studies involve various attacks such as shifting,lossy compression,scaling,rotation and median filtering on the watermarked image,and the result shows that the approach is robust to these attacks.
Fang, Li-Zhi
1998-01-01
Recent advances have shown wavelets to be an effective, and even necessary, mathematical tool for theoretical physics. This book is a timely overview of the progress of this new frontier. It includes an introduction to wavelet analysis, and applications in the fields of high energy physics, astrophysics, cosmology and statistical physics. The topics are selected for the interests of physicists and graduate students of theoretical studies. It emphasizes the need for wavelets in describing and revealing structure in physical problems, which is not easily accomplishing by other methods.
Wavelet analysis in neurodynamics
Pavlov, Aleksei N.; Hramov, Aleksandr E.; Koronovskii, Aleksei A.; Sitnikova, Evgenija Yu; Makarov, Valeri A.; Ovchinnikov, Alexey A.
2012-09-01
Results obtained using continuous and discrete wavelet transforms as applied to problems in neurodynamics are reviewed, with the emphasis on the potential of wavelet analysis for decoding signal information from neural systems and networks. The following areas of application are considered: (1) the microscopic dynamics of single cells and intracellular processes, (2) sensory data processing, (3) the group dynamics of neuronal ensembles, and (4) the macrodynamics of rhythmical brain activity (using multichannel EEG recordings). The detection and classification of various oscillatory patterns of brain electrical activity and the development of continuous wavelet-based brain activity monitoring systems are also discussed as possibilities.
Wavelets in scientific computing
Nielsen, Ole Møller
1998-01-01
such a function well. These properties of wavelets have lead to some very successful applications within the field of signal processing. This dissertation revolves around the role of wavelets in scientific computing and it falls into three parts: Part I gives an exposition of the theory of orthogonal, compactly...... is an investigation of the potential for using the special properties of wavelets for solving partial differential equations numerically. Several approaches are identified and two of them are described in detail. The algorithms developed are applied to the nonlinear Schrödinger equation and Burgers' equation...
Battle, G A
1999-01-01
WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the F 4 3 quantum field theory is presented. It is due to Battle and
Image Denoising of Wavelet based Compressed Images Corrupted by Additive White Gaussian Noise
Shyam Lal
2012-08-01
Full Text Available In this study an efficient algorithm is proposed for removal of additive white Gaussian noise from compressed natural images in wavelet based domain. First, the natural image is compressed by discrete wavelet transform and then proposed hybrid filter is applied for image denoising of compressed images corrupted by Additive White Gaussian Noise (AWGN. The proposed hybrid filter (HMCD is combination of non-linear fourth order partial differential equation and bivariate shrinkage function. The proposed hybrid filter provides better results in term of noise suppression with keeping minimum edge blurring as compared to other existing image denoising techniques for wavelet based compressed images. Simulation and experimental results on benchmark test images demonstrate that the proposed hybrid filter attains competitive image denoising performances as compared with other state-of-the-art image denoising algorithms. It is more effective particularly for the highly corrupted images in wavelet based compressed domain.
Wavelet Based Semi-blind Channel Estimation For Multiband OFDM
Sadough, Sajad; Jaffrot, Emmanuel; Duhamel, Pierre
2007-01-01
This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response in order to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ``unsignificant'' wavelet coefficients from the estimation process. Simulation results using UWB channels issued from both models and measurements show that under sparsity conditions, the proposed algorithm outperforms pilot based channel estimation in terms of mean square error and bit error rate and enhances the estimation accuracy with less computational complexity than traditional semi-blind methods.
Research of Signal De-noising Technique Based on Wavelet
Shigang Hu
2013-09-01
Full Text Available During the process of signal testing, often exposed to interference and influence of all kinds of noise signal, such as data collection and transmission and so may introduce noise. So in practical applications, before analysis of the data measured, the need for de-noising processing. The signal de-noising is a method for filtering the high frequency noise of the signal and makes the signal more precise. This paper deals with the general theory of wavelet transform, the application of wavelet transform in signal de-noising as well as the analysis of the characteristics of noise-polluted signa1. Matlab is used to be carried out the simu1ation where the different wavelet and different threshold of the same wavelet for signal de-noising are applied. An indicator of wavelet de-noising is presented , it is the indicator of smoothness. Through analysis of the experiment , considered MSE , SNR and smoothness , it can be a good way to evaluate the equality of wavelet de-noising. The results show that the wavelet transform can achieve excellent results in signal de-noising.
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study
Anestis Antoniadis
2001-06-01
Full Text Available Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced.
Optical Character Recognition for Isolated Offline Handwritten Devanagari Numerals Using Wavelets
Gaurav Y. Tawde
2014-02-01
Full Text Available This paper presents a method of recognition of isolated offline handwritten Devanagari numerals using wavelets and neural network classifier. This method of optical character recognition takes the handwritten numeral image as input. After pre-processing, it is subjected to single level wavelet decomposition using Daubechies-4 wavelet filter. This wavelet decomposition allows viewing the input numeral at multiple resolutions. The Low-Low band components are used as inputs to multilayer perceptron (MLP classifier. The feed forward back propagation algorithm is used for classification of the input numeral.
Application of adaptive wavelet transforms via lifting in image data compression
Ye, Shujiang; Zhang, Ye; Liu, Baisen
2008-10-01
The adaptive wavelet transforms via lifting is proposed. In the transform, update filter is selected by the signal's character. Perfect reconstruction is possible without any overhead cost. To make sure the system's stability, in the lifting scheme of adaptive wavelet, update step is placed before prediction step. The Adaptive wavelet transforms via lifting is benefit for the image compression, because of the high stability, the small coefficients of high frequency parts, and the perfect reconstruction. With the adaptive wavelet transforms via lifting and the SPIHT, the image compression is realized in this paper, and the result is pleasant.
Automated Classification of Glaucoma Images by Wavelet Energy Features
N.Annu
2013-04-01
Full Text Available Glaucoma is the second leading cause of blindness worldwide. As glaucoma progresses, more optic nerve tissue is lost and the optic cup grows which leads to vision loss. This paper compiles a systemthat could be used by non-experts to filtrate cases of patients not affected by the disease. This work proposes glaucomatous image classification using texture features within images and efficient glaucoma classification based on Probabilistic Neural Network (PNN. Energy distribution over wavelet sub bands is applied to compute these texture features. Wavelet features were obtained from the daubechies (db3, symlets (sym3, and biorthogonal (bio3.3, bio3.5, and bio3.7 wavelet filters. It uses a technique to extract energy signatures obtained using 2-D discrete wavelet transform and the energy obtained from the detailed coefficients can be used to distinguish between normal and glaucomatous images. We observedan accuracy of around 95%, this demonstrates the effectiveness of these methods.
Terahertz digital holography image denoising using stationary wavelet transform
Cui, Shan-Shan; Li, Qi; Chen, Guanghao
2015-04-01
Terahertz (THz) holography is a frontier technology in terahertz imaging field. However, reconstructed images of holograms are inherently affected by speckle noise, on account of the coherent nature of light scattering. Stationary wavelet transform (SWT) is an effective tool in speckle noise removal. In this paper, two algorithms for despeckling SAR images are implemented to THz images based on SWT, which are threshold estimation and smoothing operation respectively. Denoised images are then quantitatively assessed by speckle index. Experimental results show that the stationary wavelet transform has superior denoising performance and image detail preservation to discrete wavelet transform. In terms of the threshold estimation, high levels of decomposing are needed for better denoising result. The smoothing operation combined with stationary wavelet transform manifests the optimal denoising effect at single decomposition level, with 5×5 average filtering.
Climate wavelet spectrum estimation under chronology uncertainties
Lenoir, G.; Crucifix, M.
2012-04-01
Several approaches to estimate the chronology of palaeoclimate records exist in the literature: simple interpolation between the tie points, orbital tuning, alignment on other data... These techniques generate a single estimate of the chronology. More recently, statistical generators of chronologies have appeared (e.g. OXCAL, BCHRON) allowing the construction of thousands of chronologies given the tie points and their uncertainties. These techniques are based on advanced statistical methods. They allow one to take into account the uncertainty of the timing of each climatic event recorded into the core. On the other hand, when interpreting the data, scientists often rely on time series analysis, and especially on spectral analysis. Given that paleo-data are composed of a large spectrum of frequencies, are non-stationary and are highly noisy, the continuous wavelet transform turns out to be a suitable tool to analyse them. The wavelet periodogram, in particular, is helpful to interpret visually the time-frequency behaviour of the data. Here, we combine statistical methods to generate chronologies with the power of continuous wavelet transform. Some interesting applications then come up: comparison of time-frequency patterns between two proxies (extracted from different cores), between a proxy and a statistical dynamical model, and statistical estimation of phase-lag between two filtered signals. All these applications consider explicitly the uncertainty in the chronology. The poster presents mathematical developments on the wavelet spectrum estimation under chronology uncertainties as well as some applications to Quaternary data based on marine and ice cores.
Siddiqi, A. H.
2012-07-01
In this chapter, the role of wavelet methods applied to identification and characterization of oil reservoir is elaborated. The market rate of petroleum product is very much related to exploration, drilling and production cost. The main goal of researchers working in oil industry is to develop tools and techniques for minimizing cost of exploration and production. Efforts of researchers working in applications of wavelet methods in different parts of the world to achieve this goal is reviewed. Wavelet based solution of Buckley-Leverett equation modelling reservoir is discussed. Variants of Buckley-Leverett equations including its higher dimension versions are introduced. Wavelet methods for inverse problems associated with Buckley-Leverett equation, which are quite useful for oil recovery, are also explained in this chapter.
Haar wavelets with applications
Lepik, Ülo
2014-01-01
This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-08
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Wavelet despiking of fractographs
Aubry, Jean-Marie; Saito, Naoki
2000-12-01
Fractographs are elevation maps of the fracture zone of some broken material. The technique employed to create these maps often introduces noise composed of positive or negative 'spikes' that must be removed before further analysis. Since the roughness of these maps contains useful information, it must be preserved. Consequently, conventional denoising techniques cannot be employed. We use continuous and discrete wavelet transforms of these images, and the properties of wavelet coefficients related to pointwise Hoelder regularity, to detect and remove the spikes.
Getz, Neil H.
1993-11-01
The discrete wavelet transform (DWT) is adapted to functions on the discrete circle to create a discrete periodic wavelet transform (DPWT) for bounded periodic sequences. This extension also offers a solution to the problem of non-invertibility that arises in the application of the DWT to finite length sequences and provides the proper theoretical setting for the completion of some previous incomplete solutions to the invertibility problem. It is proven that the same filter coefficients used with the DWT to create orthonormal wavelets on compact support in l(infinity ) (Z) may be incorporated through the DPWT to create an orthonormal basis of discrete periodic wavelets. By exploiting transform symmetry and periodicity we arrive at easily implementable and fast synthesis and analysis algorithms.
Some properties on multivariate filter banks with a matrix factorization
LIAN Qiaofang; XIAO Hongying; CHEN Qiuhui
2005-01-01
A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
Chaudhury, Kunal Narayan
2009-01-01
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex...
Casson, Alexander J.
2015-01-01
Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via gmC circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans. PMID:26694414
Casson, Alexander J
2015-12-17
Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT) for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g(m)C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram) and EEG (electroencephalogram) signals recorded from humans.
Alexander J. Casson
2015-12-01
Full Text Available Ultra low power signal processing is an essential part of all sensor nodes, and particularly so in emerging wearable sensors for biomedical applications. Analog signal processing has an important role in these low power, low voltage, low frequency applications, and there is a key drive to decrease the power consumption of existing analog domain signal processing and to map more signal processing approaches into the analog domain. This paper presents an analog domain signal processing circuit which approximates the output of the Discrete Wavelet Transform (DWT for use in ultra low power wearable sensors. Analog filters are used for the DWT filters and it is demonstrated how these generate analog domain DWT-like information that embeds information from Butterworth and Daubechies maximally flat mother wavelet responses. The Analog DWT is realised in hardware via g m C circuits, designed to operate from a 1.3 V coin cell battery, and provide DWT-like signal processing using under 115 nW of power when implemented in a 0.18 μm CMOS process. Practical examples demonstrate the effective use of the new Analog DWT on ECG (electrocardiogram and EEG (electroencephalogram signals recorded from humans.
Implemented Wavelet Packet Tree based Denoising Algorithm in Bus Signals of a Wearable Sensorarray
Schimmack, M.; Nguyen, S.; Mercorelli, P.
2015-11-01
This paper introduces a thermosensing embedded system with a sensor bus that uses wavelets for the purposes of noise location and denoising. From the principle of the filter bank the measured signal is separated in two bands, low and high frequency. The proposed algorithm identifies the defined noise in these two bands. With the Wavelet Packet Transform as a method of Discrete Wavelet Transform, it is able to decompose and reconstruct bus input signals of a sensor network. Using a seminorm, the noise of a sequence can be detected and located, so that the wavelet basis can be rearranged. This particularly allows for elimination of any incoherent parts that make up unavoidable measuring noise of bus signals. The proposed method was built based on wavelet algorithms from the WaveLab 850 library of the Stanford University (USA). This work gives an insight to the workings of Wavelet Transformation.
Denoising method of heart sound signals based on self-construct heart sound wavelet
Cheng, Xiefeng; Zhang, Zheng
2014-08-01
In the field of heart sound signal denoising, the wavelet transform has become one of the most effective measures. The selective wavelet basis is based on the well-known orthogonal db series or biorthogonal bior series wavelet. In this paper we present a self-construct wavelet basis which is suitable for the heart sound denoising and analyze its constructor method and features in detail according to the characteristics of heart sound and evaluation criterion of signal denoising. The experimental results show that the heart sound wavelet can effectively filter out the noise of the heart sound signals, reserve the main characteristics of the signal. Compared with the traditional wavelets, it has a higher signal-to-noise ratio, lower mean square error and better denoising effect.
Denoising method of heart sound signals based on self-construct heart sound wavelet
Xiefeng Cheng
2014-08-01
Full Text Available In the field of heart sound signal denoising, the wavelet transform has become one of the most effective measures. The selective wavelet basis is based on the well-known orthogonal db series or biorthogonal bior series wavelet. In this paper we present a self-construct wavelet basis which is suitable for the heart sound denoising and analyze its constructor method and features in detail according to the characteristics of heart sound and evaluation criterion of signal denoising. The experimental results show that the heart sound wavelet can effectively filter out the noise of the heart sound signals, reserve the main characteristics of the signal. Compared with the traditional wavelets, it has a higher signal-to-noise ratio, lower mean square error and better denoising effect.
Ground extraction from airborne laser data based on wavelet analysis
Xu, Liang; Yang, Yan; Jiang, Bowen; Li, Jia
2007-11-01
With the advantages of high resolution and accuracy, airborne laser scanning data are widely used in topographic mapping. In order to generate a DTM, measurements from object features such as buildings, vehicles and vegetation have to be classified and removed. However, the automatic extraction of bare earth from point clouds acquired by airborne laser scanning equipment remains a problem in LIDAR data filtering nowadays. In this paper, a filter algorithm based on wavelet analysis is proposed. Relying on the capability of detecting discontinuities of continuous wavelet transform and the feature of multi-resolution analysis, the object points can be removed, while ground data are preserved. In order to evaluate the performance of this approach, we applied it to the data set used in the ISPRS filter test in 2003. 15 samples have been tested by the proposed approach. Results showed that it filtered most of the objects like vegetation and buildings, and extracted a well defined ground model.
Analyzing Planck-Like Data with Wavelets
Sanz, J. L.; Barreiro, R. B.; Cayón, L.; Martinez-González, E.; Ruiz, G. A.; Diaz, F. J.; Argüeso, F.; Toffolatti, L.
Basics on the continuous and discrete wavelet transform with two scales are outlined. We study maps representing anisotropies in the cosmic microwave background radiation (CMB) and the relation to the standard approach, based on the Cl's, is establised through the introduction of a wavelet spectrum. We apply this technique to small angular scale CMB map simulations of size 12.8 x 12.8 degrees and filtered with a 4'.5 Gaussian beam. This resolution resembles the experimental one expected for future high resolution experiments (e.g. the Planck mission). We consider temperature fluctuations derived from standard, open and flat-Lambda CDM models. We also introduce Gaussian noise (uniform and non-uniform) at different S/N levels and results are given regarding denoising.
Lecture notes on wavelet transforms
Debnath, Lokenath
2017-01-01
This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these ...
Affine density in wavelet analysis
Kutyniok, Gitta
2007-01-01
In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems. This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
MR Image Compression Based on Selection of Mother Wavelet and Lifting Based Wavelet
Sheikh Md. Rabiul Islam
2014-04-01
Full Text Available Magnetic Resonance (MR image is a medical image technique required enormous data to be stored and transmitted for high quality diagnostic application. Various algorithms have been proposed to improve the performance of the compression scheme. In this paper we extended the commonly used algorithms to image compression and compared its performance. For an image compression technique, we have linked different wavelet techniques using traditional mother wavelets and lifting based Cohen-Daubechies-Feauveau wavelets with the low-pass filters of the length 9 and 7 (CDF 9/7 wavelet transform with Set Partition in Hierarchical Trees (SPIHT algorithm. A novel image quality index with highlighting shape of histogram of the image targeted is introduced to assess image compression quality. The index will be used in place of existing traditional Universal Image Quality Index (UIQI “in one go”. It offers extra information about the distortion between an original image and a compressed image in comparisons with UIQI. The proposed index is designed based on modelling image compression as combinations of four major factors: loss of correlation, luminance distortion, contrast distortion and shape distortion. This index is easy to calculate and applicable in various image processing applications. One of our contributions is to demonstrate the choice of mother wavelet is very important for achieving superior wavelet compression performances based on proposed image quality indexes. Experimental results show that the proposed image quality index plays a significantly role in the quality evaluation of image compression on the open sources “BrainWeb: Simulated Brain Database (SBD ”.
Property study of integer wavelet transform lossless compression coding based on lifting scheme
Xie, Cheng Jun; Yan, Su; Xiang, Yang
2006-01-01
In this paper the algorithms and its improvement of integer wavelet transform combining SPIHT and arithmetic coding in image lossless compression is mainly studied. The experimental result shows that if the order of low-pass filter vanish matrix is fixed, the improvement of compression effect is not evident when invertible integer wavelet transform is satisfied and focusing of energy property monotonic increase with transform scale. For the same wavelet bases, the order of low-pass filter vanish matrix is more important than the order of high-pass filter vanish matrix in improving the property of image compression. Integer wavelet transform lossless compression coding based on lifting scheme has no relation to the entropy of image. The effect of compression is depended on the the focuing of energy property of image transform.
Target recognition by wavelet transform
Li Zheng Dong; He Wu Liang; Pei Chun Lan; Peng Wen; SongChen; Zheng Xiao Dong
2002-01-01
Wavelet transform has an important character of multi-resolution power, which presents pyramid structure, and this character coincides the way by which people distinguish object from coarse to fineness and from large to tiny. In addition to it, wavelet transform benefits to reducing image noise, simplifying calculation, and embodying target image characteristic point. A method of target recognition by wavelet transform is provided
Oriented wavelet transform for image compression and denoising.
Chappelier, Vivien; Guillemot, Christine
2006-10-01
In this paper, we introduce a new transform for image processing, based on wavelets and the lifting paradigm. The lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid. To maximize energy compaction, the orientation minimizing the prediction error is chosen adaptively. A fine-grained multiscale analysis is provided by iterating the decomposition on the low-frequency band. In the context of image compression, the multiresolution orientation map is coded using a quad tree. The rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate-distortion sense. For image denoising, a Markov model is used to extract the orientations from the noisy image. As long as the map is sufficiently homogeneous, interesting properties of the original wavelet are preserved such as regularity and orthogonality. Perfect reconstruction is ensured by the reversibility of the lifting scheme. The mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform. The rate-distortion performance of this new transform is evaluated for image coding using state-of-the-art subband coders. Its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods.
Relativistic Hydrodynamics with Wavelets
DeBuhr, Jackson; Anderson, Matthew; Neilsen, David; Hirschmann, Eric W
2015-01-01
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulati...
Wavelet analysis for ground penetrating radar applications: a case study
Javadi, Mehdi; Ghasemzadeh, Hasan
2017-10-01
Noises may significantly disturb ground penetrating radar (GPR) signals, therefore, filtering undesired information using wavelet analysis would be challenging, despite the fact that several methods have been presented. Noises are gathered by probe, particularly from deep locations, and they may conceal reflections, suffering from small altitudes, because of signal attenuation. Multiple engineering fields need data analysis to distinguish valued material, based on information obtained by underground observations. Using wavelets as one of the useful methods for analyzing data is considered in this paper. However, optimal wavelet analysis would be challenging in the realm of exploring GPR signals. There is no doubt that accounting for wavelet function, decomposition level, threshold estimation method and threshold transformation, in the matter of de-noising and investigating signals, is of great importance; they must be chosen with judgment as they influence the results enormously if they are not carefully designated. Multiple wavelet functions are applied to perform de-noising and reconstruction on synthetic noisy signals generated by the finite-difference time-domain (FDTD) method to account for the most appropriate function for the purpose. In addition, various possible decomposition levels, threshold estimation methods and threshold transformations in the de-noising procedure are tested. The optimal wavelet analysis is also evaluated by examining real data acquired from several antenna frequencies which are common in engineering practice.
Estimation of Upper Bound for Order of Filters used in Perfect Reconstruction Filter Banks
B. R. Nagendra
2014-07-01
Full Text Available Filter banks are widely used in variety of applications such as signal compression, multi-channel transmission, conditioning of power supply, coding and decoding of signals, etc. Perfect reconstruction filter banks are used in the applications where it is essential to reconstruct the original signal with minimum errors. Compression of satellite vibration test data is one such application where perfect reconstruction filter banks can be used to design wavelets. These wavelets are used in transform coding stage of compression algorithm. It is required to have higher order for filters used in perfect reconstruction filter banks, to ensure better filter characteristics. The study carried out in this work, estimates the upper bound for order that can be assigned to filters used in perfect reconstruction filter banks
Steerable wavelet analysis of CMB structures alignment
Vielva, P; Martínez-González, E; Vandergheynst, P
2006-01-01
This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering of the CMB signal. One the one hand, the filter steerability renders the computation of the local orientation of the CMB features affordable in terms of computation time. On the other hand, the scale-space nature of the wavelet filtering allows to explore the alignment of the local structures at different scales, probing possible different phenomena. We present the WMAP first-year data analysis recently performed by the same authors (Wiaux et al.), where an extremely significant anisotropy was found. In particular, a preferred plane was detected, having a normal direction with a northern end position close to the northern end of the CMB dipole axis. In addition, a most preferred direction was found in that plane, with a northern end direction very close to the north eclipt...
Pearlman, William A
2013-01-01
This book explains the stages necessary to create a wavelet compression system for images and describes state-of-the-art systems used in image compression standards and current research. It starts with a high level discussion of the properties of the wavelet transform, especially the decomposition into multi-resolution subbands. It continues with an exposition of the null-zone, uniform quantization used in most subband coding systems and the optimal allocation of bitrate to the different subbands. Then the image compression systems of the FBI Fingerprint Compression Standard and the JPEG2000 S
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Wavelets theory, algorithms, and applications
Montefusco, Laura
2014-01-01
Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applicat
Tree wavelet approximations with applications
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
一类紧支撑矩阵值正交小波的构造%The Construction of a Class of Compactly Supported Orthogonal Matrix-valued Wavelets
陈清江; 程传蕊; 程正兴
2006-01-01
In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets. We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory. A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.
G. Ouillon
1995-01-01
Full Text Available The classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes.
Performance Evaluation of Wavelet Based on Human Visual System%基于人的视觉系统的小波性能评价
胡海平; 莫玉龙
2002-01-01
We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function (MTF) of human visual system in the frequency domain. In this paper, we evaluate performance of the constructed wavelet, and compare it with the widely used Daubechies 9-7, Daubechies 9-3 and GBCW-9-7 wavelets. The result shows that coding performance of the constructed wavelet is better than Daubechies 9-3, and is competitive with Daubechies 9-7 and GBCW-9-7 wavelets. Like Daubechies 9-3wavelet, the filter coefficients of the constructed wavelet are all dyadic fractions, and the tap is less than Daubechies 9-7 and GBCW9-7. It has an attractive feature in the realization of discrete wavelet transform.
Region-Based Fractional Wavelet Transform Using Post Processing Artifact Reduction
Jassim M. Abdul-Jabbar
2010-06-01
Full Text Available Wavelet-based algorithms are increasingly used in the source coding of remote sensing, satellite and other geospatial imagery. At the same time, wavelet-based coding applications are also increased in robust communication and network transmission of images. Although wireless multimedia sensors are widely used to deliver multimedia content due to the availability of inexpensive CMOS cameras, their computational and memory resources are still typically very limited. It is known that allowing a low-cost camera sensor node with limited RAM size to perform a multi-level wavelet transform, will in return limit the size of the acquired image. Recently, fractional wavelet filter technique became an interesting solution to reduce communication energy and wireless bandwidth, for resource-constrained devices (e.g. digital cameras. The reduction in the required memory in these fractional wavelet transforms is achieved at the expense of the image quality. In this paper, an adaptive fractional artifacts reduction approach is proposed for efficient filtering operations according to the desired compromise between the effectiveness of artifact reduction and algorithm simplicity using some local image features to reduce boundaries artifacts caused by fractional wavelet. Applying such technique on different types of images with different sizes using CDF 9/7 wavelet filters results in a good performance.
WAVELET ANALYSIS OF ABNORMAL ECGS
Vasudha Nannaparaju
2014-02-01
Full Text Available Detection of the warning signals by the heart can be diagnosed from ECG. An accurate and reliable diagnosis of ECG is very important however which is cumbersome and at times ambiguous in time domain due to the presence of noise. Study of ECG in wavelet domain using both continuous Wavelet transform (CWT and discrete Wavelet transform (DWT, with well known wavelet as well as a wavelet proposed by the authors for this investigation is found to be useful and yields fairly reliable results. In this study, Wavelet analysis of ECGs of Normal, Hypertensive, Diabetic and Cardiac are carried out. The salient feature of the study is that detection of P and T phases in wavelet domain is feasible which are otherwise feeble or absent in raw ECGs.
An improved adaptive wavelet shrinkage for ultrasound despeckling
P Nirmala Devi; R Asokan
2014-08-01
Ultrasound imaging is the most widely used medical diagnostic technique for clinical decision making, due to its ability to make real time imaging for moving structures, low cost and safety. However, its usefulness is degraded by the presence of signal dependent speckle noise. Several wavelet-based denoising schemes have been reported in the literature for the removal of speckle noise. This study proposes a new and improved adaptive wavelet shrinkage in the translational invariant domain. It exploits the knowledge of the correlation of the wavelet coefficients within and across the resolution scales. A preliminary coefficient classification representing useful image information and noise is performed with a novel inter-scale dependency measure. The spatial context adaptation of the wavelet coefficients within a subband is achieved by a local spatial adaptivity indicator, determined by using a truncation threshold. A weighted signal variance is estimated based on this measure and used in the determination of a subband adaptive threshold. The proposed thresholding function aims to reduce the fixed bias of the soft thresholding approach. Experiments conducted with the proposed filter are compared with the existing filtering algorithms in terms of Peak-Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Structural Similarity IndexMeasure (SSIM), Equivalent Number of Looks (ENL) and Edge Preservation Index (EPI). A comparison of the results shows that the proposed filter achieves an improvement in terms of quantitative measures and in terms of visual quality of the images.
Redundant Wavelets on Graphs and High Dimensional Data Clouds
Ram, Idan; Cohen, Israel
2011-01-01
In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points. We modify the filter-bank decomposition scheme of the redundant wavelet transform by adding in each decomposition level linear operators that reorder the approximation coefficients. These reordering operators are derived by organizing the tree-node features so as to shorten the path that passes through these points. We explore the use of the proposed transform to image denoising, and show that it achieves denoising results that are close to those obtained with the BM3D algorithm.
Robust Image Watermarking in the Wavelet Domain for Copyright Protection
Dehghan, Hamed
2010-01-01
In this paper a new approach to image watermarking in wavelet domain is presented. The idea is to hide the watermark data in blocks of the block segmented image. Two schemes are presented based on this idea by embedding the watermark data in the low pass wavelet coefficients of each block. Due to low computational complexity of the proposed approach, this algorithm can be implemented in real time. Experimental results demonstrate the impercepti-bility of the proposed method and its high robustness against various attacks such as filtering, JPEG compres-sion, cropping, noise addition and geometric distortions.
Wavelet based methods for improved wind profiler signal processing
V. Lehmann
Full Text Available In this paper, we apply wavelet thresholding for removing automatically ground and intermittent clutter (airplane echoes from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop wavelet domain thresholding rules, which allow us to identify the coefficients relevant for clutter and to suppress them in order to obtain filtered reconstructions.
Key words. Meteorology and atmospheric dynamics (instruments and techniques – Radio science (remote sensing; signal processing
Research of Signal De-noising Technique Based on Wavelet
Shigang Hu; Yinglu Hu; Xiaofeng Wu; Jin Li; Zaifang Xi; Jin Zhao
2013-01-01
During the process of signal testing, often exposed to interference and influence of all kinds of noise signal, such as data collection and transmission and so may introduce noise. So in practical applications, before analysis of the data measured, the need for de-noising processing. The signal de-noising is a method for filtering the high frequency noise of the signal and makes the signal more precise. This paper deals with the general theory of wavelet transform, the application of wavelet...
Wind Speed Forecasting Using Hybrid Wavelet Transform—ARMA Techniques
Diksha Kaur
2015-01-01
Full Text Available The objective of this paper is to develop a novel wind speed forecasting technique, which produces more accurate prediction. The Wavelet Transform (WT along with the Auto Regressive Moving Average (ARMA is chosen to form a hybrid whose combination is expected to give minimum Mean Absolute Prediction Error (MAPE. A simulation study has been conducted by comparing the forecasting results using the Wavelet-ARMA with the ARMA and Artificial Neural Network (ANN-Ensemble Kalman Filter (EnKF hybrid technique to verify the effectiveness of the proposed hybrid method. Results of the proposed hybrid show significant improvements in the forecasting error.
Morphology of the galaxy distribution from wavelet denoising
Martínez, V J; Saar, E; Donoho, D L; Reynolds, S; De la Cruz, P; Paredes, S
2005-01-01
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments and hotspots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provide us with a unique and more accurate morphological description.
Morphology of the Galaxy Distribution from Wavelet Denoising
Martínez, Vicent J.; Starck, Jean-Luc; Saar, Enn; Donoho, David L.; Reynolds, Simon C.; de la Cruz, Pablo; Paredes, Silvestre
2005-11-01
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way, ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field, which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments, and hot spots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provides us with a unique and more accurate morphological description.
Image Watermarking Method Using Integer-to-Integer Wavelet Transforms
陈韬; 王京春
2002-01-01
Digital watermarking is an efficient method for copyright protection for text, image, audio, and video data. This paper presents a new image watermarking method based on integer-to-integer wavelet transforms. The watermark is embedded in the significant wavelet coefficients by a simple exclusive OR operation. The method avoids complicated computations and high computer memory requirements that are the main drawbacks of common frequency domain based watermarking algorithms. Simulation results show that the embedded watermark is perceptually invisible and robust to various operations, such as low quality joint picture expert group (JPEG) compression, random and Gaussian noises, and smoothing (mean filtering).
Denoising of single-trial matrix representations using 2D nonlinear diffusion filtering.
Mustaffa, I; Trenado, C; Schwerdtfeger, K; Strauss, D J
2010-01-15
In this paper we present a novel application of denoising by means of nonlinear diffusion filters (NDFs). NDFs have been successfully applied for image processing and computer vision areas, particularly in image denoising, smoothing, segmentation, and restoration. We apply two types of NDFs for the denoising of evoked responses in single-trials in a matrix form, the nonlinear isotropic and the anisotropic diffusion filters. We show that by means of NDFs we are able to denoise the evoked potentials resulting in a better extraction of physiologically relevant morphological features over the ongoing experiment. This technique offers the advantage of translation-invariance in comparison to other well-known methods, e.g., wavelet denoising based on maximally decimated filter banks, due to an adaptive diffusion feature. We compare the proposed technique with a wavelet denoising scheme that had been introduced before for evoked responses. It is concluded that NDFs represent a promising and useful approach in the denoising of event related potentials. Novel NDF applications of single-trials of auditory brain responses (ABRs) and the transcranial magnetic stimulation (TMS) evoked electroencephalographic responses denoising are presented in this paper.
Søgaard, Andreas
For the LHC Run 2 and beyond, experiments are pushing both the energy and the intensity frontier so the need for robust and efficient pile-up mitigation tools becomes ever more pressing. Several methods exist, relying on uniformity of pile-up, local correlations of charged to neutral particles, and parton shower shapes, all in $y − \\phi$ space. Wavelets are presented as tools for pile-up removal, utilising their ability to encode position and frequency information simultaneously. This allows for the separation of individual hadron collision events by angular scale and thus for subtracting of soft, diffuse/wide-angle contributions while retaining the hard, small-angle components from the hard event. Wavelet methods may utilise the same assumptions as existing methods, the difference being the underlying, novel representation. Several wavelet methods are proposed and their effect studied in simple toy simulation under conditions relevant for the LHC Run 2. One full pile-up mitigation tool (‘wavelet analysis...
孙文昌; 周性伟
2000-01-01
For the non-band-limited function ψ, a sufficient condition is presented under whichis a frame for L2(R). The stability of these frames is studied. For the wavelets frequently used in signal processing, some concrete results are given.
无
2000-01-01
For the non-band-limited function ψ, a sufficient condition is presented under which{√sjψ(sj·-kb)} is a frame for L2(R). The stability of these frames is studied. For the wavelets frequently used in signal processing, some concrete results are given.
陈清江; 刘洪运
2008-01-01
The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed.A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory.An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented.Their characteristics is discussed by virtue of operator theory,time-frequency method.Moreover,it is shown how to design various orthonormal bases of space L2(R,Cn) from these wavelet packets.
WAVELET TECHNIQUE RECOVERING IMAGE BLURRED BY MIXED GAUSSIAN AND SALT-PEPPER NOISE
Hu Junquan; Huang Daren; Wang Zhenwu; Zhang Zeyin
2003-01-01
In this paper, we propose a new method to removing the mixed Gaussian and salt-pepper noise based on wavelet. To estimate outlier, A scheme called max-min method is adopted after DWT. Experimental results show that this method is more effective than common image restoration methods, such as Median filter, center weighted median filter.
Min Wang
2015-01-01
Full Text Available This paper proposes an image denoising method, using the wavelet transform and the singular value decomposition (SVD, with the enhancement of the directional features. First, use the single-level discrete 2D wavelet transform to decompose the noised image into the low-frequency image part and the high-frequency parts (the horizontal, vertical, and diagonal parts, with the edge extracted and retained to avoid edge loss. Then, use the SVD to filter the noise of the high-frequency parts with image rotations and the enhancement of the directional features: to filter the diagonal part, one needs first to rotate it 45 degrees and rotate it back after filtering. Finally, reconstruct the image from the low-frequency part and the filtered high-frequency parts by the inverse wavelet transform to get the final denoising image. Experiments show the effectiveness of this method, compared with relevant methods.
Blind and readable image watermarking using wavelet tree quantization
HU Yuping; YU Shengsheng; ZHOU JingLi; SHI Lei
2004-01-01
A blind and readable image watermarking scheme using wavelet tree quantization is proposed. In order to increase the algorithm robustness and ensure the watermark integrity,error correction coding techniques are used to encode the embedded watermark. In the watermark embedding process, the wavelet coefficients of the host image are grouped into wavelet trees and each watermark bit is embedded by using two trees. The trees are so quantized that they exhibit a large enough statistical difference, which will later be used for watermark extraction. The experimental results show that the proposed algorithm is effective and robust to common image processing operations and some geometric operations such as JPEG compression,JPEG2000 compression, filtering, Gaussian noise attack, and row-column removal. It is demonstrated that the proposed technique is practical.
Global and Local Distortion Inference During Embedded Zerotree Wavelet Decompression
Huber, A. Kris; Budge, Scott E.
1996-01-01
This paper presents algorithms for inferring global and spatially local estimates of the squared-error distortion measures for the Embedded Zerotree Wavelet (EZW) image compression algorithm. All distortion estimates are obtained at the decoder without significantly compromising EZW's rate-distortion performance. Two methods are given for propagating distortion estimates from the wavelet domain to the spatial domain, thus giving individual estimates of distortion for each pixel of the decompressed image. These local distortion estimates seem to provide only slight improvement in the statistical characterization of EZW compression error relative to the global measure, unless actual squared errors are propagated. However, they provide qualitative information about the asymptotic nature of the error that may be helpful in wavelet filter selection for low bit rate applications.
Adaptively wavelet-based image denoising algorithm with edge preserving
Yihua Tan; Jinwen Tian; Jian Liu
2006-01-01
@@ A new wavelet-based image denoising algorithm, which exploits the edge information hidden in the corrupted image, is presented. Firstly, a canny-like edge detector identifies the edges in each subband.Secondly, multiplying the wavelet coefficients in neighboring scales is implemented to suppress the noise while magnifying the edge information, and the result is utilized to exclude the fake edges. The isolated edge pixel is also identified as noise. Unlike the thresholding method, after that we use local window filter in the wavelet domain to remove noise in which the variance estimation is elaborated to utilize the edge information. This method is adaptive to local image details, and can achieve better performance than the methods of state of the art.
Adaptive Image Transmission Scheme over Wavelet-Based OFDM System
GAOXinying; YUANDongfeng; ZHANGHaixia
2005-01-01
In this paper an adaptive image transmission scheme is proposed over Wavelet-based OFDM (WOFDM) system with Unequal error protection (UEP) by the design of non-uniform signal constellation in MLC. Two different data division schemes: byte-based and bitbased, are analyzed and compared. Different bits are protected unequally according to their different contribution to the image quality in bit-based data division scheme, which causes UEP combined with this scheme more powerful than that with byte-based scheme. Simulation results demonstrate that image transmission by UEP with bit-based data division scheme presents much higher PSNR values and surprisingly better image quality. Furthermore, by considering the tradeoff of complexity and BER performance, Haar wavelet with the shortest compactly supported filter length is the most suitable one among orthogonal Daubechies wavelet series in our proposed system.
Lossy Compression Color Medical Image Using CDF Wavelet Lifting Scheme
M. beladghem
2013-09-01
Full Text Available As the coming era is that of digitized medical information, an important challenge to deal with is the storage and transmission requirements of enormous data, including color medical images. Compression is one of the indispensable techniques to solve this problem. In this work, we propose an algorithm for color medical image compression based on a biorthogonal wavelet transform CDF 9/7 coupled with SPIHT coding algorithm, of which we applied the lifting structure to improve the drawbacks of wavelet transform. In order to enhance the compression by our algorithm, we have compared the results obtained with wavelet based filters bank. Experimental results show that the proposed algorithm is superior to traditional methods in both lossy and lossless compression for all tested color images. Our algorithm provides very important PSNR and MSSIM values for color medical images.
Adaptive Dual-Threshold Edge Detection Based on Wavelet Transform
侯舒娟; 梅文博; 张志明
2003-01-01
In order to solve the problems of local-maximum modulus extraction and threshold selection in the edge detection of finite-resolution digital images, a new wavelet transform based adaptive dual-threshold edge detection algorithm is proposed. The local-maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual-threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self-adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise-tampered images.
Design of wavelet-based ECG detector for implantable cardiac pacemakers.
Min, Young-Jae; Kim, Hoon-Ki; Kang, Yu-Ri; Kim, Gil-Su; Park, Jongsun; Kim, Soo-Won
2013-08-01
A wavelet Electrocardiogram (ECG) detector for low-power implantable cardiac pacemakers is presented in this paper. The proposed wavelet-based ECG detector consists of a wavelet decomposer with wavelet filter banks, a QRS complex detector of hypothesis testing with wavelet-demodulated ECG signals, and a noise detector with zero-crossing points. In order to achieve high detection accuracy with low power consumption, a multi-scaled product algorithm and soft-threshold algorithm are efficiently exploited in our ECG detector implementation. Our algorithmic and architectural level approaches have been implemented and fabricated in a standard 0.35 μm CMOS technology. The testchip including a low-power analog-to-digital converter (ADC) shows a low detection error-rate of 0.196% and low power consumption of 19.02 μW with a 3 V supply voltage.
Goodman, Roe W
2016-01-01
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Self-similar prior and wavelet bases for hidden incompressible turbulent motion
Héas, Patrick; Kadri-Harouna, Souleymane
2013-01-01
This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition ...
Denoising portal images by means of wavelet techniques
Gonzalez Lopez, Antonio Francisco
Portal images are used in radiotherapy for the verification of patient positioning. The distinguishing feature of this image type lies in its formation process: the same beam used for patient treatment is used for image formation. The high energy of the photons used in radiotherapy strongly limits the quality of portal images: Low contrast between tissues, low spatial resolution and low signal to noise ratio. This Thesis studies the enhancement of these images, in particular denoising of portal images. The statistical properties of portal images and noise are studied: power spectra, statistical dependencies between image and noise and marginal, joint and conditional distributions in the wavelet domain. Later, various denoising methods are applied to noisy portal images. Methods operating in the wavelet domain are the basis of this Thesis. In addition, the Wiener filter and the non local means filter (NLM), operating in the image domain, are used as a reference. Other topics studied in this Thesis are spatial resolution, wavelet processing and image processing in dosimetry in radiotherapy. In this regard, the spatial resolution of portal imaging systems is studied; a new method for determining the spatial resolution of the imaging equipments in digital radiology is presented; the calculation of the power spectrum in the wavelet domain is studied; reducing uncertainty in film dosimetry is investigated; a method for the dosimetry of small radiation fields with radiochromic film is presented; the optimal signal resolution is determined, as a function of the noise level and the quantization step, in the digitization process of films and the useful optical density range is set, as a function of the required uncertainty level, for a densitometric system. Marginal distributions of portal images are similar to those of natural images. This also applies to the statistical relationships between wavelet coefficients, intra-band and inter-band. These facts result in a better
Study of Denoising in TEOAE Signals Using an Appropriate Mother Wavelet Function
Habib Alizadeh Dizaji
2007-06-01
Full Text Available Background and Aim: Matching a mother wavelet to class of signals can be of interest in signal analysis and denoising based on wavelet multiresolution analysis and decomposition. As transient evoked otoacoustic emissions (TEOAES are contaminated with noise, the aim of this work was to provide a quantitative approach to the problem of matching a mother wavelet to TEOAE signals by using tuning curves and to use it for analysis and denoising TEOAE signals. Approximated mother wavelet for TEOAE signals was calculated using an algorithm for designing wavelet to match a specified signal.Materials and Methods: In this paper a tuning curve has used as a template for designing a mother wavelet that has maximum matching to the tuning curve. The mother wavelet matching was performed on tuning curves spectrum magnitude and phase independent of one another. The scaling function was calculated from the matched mother wavelet and by using these functions, lowpass and highpass filters were designed for a filter bank and otoacoustic emissions signal analysis and synthesis. After signal analyzing, denoising was performed by time windowing the signal time-frequency component.Results: Aanalysis indicated more signal reconstruction improvement in comparison with coiflets mother wavelet and by using the purposed denoising algorithm it is possible to enhance signal to noise ratio up to dB.Conclusion: The wavelet generated from this algorithm was remarkably similar to the biorthogonal wavelets. Therefore, by matching a biorthogonal wavelet to the tuning curve and using wavelet packet analysis, a high resolution time-frequency analysis for the otoacoustic emission signals is possible.
B.Karuna kumar
2009-09-01
Full Text Available Fingerprints are today the most widely used biometric features for personal identification. With the increasing usage of biometric systems the question arises naturally how to store and handle the acquired sensor data. Our algorithm for the digitized images is based on adaptive uniform scalar quantization of discrete wavelet transform sub band decomposition. This technique referred to as the wavelet scalar quantization method. The algorithm produces archival quality images at compression ratios of around 15 to 1 and will allow the current database of paper finger print cards to be replaced by digital imagery. A compliance testing program is also being implemented to ensure high standards of image quality and interchangeability of data between different implementations.
Profit maximization mitigates competition
Dierker, Egbert; Grodal, Birgit
1996-01-01
We consider oligopolistic markets in which the notion of shareholders' utility is well-defined and compare the Bertrand-Nash equilibria in case of utility maximization with those under the usual profit maximization hypothesis. Our main result states that profit maximization leads to less price...... competition than utility maximization. Since profit maximization tends to raise prices, it may be regarded as beneficial for the owners as a whole. Moreover, if profit maximization is a good proxy for utility maximization, then there is no need for a general equilibrium analysis that takes the distribution...... of profits among consumers fully into account and partial equilibrium analysis suffices...
2007-11-02
Daubechies-DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman...DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49...Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49/49 Wavelet
Alshahrani, S; Abbod, M; Alamri, B; Taylor, G.
2015-01-01
In this paper, detection method and classification technique of power quality disturbances is presented. Due to the increase of nonlinear load recently, it becomes an essential requirement to insure high level of power supply and efficient commotional consuming. Wavelet Transform represents a powerful mathematical platform which is needed especially at non-stationary situations. Disturbances are fed into wavelets to filter, detect and extract its features at different frequencies. Training of...
Wavelet transform domain communication systems
Orr, Richard S.; Pike, Cameron; Lyall, Michael J.
1995-04-01
In this paper we introduce a new class of communications systems called wavelet transform domain (WTD) systems. WTD systems are transmultiplexer (TMUX) structures in which information to be communicated over a channel is encoded, via an inverse discrete wavelet transform (IDWT), as the wavelet coefficients of the transmitted signal, and extracted at the receiver by a discrete wavelet transform (DWT). WTD constructs can be used for covert, or low probability of intercept/detection (LPI/D) communications, baseband bandwidth efficient communications, or code-division multiple access (CDMA). This paper concentrates on the spread spectrum applications.
Zahra, Noor e; Sevindir, Huliya A.; Aslan, Zafar; Siddiqi, A. H. [Sharda University, SET, Department of Electronics and Communication, Knowledge Park 3rd, Gr. Noida (India); University of Kocaeli, Department of Mathematics, 41380 Kocaeli (Turkey); Istanbul Aydin University, Department of Computer Engineering, 34295 Istanbul (Turkey); Sharda University, SET, Department of Mathematics, 32-34 Knowledge Park 3rd, Greater Noida (India)
2012-07-17
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
Application of wavelet transforms as a time-series analysis tool for nuclear thermalhydraulics
Pohl, D.J.; Pascoe, J.; Popescu, A.I., E-mail: daniel.pohl@amec.com, E-mail: jason.pascoe@amec.com, E-mail: adrian.popescu@amec.com [AMEC NSS Limited, Toronto, Ontario (Canada)
2011-07-01
Wavelet transforms can be a valuable time-series analysis tool in the field of nuclear thermalhydraulics. As an example, the Morlet wavelet transform can be used to reduce the aleatory (random) uncertainty of a voiding transient in a large loss of coolant accident (LOCA). The wavelet transform is used to determine the cutoff frequency for a low pass Butterworth filter in order to remove the noisy part of the signal without infringing upon the characteristic frequencies of the phenomenon. This technique successfully reduced the standard random uncertainty by 42.4%. (author)
Implementation of Time-Scale Transformation Based on Continuous Wavelet Theory
无
2000-01-01
The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties.This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform.For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform.The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.
Audio watermarking based on psychoacoustic model and critical band wavelet transform
TAO Zhi; ZHAO Heming; GU Jihua; WU Di
2007-01-01
Watermark embedding algorithm based on critical band wavelet transform of digital audio signal is proposed in this paper. The masking threshold for each audio signal segment was calculated on the basic of psychoacoustic model. According to the similarity between critical band of human auditory system and critical band wavelet transform, a watermark was embedded into the low-band and mid-band coefficients of digital wavelet. The embedding strength was adaptively controlled by the masking threshold. The experiment results show that the embedded watermark signal is inaudible, and the watermarked audio signal has good robustness against many attacks such as compression, noise, re-sampling, low-pass filtering.
Coherent noise removal in seismic data with dual-tree M-band wavelets
Duval, Laurent; Chaux, Caroline; Ker, Stéphan
2007-09-01
Seismic data and their complexity still challenge signal processing algorithms in several applications. The advent of wavelet transforms has allowed improvements in tackling denoising problems. We propose here coherent noise filtering in seismic data with the dual-tree M-band wavelet transform. They offer the possibility to decompose data locally with improved multiscale directions and frequency bands. Denoising is performed in a deterministic fashion in the directional subbands, depending of the coherent noise properties. Preliminary results show that they consistently better preserve seismic signal of interest embedded in highly energetic directional noises than discrete critically sampled and redundant separable wavelet transforms.
Impedance cardiography signal denoising using discrete wavelet transform.
Chabchoub, Souhir; Mansouri, Sofienne; Salah, Ridha Ben
2016-09-01
Impedance cardiography (ICG) is a non-invasive technique for diagnosing cardiovascular diseases. In the acquisition procedure, the ICG signal is often affected by several kinds of noise which distort the determination of the hemodynamic parameters. Therefore, doctors cannot recognize ICG waveform correctly and the diagnosis of cardiovascular diseases became inaccurate. The aim of this work is to choose the most suitable method for denoising the ICG signal. Indeed, different wavelet families are used to denoise the ICG signal. The Haar, Daubechies (db2, db4, db6, and db8), Symlet (sym2, sym4, sym6, sym8) and Coiflet (coif2, coif3, coif4, coif5) wavelet families are tested and evaluated in order to select the most suitable denoising method. The wavelet family with best performance is compared with two denoising methods: one based on Savitzky-Golay filtering and the other based on median filtering. Each method is evaluated by means of the signal to noise ratio (SNR), the root mean square error (RMSE) and the percent difference root mean square (PRD). The results show that the Daubechies wavelet family (db8) has superior performance on noise reduction in comparison to other methods.
The berkeley wavelet transform: a biologically inspired orthogonal wavelet transform.
Willmore, Ben; Prenger, Ryan J; Wu, Michael C-K; Gallant, Jack L
2008-06-01
We describe the Berkeley wavelet transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single constant term), the wavelets form a complete, orthonormal basis in two dimensions. The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localized in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial frequency and orientation bandwidths that are comparable with biological values. Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis and is therefore inexpensive to compute, manipulate, and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.
Kalman Filtering with Real-Time Applications
Chui, Charles K
2009-01-01
Kalman Filtering with Real-Time Applications presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering.
Grating geophone signal processing based on wavelet transform
Li, Shuqing; Zhang, Huan; Tao, Zhifei
2008-12-01
Grating digital geophone is designed based on grating measurement technique benefiting averaging-error effect and wide dynamic range to improve weak signal detected precision. This paper introduced the principle of grating digital geophone and its post signal processing system. The signal acquisition circuit use Atmega 32 chip as core part and display the waveform on the Labwindows through the RS232 data link. Wavelet transform is adopted this paper to filter the grating digital geophone' output signal since the signal is unstable. This data processing method is compared with the FIR filter that widespread use in current domestic. The result indicates that the wavelet algorithm has more advantages and the SNR of seismic signal improve obviously.
Wavelet-based deconvolution of ultrasonic signals in nondestructive evaluation
HERRERA Roberto Henry; OROZCO Rubén; RODRIGUEZ Manuel
2006-01-01
In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in the nondestructive evaluation field, which is based on the theory of Fourier-Wavelet regularized deconvolution (ForWaRD). This new approach can be viewed as a solution to the open problem of adaptation of the ForWaRD framework to perform the convolution kernel estimation and deconvolution interdependently. The results indicate stable solutions of the estimated pulse and an improvement in the radio-frequency (RF) signal taking into account its signal-to-noise ratio (SNR) and axial resolution. Simulations and experiments showed that the proposed approach can provide robust and optimal estimates of the reflectivity function.
Sheppard, Colin J. R.; Campos, Juan; Escalera, Juan C.; Ledesma, Silvia
2008-03-01
The performance of pupil filters consisting of two zones each of constant complex amplitude transmittance is investigated. For filters where the transmittance is real, different classes of potentially useful filter are identified and optimized. These include leaky filters with an inner zone of low amplitude transmittance, pure phase filters with phase change of π, and equal area filters. The first of these minimizes the relative power in the outer rings for a given axial resolution, the second maximizes the Strehl ratio for a given transverse resolution, and the third minimizes the relative power in the outer rings for a given transverse resolution. Complex filters can give an axially shifted maximum in intensity: the performance parameters calculated relative to the true focus are investigated for some different classes of filter, but filters with phase change not equal to π are found to give inferior performance to the real value filters.
Wavelet frames and their duals
Lemvig, Jakob
2008-01-01
structure. The dilation of the wavelet building blocks in higher dimension is done via a square matrix which is usually taken to be integer valued. In this thesis we step away from the "usual" integer, expansive dilation and consider more general, expansive dilations. In most applications of wavelet frames...
Spherical 3D Isotropic Wavelets
Lanusse, F; Starck, J -L
2011-01-01
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the Fourier-Bessel decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large...
Wavelet-fractional Fourier transforms
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Wavelet approach to the determination of gravity tide parameters
柳林涛; 许摩泽; 孙和平; 郝兴华
2000-01-01
A new approach is proposed for the determination of gravity tide parameters. Three pairs of compactly supported wavelet filters are introduced in the approach. They can efficiently extract the objective tides from the gravity observation series. The new approach guarantees a direct and precise analysis on the tidal gravity records of any sampling length. The new approach is applied to the harmonic analysis on Wuhan superconducting gravimeter records. The results clearly show the resonant effects of the Earth Nearly Diurnal Free Wobble (NDFW).
Morlet Wavelets in Quantum Mechanics
John Ashmead
2012-11-01
Full Text Available Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets in particular are well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. But to take full advantage of Morlet wavelets we need to supply an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We construct both here.Quanta 2012; 1: 58–70.
Wavelet Based Image Denoising Technique
Sachin D Ruikar
2011-03-01
Full Text Available This paper proposes different approaches of wavelet based image denoising methods. The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. Wavelet algorithms are useful tool for signal processing such as image compression and denoising. Multi wavelets can be considered as an extension of scalar wavelets. The main aim is to modify the wavelet coefficients in the new basis, the noise can be removed from the data. In this paper, we extend the existing technique and providing a comprehensive evaluation of the proposed method. Results based on different noise, such as Gaussian, Poissonâ€™s, Salt and Pepper, and Speckle performed in this paper. A signal to noise ratio as a measure of the quality of denoising was preferred.
Optimization of wavelet- and curvelet-based denoising algorithms by multivariate SURE and GCV
Mortezanejad, R.; Gholami, A.
2016-06-01
One of the most crucial challenges in seismic data processing is the reduction of noise in the data or improving the signal-to-noise ratio (SNR). Wavelet- and curvelet-based denoising algorithms have become popular to address random noise attenuation for seismic sections. Wavelet basis, thresholding function, and threshold value are three key factors of such algorithms, having a profound effect on the quality of the denoised section. Therefore, given a signal, it is necessary to optimize the denoising operator over these factors to achieve the best performance. In this paper a general denoising algorithm is developed as a multi-variant (variable) filter which performs in multi-scale transform domains (e.g. wavelet and curvelet). In the wavelet domain this general filter is a function of the type of wavelet, characterized by its smoothness, thresholding rule, and threshold value, while in the curvelet domain it is only a function of thresholding rule and threshold value. Also, two methods, Stein’s unbiased risk estimate (SURE) and generalized cross validation (GCV), evaluated using a Monte Carlo technique, are utilized to optimize the algorithm in both wavelet and curvelet domains for a given seismic signal. The best wavelet function is selected from a family of fractional B-spline wavelets. The optimum thresholding rule is selected from general thresholding functions which contain the most well known thresholding functions, and the threshold value is chosen from a set of possible values. The results obtained from numerical tests show high performance of the proposed method in both wavelet and curvelet domains in comparison to conventional methods when denoising seismic data.
Image Compression using Haar and Modified Haar Wavelet Transform
Mohannad Abid Shehab Ahmed
2013-04-01
Full Text Available Efficient image compression approaches can provide the best solutions to the recent growth of the data intensive and multimedia based applications. As presented in many papers the Haar matrix–based methods and wavelet analysis can be used in various areas of image processing such as edge detection, preserving, smoothing or filtering. In this paper, color image compression analysis and synthesis based on Haar and modified Haar is presented. The standard Haar wavelet transformation with N=2 is composed of a sequence of low-pass and high-pass filters, known as a filter bank, the vertical and horizontal Haar filters are composed to construct four 2-dimensional filters, such filters applied directly to the image to speed up the implementation of the Haar wavelet transform. Modified Haar technique is studied and implemented for odd based numbers i.e. (N=3 & N=5 to generate many solution sets, these sets are tested using the energy function or numerical method to get the optimum one.The Haar transform is simple, efficient in memory usage due to high zero value spread (it can use sparse principle, and exactly reversible without the edge effects as compared to DCT (Discrete Cosine Transform. The implemented Matlab simulation results prove the effectiveness of DWT (Discrete Wave Transform algorithms based on Haar and Modified Haar techniques in attaining an efficient compression ratio (C.R, achieving higher peak signal to noise ratio (PSNR, and the resulting images are of much smoother as compared to standard JPEG especially for high C.R. A comparison between standard JPEG, Haar, and Modified Haar techniques is done finally which approves the highest capability of Modified Haar between others.
Maximally incompatible quantum observables
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Toigo, Alessandro, E-mail: alessandro.toigo@polimi.it [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy); Ziman, Mario, E-mail: ziman@savba.sk [RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava (Slovakia); Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno (Czech Republic)
2014-05-01
The existence of maximally incompatible quantum observables in the sense of a minimal joint measurability region is investigated. Employing the universal quantum cloning device it is argued that only infinite dimensional quantum systems can accommodate maximal incompatibility. It is then shown that two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible.
Local Extrema of Periodic Function's Wavelet Transform
FAN Qi-bin; SONG Xiao-yan
2005-01-01
The theory of detecting ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges. To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal's instantaneous amplitude and period.
An Introduction to Wavelet Theory and Analysis
Miner, N.E.
1998-10-01
This report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides tiormation about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet amdysis algorithms. The most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelet transforms for signal reconstruction are presented. This report is intended to be approachable by non- mathematicians, although a basic understanding of engineering mathematics is necessary.
王红霞; 陈波; 成礼智
2006-01-01
The conception of "main direction" of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis (MRA) of L2(R2). Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods are given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.
Four-Point Wavelets and Their Applications
魏国富; 陈发来
2002-01-01
Multiresolution analysis (MRA) and wavelets provide useful and efficient tools for representing functions at multiple levels of details. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation and numerical analysis. In this paper, the authors construct a new class of wavelets, called four-point wavelets,based on an interpolatory four-point subdivision scheme. They are of local support, symmetric and stable. The analysis and synthesis algorithms have linear time complexity. Depending on different weight parameters w, the scaling functions and wavelets generated by the four-point subdivision scheme are of different degrees of smoothness. Therefore the user can select better wavelets relevant to the practice among the classes of wavelets. The authors apply the fourpoint wavelets in signal compression. The results show that the four-point wavelets behave much better than B-spline wavelets in many situations.
Multiple description scalable video coding based on 3D lifted wavelet transform
JIANG Gang-yi; YU Mei; YU Zhou; YE Xi-en; ZHANG Wen-qin; KIM Yong-deak
2006-01-01
In this work, a new method to deal with the unconnected pixels in motion compensated temporal filtering (MCTF) is presented, which is designed to improve the performance of 3D lifted wavelet coding. Furthermore, multiple description scalable coding (MDSC) is investigated, and novel MDSC schemes based on 3D wavelet coding are proposed, using the lifting implementation of temporal filtering. The proposed MDSC schemes can avoid the mismatch problem in multiple description video coding, and have high scalability and robustness of video transmission. Experimental results showed that the proposed schemes are feasible and adequately effective.
AN EFFICIENT 3-DIMENSIONAL DISCRETE WAVELET TRANSFORM ARCHITECTURE FOR VIDEO PROCESSING APPLICATION
Ganapathi Hegde; Pukhraj Vaya
2012-01-01
This paper presents an optimized 3-D Discrete Wavelet Transform (3-DDWT) architecture.1-DDWT employed for the design of 3-DDWT architecture uses reduced lifting scheme approach.Further the architecture is optimized by applying block enabling technique,scaling,and rounding of the filter coefficients.The proposed architecture uses biorthogonal (9/7) wavelet filter.The architecture is modeled using Verilog HDL,simulated using ModelSim,synthesized using Xilinx ISE and finally implemented on Virtex-5 FPGA.The proposed 3-DDWT architecture has slice register utilization of 5％,operating frequency of 396 MHz and a power consumption of 0.45 W.
Kalman filtering with real-time applications
Chui, Charles K
2017-01-01
This new edition presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering. Over 100 exercises and problems with solutions help de...
Wavelet Transform Signal Processing Applied to Ultrasonics.
1995-05-01
THE WAVELET TRANSFORM IS APPLIED TO THE ANALYSIS OF ULTRASONIC WAVES FOR IMPROVED SIGNAL DETECTION AND ANALYSIS OF THE SIGNALS. In instances where...the mother wavelet is well defined, the wavelet transform has relative insensitivity to noise and does not need windowing. Peak detection of...ultrasonic pulses using the wavelet transform is described and results show good detection even when large white noise was added. The use of the wavelet
Optical encryption with cascaded fractional wavelet transforms
BAO Liang-hua; CHEN Lin-fei; ZHAO Dao-mu
2006-01-01
On the basis of fractional wavelet transform, we propose a new method called cascaded fractional wavelet transform to encrypt images. It has the virtues of fractional Fourier transform and wavelet transform. Fractional orders, standard focal lengths and scaling factors are its keys. Multistage fractional Fourier transforms can add the keys easily and strengthen information security. This method can also realize partial encryption just as wavelet transform and fractional wavelet transform. Optical realization of encryption and decryption is proposed. Computer simulations confirmed its possibility.
Spherical 3D isotropic wavelets
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
Spatial mask filtering algorithm for partial discharge pulse extraction of large generators
无
2006-01-01
A spatial mask filter algorithm (SMF) for partial discharge (PD) pulse extraction is proposed in this then direct multiplication of coefficients at two adjacent scales is used to detect singularity points of the signal tain the last spatial mask filter. By multiplication of wavelet coefficients with the final mask filter and wavelet reconstruction process, partial discharge pulses are extracted. The results of digital simulation and practical experiment show that this method is superior to traditional wavelet shrinkage method (TWS). This algorithm not only can increase the signal to noise ratio (SNR), but also can preserve the energy and pulse amplitude.
Inertial Sensor Signals Denoising with Wavelet Transform
Ioana-Raluca EDU
2015-03-01
Full Text Available In the current paper we propose a new software procedure for processing data from an inertial navigation system boarded on a moving vehicle, in order to achieve accurate navigation information on the displacement of the vehicle in terms of position, speed, acceleration and direction. We divided our research in three phases. In the first phase of our research, we implemented a real-time evaluation criterion with the intention of achieving real-time data from an accelerometer. It is well-known that most errors in the detection of position, velocity and attitude in inertial navigation occur due to difficult numerical integration of noise. In the second phase, we were interested in achieving a better estimation and compensation of the gyro sensor angular speed measurements. The errors of these sensors occur because of their miniaturization, they cannot be eliminated but can be modelled by applying specific signal processing methods. The objective of both studies was to propose a signal processing algorithm, based on Wavelet filter, along with a criterion for evaluating and updating the optimal decomposition level of Wavelet transform for achieving accurate information from inertial sensors. In the third phase of our work we are suggesting the utility of a new complex algorithm for processing data from an inertial measurement unit, containing both miniaturized accelerometers and gyros, after undergoing a series of numerical simulations and after obtaining accurate information on vehicle displacement
Wavelet Based Hilbert Transform with Digital Design and Application to QCM-SS Watermarking
S. P. Maity
2008-04-01
Full Text Available In recent time, wavelet transforms are used extensively for efficient storage, transmission and representation of multimedia signals. Hilbert transform pairs of wavelets is the basic unit of many wavelet theories such as complex filter banks, complex wavelet and phaselet etc. Moreover, Hilbert transform finds various applications in communications and signal processing such as generation of single sideband (SSB modulation, quadrature carrier multiplexing (QCM and bandpass representation of a signal. Thus wavelet based discrete Hilbert transform design draws much attention of researchers for couple of years. This paper proposes an (i algorithm for generation of low computation cost Hilbert transform pairs of symmetric filter coefficients using biorthogonal wavelets, (ii approximation to its rational coefficients form for its efficient hardware realization and without much loss in signal representation, and finally (iii development of QCM-SS (spread spectrum image watermarking scheme for doubling the payload capacity. Simulation results show novelty of the proposed Hilbert transform design and its application to watermarking compared to existing algorithms.
Design Methodology of a New Wavelet Basis Function for Fetal Phonocardiographic Signals
Vijay S. Chourasia
2013-01-01
Full Text Available Fetal phonocardiography (fPCG based antenatal care system is economical and has a potential to use for long-term monitoring due to noninvasive nature of the system. The main limitation of this technique is that noise gets superimposed on the useful signal during its acquisition and transmission. Conventional filtering may result into loss of valuable diagnostic information from these signals. This calls for a robust, versatile, and adaptable denoising method applicable in different operative circumstances. In this work, a novel algorithm based on wavelet transform has been developed for denoising of fPCG signals. Successful implementation of wavelet theory in denoising is heavily dependent on selection of suitable wavelet basis function. This work introduces a new mother wavelet basis function for denoising of fPCG signals. The performance of newly developed wavelet is found to be better when compared with the existing wavelets. For this purpose, a two-channel filter bank, based on characteristics of fPCG signal, is designed. The resultant denoised fPCG signals retain the important diagnostic information contained in the original fPCG signal.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Fourier-wavelet restoration in PET/CT brain studies
Knesaurek, Karin, E-mail: karin.knesaurek@mssm.edu [Division of Nuclear Medicine, The Mount Sinai Medical Center, One Gustave L. Levy Place, New York, NY 10029 (United States)
2012-10-11
Our goal is to improve brain PET imaging through the application of a novel, hybrid Fourier-wavelet (WFT) restoration technique. The major limitation of PET studies is a relatively poor resolution in comparison with MRI and CT imaging and there is a need for improved PET imaging. A GE DLS PET/CT 16 slice system was used to acquire the studies. In order to create restoration filters the point source study was performed. The 6-fillable spheres and 3D Hoffman brain phantom studies were acquired and used to test and optimize the restoration approach. The patient data used in the study were acquired in a 3D PET mode, using the standard clinical protocol. Here, we have implemented Fourier-wavelet regularized restoration. In the Fourier domain, the inverse of modulation transfer function was multiplied by a Butterworth low-pass filter, order n=6 and cut-off frequency f=0.35 cycles/pixel. In addition, wavelet (Daubechies, order 2) noise suppression was applied by 'hard threshold'. Hot spheres and 3D Hoffman brain studies showed that the restoration process not only improves resolution and contrast but also improves quantification in 3D PET/CT imaging. The average contrast increase was 19% and the quantification improved in the range 8-20% depending on sphere size. In the restored images, there was no significant increase in noise when compared with the original images. The clinical studies followed brain phantom findings, i.e., the restored images had better contrast and resolution properties, when compared with the original images. The results of the study demonstrate that the quality and quantification of 3D brain {sup 18}F FDG PET images can be significantly improved by Fourier-wavelet (WFT) restoration filtering.
Fourier-wavelet restoration in PET/CT brain studies
Knešaurek, Karin
2012-10-01
Our goal is to improve brain PET imaging through the application of a novel, hybrid Fourier-wavelet (WFT) restoration technique. The major limitation of PET studies is a relatively poor resolution in comparison with MRI and CT imaging and there is a need for improved PET imaging. A GE DLS PET/CT 16 slice system was used to acquire the studies. In order to create restoration filters the point source study was performed. The 6-fillable spheres and 3D Hoffman brain phantom studies were acquired and used to test and optimize the restoration approach. The patient data used in the study were acquired in a 3D PET mode, using the standard clinical protocol. Here, we have implemented Fourier-wavelet regularized restoration. In the Fourier domain, the inverse of modulation transfer function was multiplied by a Butterworth low-pass filter, order n=6 and cut-off frequency f=0.35 cycles/pixel. In addition, wavelet (Daubechies, order 2) noise suppression was applied by “hard threshold”. Hot spheres and 3D Hoffman brain studies showed that the restoration process not only improves resolution and contrast but also improves quantification in 3D PET/CT imaging. The average contrast increase was 19% and the quantification improved in the range 8-20% depending on sphere size. In the restored images, there was no significant increase in noise when compared with the original images. The clinical studies followed brain phantom findings, i.e., the restored images had better contrast and resolution properties, when compared with the original images. The results of the study demonstrate that the quality and quantification of 3D brain 18F FDG PET images can be significantly improved by Fourier-wavelet (WFT) restoration filtering.
Evidence of self-organization in brain electrical activity using wavelet-based informational tools
Rosso, O. A.; Martin, M. T.; Plastino, A.
2005-03-01
In the present work, we show that appropriate information-theory tools based on the wavelet transform (relative wavelet energy; normalized total wavelet entropy, H; generalized wavelet complexity, CW), when applied to tonic-clonic epileptic EEG data, provide one with valuable insights into the dynamics of neural activity. Twenty tonic-clonic secondary generalized epileptic records pertaining to eight patients have been analyzed. If the electromyographic activity is excluded the difference between the ictal and pre-ictal mean entropic values (ΔH=-) is negative in 95% of the cases (pictal)>-ictal)>) is positive in 85% of the cases (p=0.0002). Thus during the seizure entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus in this kind of seizures triggers a self-organized brain state characterized by both order and maximal complexity.
Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence
Zhen-yan XIA; Yan TIAN; Nan JIANG
2009-01-01
The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. Wavelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation or breakup of eddies are related to the vertical position in the boundary layer, and the energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.
Development of content based image retrieval system using wavelet and Gabor transform
Manish Sharma
2013-06-01
Full Text Available A novel approach to image retrieval using color, texture and spatial information is proposed. The color information of an image is represented by the proposed color hologram, which takes into account both the occurrence of colors of pixels and the colors of their neighboring pixels. The proposed Fuzzy Color homogeneity, encoded by fuzzy sets, is incorporated in the color hologram computation. The texture information is described by the mean, variance and energy of wavelet decomposition coefficients in all sub bands. The spatial information is characterized by the class parameters obtained automatically from a unique unsupervised segmentation algorithm in combination with wavelet decomposition. Multi-stage filtering is applied to query processing to reduce the search range to speed up the query. Color homogram filter, wavelet texture filter, and spatial filter are used in sequence to eliminate images that are dissimilar to a query image in color, texture, and spatial information from the search ranges respectively. The proposed texture distance measure used in the wavelet texture filter considers the relationship between the coefficient value ranges and the decomposition levels, thus improving the retrieval performance.
Enhancement of damage indicators in wavelet and curvature analysis
B K Raghu Prasad; N Lakshmanan; K Muthumani; N Gopalakrishnan
2006-08-01
Damage in a structural element induces a small perturbation in its static or dynamic displacement proﬁle which can be captured by wavelet analysis. The paper presents the wavelet analysis of damaged linear structural elements using DB4 or BIOR6·8 family of wavelets. An expression is developed for computing the natural frequencies of a damaged beam using ﬁrst order perturbation theory. Starting with a localized reduction of EI at the mid-span of a simply supported beam, damage modelling is done for a typical steel beam element. Wavelet analysis is performed for this damage model for displacement, rotation and curvature mode shapes as well as static displacement proﬁles. Damage indicators like displacement, slope and curvature are magniﬁed under higher modes. Instantaneous step-wise linearity is assumed for all the nonlinear elements. A localization scheme with arbitrararily located curvature nodes within a pseudo span is developed for steady state dynamic loads, such that curvature response and damages are maximized and the scheme is numerically tested and proved.
Ashkenazy, Yu; Levitan, J; Moelgaard, H; Bloch-Thomsen, P E; Saermark, K
1998-01-01
We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.
Anutam
2014-10-01
Full Text Available Image Denoising is an important part of diverse image processing and computer vision problems. The important property of a good image denoising model is that it should completely remove noise as far as possible as well as preserve edges. One of the most powerful and perspective approaches in this area is image denoising using discrete wavelet transform (DWT. In this paper, comparison of various Wavelets at different decomposition levels has been done. As number of levels increased, Peak Signal to Noise Ratio (PSNR of image gets decreased whereas Mean Absolute Error (MAE and Mean Square Error (MSE get increased . A comparison of filters and various wavelet based methods has also been carried out to denoise the image. The simulation results reveal that wavelet based Bayes shrinkage method outperforms other methods.
Spline and spline wavelet methods with applications to signal and image processing
Averbuch, Amir Z; Zheludev, Valery A
This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images upsampling. In addition to the design of a diverse library of splines, SW, SWP a...
Higher-order graph wavelets and sparsity on circulant graphs
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
Review of Wavelet Theory and Its Application Toimage Data Compression
Othman Omran Khalifa
2012-10-01
Full Text Available The fast development of computing multimedia has led to the demand of using digital images. The manipulation, storage and transmission of these images in their raw form is very expensive, it significantly slows the transmission and makes storage costly. In this paper, a brief review of wavelet transform theory is given using filters as examples to show the related multiresolution analysis. Advantages over Fourier transform is investigated and several results are derived. The pyramid algorithm is also presented and some features of wavelets in image data compression are given. A modified version of Lind Boze and Gray (LBG algorithm using Partial Search Partial Distortion (PSPD is presented for coding the wavelet coefficients to speed up the codebook generation and the search required for nearest neighbour codevector of input image. The proposed scheme can save 70 - 80 % of the Vector Quantization (VQ encoding time as compared to fully search VQ and reduced arithmetic complexity with less sacrificing performance.Key Words: Image compression, Wavelets transform, Vector qQuantization
Parker, Andrew M.; Wandi Bruine de Bruin; Baruch Fischhoff
2007-01-01
Our previous research suggests that people reporting a stronger desire to maximize obtain worse life outcomes (Bruine de Bruin et al., 2007). Here, we examine whether this finding may be explained by the decision-making styles of self-reported maximizers. Expanding on Schwartz et al. (2002), we find that self-reported maximizers are more likely to show problematic decision-making styles, as evidenced by self-reports of less behavioral coping, greater dependence on others when making decisions...
Iris Recognition Using Wavelet
Khaliq Masood
2013-08-01
Full Text Available Biometric systems are getting more attention in the present era. Iris recognition is one of the most secure and authentic among the other biometrics and this field demands more authentic, reliable and fast algorithms to implement these biometric systems in real time. In this paper, an efficient localization technique is presented to identify pupil and iris boundaries using histogram of the iris image. Two small portions of iris have been used for polar transformation to reduce computational time and to increase the efficiency of the system. Wavelet transform is used for feature vector generation. Rotation of iris is compensated without shifts in the iris code. System is tested on Multimedia University Iris Database and results show that proposed system has encouraging performance.
Hannu Olkkonen
2013-01-01
Full Text Available In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG. Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.
Large Scale Isosurface Bicubic Subdivision-Surface Wavelets for Representation and Visualization
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-01-05
We introduce a new subdivision-surface wavelet transform for arbitrary two-manifolds with boundary that is the first to use simple lifting-style filtering operations with bicubic precision. We also describe a conversion process for re-mapping large-scale isosurfaces to have subdivision connectivity and fair parameterizations so that the new wavelet transform can be used for compression and visualization. The main idea enabling our wavelet transform is the circular symmetrization of the filters in irregular neighborhoods, which replaces the traditional separation of filters into two 1-D passes. Our wavelet transform uses polygonal base meshes to represent surface topology, from which a Catmull-Clark-style subdivision hierarchy is generated. The details between these levels of resolution are quickly computed and compactly stored as wavelet coefficients. The isosurface conversion process begins with a contour triangulation computed using conventional techniques, which we subsequently simplify with a variant edge-collapse procedure, followed by an edge-removal process. This provides a coarse initial base mesh, which is subsequently refined, relaxed and attracted in phases to converge to the contour. The conversion is designed to produce smooth, untangled and minimally-skewed parameterizations, which improves the subsequent compression after applying the transform. We have demonstrated our conversion and transform for an isosurface obtained from a high-resolution turbulent-mixing hydrodynamics simulation, showing the potential for compression and level-of-detail visualization.
Wavelet transforms and their applications
Debnath, Lokenath
2015-01-01
This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Numerous standard and challenging topics, applications, and exercises are included in this edition, which will stimulate research interest among senior undergraduate and graduate students. The book contains a large number of examples, which are either directly associated with applications or formulated in terms of the mathematical, physical, and engineering context in which wavelet theory arises. Topics and Features of the Second Edition: · Expanded and revised the historical introduction by including many new topics such as the fractional Fourier transform, and the construction of wavelet bases in various spaces ...
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Lossless Image Compression Using New Biorthogonal Wavelets
M. Santhosh
2013-12-01
Full Text Available Even though a large number of wavelets exist, one n eeds new wavelets for their specific applications. One of the basic wavelet categories is orthogonal wavel ets. But it was hard to find orthogonal and symmetric wavelets. Symmetricity is required for perfect reconstruction. Hence, a need for orthogonal and symmetric arises. The solution was in the form of biorthogonal wavelets which preserves perfect reconstruction condition. Though a number of biorthogonal wavelets are proposed in the literature, in this paper four new biorthogonal wavelets are proposed which gives bett er compression performance. The new wavelets are compared with traditional wavelets by using the des ign metrics Peak Signal to Noise Ratio (PSNR and Compression Ratio (CR. Set Partitioning in Hierarc hical Trees (SPIHT coding algorithm was utilized to incorporate compression of images.
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Heart Disease Detection Using Wavelets
González S., A.; Acosta P., J. L.; Sandoval M., M.
2004-09-01
We develop a wavelet based method to obtain standardized gray-scale chart of both healthy hearts and of hearts suffering left ventricular hypertrophy. The hypothesis that early bad functioning of heart can be detected must be tested by comparing the wavelet analysis of the corresponding ECD with the limit cases. Several important parameters shall be taken into account such as age, sex and electrolytic changes.
Verônica Isabela Quandt
Full Text Available Introduction Crackles are discontinuous, non-stationary respiratory sounds and can be characterized by their duration and frequency. In the literature, many techniques of filtering, feature extraction, and classification were presented. Although the discrete wavelet transform (DWT is a well-known tool in this area, issues like signal border extension, mother-wavelet selection, and its subbands were not properly discussed. Methods In this work, 30 different mother-wavelets 8 subbands were assessed, and 9 border extension modes were evaluated. The evaluations were done based on the energy representation of the crackle considering the mother-wavelet and the border extension, allowing a reduction of not representative subbands. Results Tests revealed that the border extension mode considered during the DWT affects crackle characterization, whereas SP1 (Smooth-Padding of order 1 and ASYMW (Antisymmetric-Padding (whole-point modes shall not be used. After DWT, only 3 subbands (D3, D4, and D5 were needed to characterize crackles. Finally, from the group of mother-wavelets tested, Daubechies 7 and Symlet 7 were found to be the most adequate for crackle characterization. Discussion DWT can be used to characterize crackles when proper border extension mode, mother-wavelet, and subbands are taken into account.
TRANSMISSION LINE FAULT ANALYSIS USING WAVELET THEORY
Ravindra Malkar
2012-06-01
Full Text Available This paper describes a Wavelet transform technique to analyze power system disturbance such as transmission line faults with Biorthogonal and Haar wavelets. In this work, wavelet transform based approach,which is used to detect transmission line faults, is proposed. The coefficient of discrete approximation of the dyadic wavelet transform with different wavelets are used to be an index for transmission line fault detection and faulted – phase selection and select which wavelet is suitable for this application. MATLAB/Simulation is used to generate fault signals. Simulation results reveal that the performance of the proposed fault detection indicator is promising and easy to implement for computer relaying application.
Signal Analysis by New Mother Wavelets
NIU Jin-Bo; FAN Hong-Yi; QI Kai-Guo
2009-01-01
Based on the general formula for finding qualified mother wavelets [Opt. Lett. 31 (2006) 407] we make wavelet transforms computed with the newly found mother wavelets (characteristic of the power 2n) for some optical Gaussian pulses, which exhibit the ability to measure frequency of the pulse more precisely and clearly. We also work with complex mother wavelets composed of new real mother wavelets, which offer the ability of obtaining phase information of the pulse as well as amplitude information. The analogy between the behavior of Hermite-Gauss beams and that of new wavelet transforms is noticed.
Wavelet transform analysis of transient signals: the seismogram and the electrocardiogram
Anant, K.S.
1997-06-01
In this dissertation I quantitatively demonstrate how the wavelet transform can be an effective mathematical tool for the analysis of transient signals. The two key signal processing applications of the wavelet transform, namely feature identification and representation (i.e., compression), are shown by solving important problems involving the seismogram and the electrocardiogram. The seismic feature identification problem involved locating in time the P and S phase arrivals. Locating these arrivals accurately (particularly the S phase) has been a constant issue in seismic signal processing. In Chapter 3, I show that the wavelet transform can be used to locate both the P as well as the S phase using only information from single station three-component seismograms. This is accomplished by using the basis function (wave-let) of the wavelet transform as a matching filter and by processing information across scales of the wavelet domain decomposition. The `pick` time results are quite promising as compared to analyst picks. The representation application involved the compression of the electrocardiogram which is a recording of the electrical activity of the heart. Compression of the electrocardiogram is an important problem in biomedical signal processing due to transmission and storage limitations. In Chapter 4, I develop an electrocardiogram compression method that applies vector quantization to the wavelet transform coefficients. The best compression results were obtained by using orthogonal wavelets, due to their ability to represent a signal efficiently. Throughout this thesis the importance of choosing wavelets based on the problem at hand is stressed. In Chapter 5, I introduce a wavelet design method that uses linear prediction in order to design wavelets that are geared to the signal or feature being analyzed. The use of these designed wavelets in a test feature identification application led to positive results. The methods developed in this thesis; the
Analisis Perbandingan Kompresi Haar Wavelet Transform dengan Embedded Zerotree Wavelet pada Citra
LEDYA NOVAMIZANTI
2016-02-01
Full Text Available Abstrak Kompresi data merupakan salah satu teknologi pemicu revolusi multimedia. Haar Wavelet mampu merepresentasikan ciri tekstur dan bentuk, sedangkan Embedded Zerotree Wavelet (EZW mampu menyusun bit-bit menurut tingkat prioritas, sehingga mampu mencapai kompresi maksimal. Pada penelitian ini telah dilakukan perbandingan Haar Wavelet Transform dengan Embendded Zerotree Wavelet untuk kompresi citra. Pengujian menggunakan 4 citra grayscale berformat bitmap (.bmp dengan resolusi 256x256 dan 512x512. Rasio Kompresi yang diperoleh dengan menggunakan algoritma Embedded Zerotree Wavelet dan Haar Wavelet, yaitu 99.54% dan 95.35% pada threshold 80. Laju bit antara Embedded Zerotree Wavelet lebih rendah dibandingkan Haar Wavelet, yaitu 0.06 bpp dan 0.13 bpp. Algoritma Haar Wavelet memberikan waktu kompresi lebih baik dibandingkan EZW dimana selisih antara keduanya sekitar 8 detik. Kata kunci: kompresi citra, threshold, Haar Wavelet, Embedded Zerotree Wavelet Abstract Data compression is one of the triggers of the revolution multimedia technology. Haar Wavelet able to represent the characteristics of texture and shape, while Embedded Zerotree Wavelet (EZW is able to arrange the bits according to priority level, so as to achieve maximum compression. In this study, we had conducted comparison between Haar Wavelet Transform with Embedded Zerotree Wavelet algorithm for image compression. The tests using 4 image format grayscale bitmap (.bmp with resolution of 256x256 pixels and 512x512 pixels. Compression ratio obtained using Embedded Zerotree Wavelet and Wavelet Haar algorithm, which are 99.54% and 95.35% respectively, at the threshold of 80. The bit rate on Embedded Zerotree Wavelet is lower than Haar wavelet, that is 0:06 bpp and 0:13 bpp respectively. Haar Wavelet algorithm gives a better compression time than the EZW, with the difference between the two is about 8 seconds. Keywords: image compression, threshold, Haar Wavelet, Embedded Zerotree
Smart-phone based electrocardiogram wavelet decomposition and neural network classification
Jannah, N.; Hadjiloucas, S.; Hwang, F.; Galvão, R. K. H.
2013-06-01
This paper discusses ECG classification after parametrizing the ECG waveforms in the wavelet domain. The aim of the work is to develop an accurate classification algorithm that can be used to diagnose cardiac beat abnormalities detected using a mobile platform such as smart-phones. Continuous time recurrent neural network classifiers are considered for this task. Records from the European ST-T Database are decomposed in the wavelet domain using discrete wavelet transform (DWT) filter banks and the resulting DWT coefficients are filtered and used as inputs for training the neural network classifier. Advantages of the proposed methodology are the reduced memory requirement for the signals which is of relevance to mobile applications as well as an improvement in the ability of the neural network in its generalization ability due to the more parsimonious representation of the signal to its inputs.
Ming Yi WANG; Guo ZHAO
2005-01-01
A right R-module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R-homomorphism f : m → E can be extended to an R-homomorphism f' : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R-module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R-module over any left perfect right self-injective ring R is the injective hull of a projective submodule.
Andrew M. Parker
2007-12-01
Full Text Available Our previous research suggests that people reporting a stronger desire to maximize obtain worse life outcomes (Bruine de Bruin et al., 2007. Here, we examine whether this finding may be explained by the decision-making styles of self-reported maximizers. Expanding on Schwartz et al. (2002, we find that self-reported maximizers are more likely to show problematic decision-making styles, as evidenced by self-reports of less behavioral coping, greater dependence on others when making decisions, more avoidance of decision making, and greater tendency to experience regret. Contrary to predictions, self-reported maximizers were more likely to report spontaneous decision making. However, the relationship between self-reported maximizing and worse life outcomes is largely unaffected by controls for measures of other decision-making styles, decision-making competence, and demographic variables.
Brüstle, Thomas; Pérotin, Matthieu
2012-01-01
Maximal green sequences are particular sequences of quiver mutations which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. Our aim is to initiate a systematic study of these sequences from a combinatorial point of view. Interpreting maximal green sequences as paths in various natural posets arising in representation theory, we prove the finiteness of the number of maximal green sequences for cluster finite quivers, affine quivers and acyclic quivers with at most three vertices. We also give results concerning the possible numbers and lengths of these maximal green sequences. Finally we describe an algorithm for computing maximal green sequences for arbitrary valued quivers which we used to obtain numerous explicit examples that we present.
A novel audio watermarking scheme using multiscale wavelet modulation
JI Bing; ZHANG De; JI Xiaoyong
2004-01-01
A novel audio watermarking scheme to embed robust and inaudible watermarks for the purpose of copyright protection is proposed. The key innovation is to add time-frequency redundancy into watermark signals by multiscale wavelet modulation. In order to maximize the watermarking strength within perceptual constraints, the signals synthesized from different scales are masked using a frequency auditory model, respectively, and then intergrated to form the final watermark signal. The detection structure is built using the redundancy in watermark signals, and the performance is further enhanced by modeling the statistical behaviors of wavelet coefficients as generalized Gaussian distribution. The use of original audio signal is not required in watermark detection. The experimental results show that our approach can achieve not only good transparency but also satisfying robustness to common audio manipulations.
A Steganographic Method Based on Integer Wavelet Transform & Genatic Algorithm
Preeti Arora
2014-05-01
Full Text Available The proposed system presents a novel approach of building a secure data hiding technique of steganography using inverse wavelet transform along with Genetic algorithm. The prominent focus of the proposed work is to develop RS-analysis proof design with higest imperceptibility. Optimal Pixal Adjustment process is also adopted to minimize the difference error between the input cover image and the embedded-image and in order to maximize the hiding capacity with low distortions respectively. The analysis is done for mapping function, PSNR, image histogram, and parameter of RS analysis. The simulation results highlights that the proposed security measure basically gives better and optimal results in comparison to prior research work conducted using wavelets and genetic algorithm.
Luis A. Vázquez
2015-01-01
Full Text Available A decentralized recurrent wavelet first-order neural network (RWFONN structure is presented. The use of a wavelet Morlet activation function allows proposing a neural structure in continuous time of a single layer and a single neuron in order to identify online in a series-parallel configuration, using the filtered error (FE training algorithm, the dynamics behavior of each joint for a two-degree-of-freedom (DOF vertical robot manipulator, whose parameters such as friction and inertia are unknown. Based on the RWFONN subsystem, a decentralized neural controller is designed via backstepping approach. The performance of the decentralized wavelet neural controller is validated via real-time results.
Complex Wavelet Transform-Based Face Recognition
2009-03-01
Full Text Available Complex approximately analytic wavelets provide a local multiscale description of images with good directional selectivity and invariance to shifts and in-plane rotations. Similar to Gabor wavelets, they are insensitive to illumination variations and facial expression changes. The complex wavelet transform is, however, less redundant and computationally efficient. In this paper, we first construct complex approximately analytic wavelets in the single-tree context, which possess Gabor-like characteristics. We, then, investigate the recently developed dual-tree complex wavelet transform (DT-CWT and the single-tree complex wavelet transform (ST-CWT for the face recognition problem. Extensive experiments are carried out on standard databases. The resulting complex wavelet-based feature vectors are as discriminating as the Gabor wavelet-derived features and at the same time are of lower dimension when compared with that of Gabor wavelets. In all experiments, on two well-known databases, namely, FERET and ORL databases, complex wavelets equaled or surpassed the performance of Gabor wavelets in recognition rate when equal number of orientations and scales is used. These findings indicate that complex wavelets can provide a successful alternative to Gabor wavelets for face recognition.
曾敬枫
2016-01-01
Through the introduction of wavelet image denoising method and wavelet threshold denoising steps,this paper discusses the role of wavelet bases in wavelet threshold denoising, and describes the characteristics of several common wavelet bases and their correlation properties. Finally, respectively with a db2 and sym4 two kinds of wavelet bases by MATLAB, to denoise wavelet threshold realizes the image filtering and reconstruction of high frequency coefficients, so the conclusion is obtained that using different wavelet bases affects the results of image denoising.%通过介绍小波图像去噪的方法和小波阈值去噪的步骤，讨论小波基在小波阈值去噪中的作用，阐述了常见的几种小波基的特征及其相关性质的比较。最后通过在MATLAB下，分别选择了db2和sym4两种小波基，进行小波阈值去噪实现图像高频系数的滤波并重建，得到采用不同的小波基影响图像去噪效果的结论。
Remote Sensing Image Fusion Using Ica and Optimized Wavelet Transform
Hnatushenko, V. V.; Vasyliev, V. V.
2016-06-01
In remote-sensing image processing, fusion (pan-sharpening) is a process of merging high-resolution panchromatic and lower resolution multispectral (MS) imagery to create a single high-resolution color image. Many methods exist to produce data fusion results with the best possible spatial and spectral characteristics, and a number have been commercially implemented. However, the pan-sharpening image produced by these methods gets the high color distortion of spectral information. In this paper, to minimize the spectral distortion we propose a remote sensing image fusion method which combines the Independent Component Analysis (ICA) and optimization wavelet transform. The proposed method is based on selection of multiscale components obtained after the ICA of images on the base of their wavelet decomposition and formation of linear forms detailing coefficients of the wavelet decomposition of images brightness distributions by spectral channels with iteratively adjusted weights. These coefficients are determined as a result of solving an optimization problem for the criterion of maximization of information entropy of the synthesized images formed by means of wavelet reconstruction. Further, reconstruction of the images of spectral channels is done by the reverse wavelet transform and formation of the resulting image by superposition of the obtained images. To verify the validity, the new proposed method is compared with several techniques using WorldView-2 satellite data in subjective and objective aspects. In experiments we demonstrated that our scheme provides good spectral quality and efficiency. Spectral and spatial quality metrics in terms of RASE, RMSE, CC, ERGAS and SSIM are used in our experiments. These synthesized MS images differ by showing a better contrast and clarity on the boundaries of the "object of interest - the background". The results show that the proposed approach performs better than some compared methods according to the performance metrics.
Wavelet-based zerotree coding of aerospace images
Franques, Victoria T.; Jain, Vijay K.
1996-06-01
This paper presents a wavelet based image coding method achieving high levels of compression. A multi-resolution subband decomposition system is constructed using Quadrature Mirror Filters. Symmetric extension and windowing of the multi-scaled subbands are incorporated to minimize the boundary effects. Next, the Embedded Zerotree Wavelet coding algorithm is used for data compression method. Elimination of the isolated zero symbol, for certain subbands, leads to an improved EZW algorithm. Further compression is obtained with an adaptive arithmetic coder. We achieve a PSNR of 26.91 dB at a bit rate of 0.018, 35.59 dB at a bit rate of 0.149, and 43.05 dB at 0.892 bits/pixel for the aerospace image, Refuel.
Wavelet-Based Diffusion Approach for DTI Image Restoration
ZHANG Xiang-fen; CHEN Wu-fan; TIAN Wei-feng; YE Hong
2008-01-01
The Rician noise introduced into the diffusion tensor images (DTIs) can bring serious impacts on tensor calculation and fiber tracking. To decrease the effects of the Rician noise, we propose to consider the wavelet-based diffusion method to denoise multichannel typed diffusion weighted (DW) images. The presented smoothing strategy, which utilizes anisotropic nonlinear diffusion in wavelet domain, successfully removes noise while preserving both texture and edges. To evaluate quantitatively the efficiency of the presented method in accounting for the Rician noise introduced into the DW images, the peak-to-peak signal-to-noise ratio (PSNR) and signal-to-mean squared error ratio (SMSE) metrics are adopted. Based on the synthetic and real data, we calculated the apparent diffusion coefficient (ADC) and tracked the fibers. We made comparisons between the presented model,the wave shrinkage and regularized nonlinear diffusion smoothing method. All the experiment results prove quantitatively and visually the better performance of the presented filter.
Remote Sensing Image Resolution Enlargement Algorithm Based on Wavelet Transformation
Samiul Azam
2014-05-01
Full Text Available In this paper, we present a new image resolution enhancement algorithm based on cycle spinning and stationary wavelet subband padding. The proposed technique or algorithm uses stationary wavelet transformation (SWT to decompose the low resolution (LR image into frequency subbands. All these frequency subbands are interpolated using either bicubic or lanczos interpolation, and these interpolated subbands are put into inverse SWT process for generating intermediate high resolution (HR image. Finally, cycle spinning (CS is applied on this intermediate high resolution image for reducing blocking artifacts, followed by, traditional Laplacian sharpening filter is used to make the generated high resolution image sharper. This new technique has been tested on several satellite images. Experimental result shows that the proposed technique outperforms the conventional and the state-of-the-art techniques in terms of peak signal to noise ratio, root mean square error, entropy, as well as, visual perspective.
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Wavelet-based Image Enhancement Using Fourth Order PDE
Nadernejad, Ehsan; Forchhammer, Søren
2011-01-01
The presence of noise interference signal may cause problems in signal and image analysis; hence signal and image de-noising is often used as a preprocessing stage in many signal processing applications. In this paper, a new method is presented for image de-noising based on fourth order partial...... differential equations (PDEs) and wavelet transform. In the existing wavelet thresholding methods, the final noise reduced image has limited improvement. It is due to keeping the approximate coefficients of the image unchanged. These coefficients have the main information of the image. Since noise affects both...... indicate superiority of the proposed method over the existing waveletbased image de-noising, anisotropic diffusion, and wiener filtering techniques....
On The Fourier And Wavelet Analysis Of Coronal Time Series
Auchère, F; Bocchialini, K; Buchlin, E; Solomon, J
2016-01-01
Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default c...
Cycle-slip Detection of GPS Carrier Phase with Methodology of SA4 Multi-wavelet Transform
HUO Guoping; MIAO Lingjuan
2012-01-01
That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system (GPS).In this paper,an algorithm based on length-4 symmetric/anti-symmetrc (SA4) orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements.Associated with the local singularity detection principle,cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform.Firstly,studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust (GHM),Chui-Lian (CL) and SA4.Moreover,the mathematical characterization of singularities with Lipschitz exponents is explained,the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation.Finally,field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm.Because SA4 possesses the specific nature of good multi-filter properties (GMPs),it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly,and for the half-cycle slip,it also remains better detection,location ability and the equal complexity of wavelet transform.
Wavelet Transforms using VTK-m
Li, Shaomeng [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sewell, Christopher Meyer [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-27
These are a set of slides that deal with the topics of wavelet transforms using VTK-m. First, wavelets are discussed and detailed, then VTK-m is discussed and detailed, then wavelets and VTK-m are looked at from a performance comparison, then from an accuracy comparison, and finally lessons learned, conclusion, and what is next. Lessons learned are the following: Launching worklets is expensive; Natural logic of performing 2D wavelet transform: Repeat the same 1D wavelet transform on every row, repeat the same 1D wavelet transform on every column, invoke the 1D wavelet worklet every time: num_rows x num_columns; VTK-m approach of performing 2D wavelet transform: Create a worklet for 2D that handles both rows and columns, invoke this new worklet only one time; Fast calculation, but cannot reuse 1D implementations.
A Mellin transform approach to wavelet analysis
Alotta, Gioacchino; Di Paola, Mario; Failla, Giuseppe
2015-11-01
The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.
Adaptive inpainting algorithm based on DCT induced wavelet regularization.
Li, Yan-Ran; Shen, Lixin; Suter, Bruce W
2013-02-01
In this paper, we propose an image inpainting optimization model whose objective function is a smoothed l(1) norm of the weighted nondecimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a nondifferentiable term, we present a basic algorithm inspired by Beck and Teboulle's recent work on the model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them in each iteration. The DCT as an orthogonal transform is used in various applications. We view the rows of a DCT matrix as the filters associated with a multiresolution analysis. Nondecimated wavelet transforms with these filters are explored in order to analyze the images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a DCT matrix demonstrate promise for the task of image inpainting.
Orthogonal Matrix-Valued Wavelet Packets
Qingjiang Chen; Cuiling Wang; Zhengxing Cheng
2007-01-01
In this paper,we introduce matrix-valued multiresolution analysis and matrixvalued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular,a new orthonormal basis of L2(R,Cs×s) is obtained from the matrix-valued wavelet packets.
Wavelet-OFDM vs. OFDM: Performance Comparison
Chafii, Marwa; Harbi, Yahya,; Burr, Alister
2016-01-01
International audience; Wavelet-OFDM based on the discrete wavelet transform , has received a considerable attention in the scientific community, because of certain promising characteristics. In this paper, we compare the performance of Wavelet-OFDM based on Meyer wavelet, and OFDM in terms of peak-to-average power ratio (PAPR), bit error rate (BER) for different channels and different equalizers, complexity of implementation, and power spectral density. The simulation results show that, with...
Wavelet-based Evapotranspiration Forecasts
Bachour, R.; Maslova, I.; Ticlavilca, A. M.; McKee, M.; Walker, W.
2012-12-01
Providing a reliable short-term forecast of evapotranspiration (ET) could be a valuable element for improving the efficiency of irrigation water delivery systems. In the last decade, wavelet transform has become a useful technique for analyzing the frequency domain of hydrological time series. This study shows how wavelet transform can be used to access statistical properties of evapotranspiration. The objective of the research reported here is to use wavelet-based techniques to forecast ET up to 16 days ahead, which corresponds to the LANDSAT 7 overpass cycle. The properties of the ET time series, both physical and statistical, are examined in the time and frequency domains. We use the information about the energy decomposition in the wavelet domain to extract meaningful components that are used as inputs for ET forecasting models. Seasonal autoregressive integrated moving average (SARIMA) and multivariate relevance vector machine (MVRVM) models are coupled with the wavelet-based multiresolution analysis (MRA) results and used to generate short-term ET forecasts. Accuracy of the models is estimated and model robustness is evaluated using the bootstrap approach.
Rudiger Bubner
1998-12-01
Full Text Available Even though the maxims' theory is not at thecenter of Kant's ethics, it is the unavoidable basis of the categoric imperative's formulation. Kant leanson the transmitted representations of modem moral theory. During the last decades, the notion of maxims has deserved more attention, due to the philosophy of language's debates on rules, and due to action theory's interest in this notion. I here by brietly expound my views in these discussions.
Robert M. Pasternack; Zhen Qian; Jing-Yi Zheng; Dimitris N. Metaxas; Nada N. Boustany
2009-01-01
.... The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal...
Wavelets for Sparse Representation of Music
Endelt, Line Ørtoft; Harbo, Anders La-Cour
2004-01-01
to the number of vanishing moments of the mother wavelet, and to the smoothness of the signal. In this paper we present the result of applying two classical families of wavelets to a series of musical signals. The purpose is to determine a general relation between the number of vanishing moments of the wavelet...
Oversampling of wavelet frames for real dilations
Bownik, Marcin; Lemvig, Jakob
2012-01-01
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain...
Digital Watermarking in Wavelet Transform Domain
D. Levicky
2001-06-01
Full Text Available This paper presents a technique for the digital watermarking ofstill images based on the wavelet transform. The watermark (binaryimage is embedded into original image in its wavelet domain. Theoriginal unmarked image is required for watermark extraction. Themethod of embedding of digital watermarks in wavelet transform domainwas analyzed and verified on grey scale static images.
Spectral diagonal ensemble Kalman filters
Kasanický, Ivan; Vejmelka, Martin
2015-01-01
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields, which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
Wavelet Representation of Contour Sets
Bertram, M; Laney, D E; Duchaineau, M A; Hansen, C D; Hamann, B; Joy, K I
2001-07-19
We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.
A Real-Time Wavelet-Domain Video Denoising Implementation in FPGA
Pižurica Aleksandra
2006-01-01
Full Text Available The use of field-programmable gate arrays (FPGAs for digital signal processing (DSP has increased with the introduction of dedicated multipliers, which allow the implementation of complex algorithms. This architecture is especially effective for data-intensive applications with extremes in data throughput. Recent studies prove that the FPGAs offer better solutions for real-time multiresolution video processing than any available processor, DSP or general-purpose. FPGA design of critically sampled discrete wavelet transforms has been thoroughly studied in literature over recent years. Much less research was done towards FPGA design of overcomplete wavelet transforms and advanced wavelet-domain video processing algorithms. This paper describes the parallel implementation of an advanced wavelet-domain noise filtering algorithm, which uses a nondecimated wavelet transform and spatially adaptive Bayesian wavelet shrinkage. The implemented arithmetic is decentralized and distributed over two FPGAs. The standard composite television video stream is digitalized and used as a source for real-time video sequences. The results demonstrate the effectiveness of the developed scheme for real-time video processing.
A Real-Time Wavelet-Domain Video Denoising Implementation in FPGA
Wilfried Philips
2006-07-01
Full Text Available The use of field-programmable gate arrays (FPGAs for digital signal processing (DSP has increased with the introduction of dedicated multipliers, which allow the implementation of complex algorithms. This architecture is especially effective for data-intensive applications with extremes in data throughput. Recent studies prove that the FPGAs offer better solutions for real-time multiresolution video processing than any available processor, DSP or general-purpose. FPGA design of critically sampled discrete wavelet transforms has been thoroughly studied in literature over recent years. Much less research was done towards FPGA design of overcomplete wavelet transforms and advanced wavelet-domain video processing algorithms. This paper describes the parallel implementation of an advanced wavelet-domain noise filtering algorithm, which uses a nondecimated wavelet transform and spatially adaptive Bayesian wavelet shrinkage. The implemented arithmetic is decentralized and distributed over two FPGAs. The standard composite television video stream is digitalized and used as a source for real-time video sequences. The results demonstrate the effectiveness of the developed scheme for real-time video processing.
Improved deadzone modeling for bivariate wavelet shrinkage-based image denoising
DelMarco, Stephen
2016-05-01
Modern image processing performed on-board low Size, Weight, and Power (SWaP) platforms, must provide high- performance while simultaneously reducing memory footprint, power consumption, and computational complexity. Image preprocessing, along with downstream image exploitation algorithms such as object detection and recognition, and georegistration, place a heavy burden on power and processing resources. Image preprocessing often includes image denoising to improve data quality for downstream exploitation algorithms. High-performance image denoising is typically performed in the wavelet domain, where noise generally spreads and the wavelet transform compactly captures high information-bearing image characteristics. In this paper, we improve modeling fidelity of a previously-developed, computationally-efficient wavelet-based denoising algorithm. The modeling improvements enhance denoising performance without significantly increasing computational cost, thus making the approach suitable for low-SWAP platforms. Specifically, this paper presents modeling improvements to the Sendur-Selesnick model (SSM) which implements a bivariate wavelet shrinkage denoising algorithm that exploits interscale dependency between wavelet coefficients. We formulate optimization problems for parameters controlling deadzone size which leads to improved denoising performance. Two formulations are provided; one with a simple, closed form solution which we use for numerical result generation, and the second as an integral equation formulation involving elliptic integrals. We generate image denoising performance results over different image sets drawn from public domain imagery, and investigate the effect of wavelet filter tap length on denoising performance. We demonstrate denoising performance improvement when using the enhanced modeling over performance obtained with the baseline SSM model.
A hardware implementation of multiresolution filtering for broadband instrumentation
Kercel, S.W.; Dress, W.B.
1995-12-01
The authors have constructed a wavelet processing board that implements a 14-level wavelet transform. The board uses a high-speed, analog-to-digital (A/D) converter, a hardware queue, and five fixed-point digital signal processing (DSP) chips in a parallel pipeline architecture. All five processors are independently programmable. The board is designed as a general purpose engine for instrumentation applications requiring near real-time wavelet processing or multiscale filtering. The present application is the processing engine of a magnetic field monitor that covers 305 Hz through 5 MHz. The monitor is used for the detection of peak values of magnetic fields in nuclear power plants. This paper describes the design, development, simulation, and testing of the system. Specific issues include the conditioning of real-world signals for wavelet processing, practical trade-offs between queue length and filter length, selection of filter coefficients, simulation of a 14-octave filter bank, and limitations imposed by a fixed-point processor. Test results from the completed wavelet board are included.
Li, Fang; Wang, Ji-hua; Lu, An-xiang; Han, Ping
2015-04-01
The concentration of Cr, Cu, Zn, As and Pb in soil was tested by portable X-ray fluorescence spectrometer. Each sample was tested for 3 times, then after using wavelet threshold noise filtering method for denoising and smoothing the spectra, a standard curve for each heavy metal was established according to the standard values of heavy metals in soil and the corresponding counts which was the average of the 3 processed spectra. The signal to noise ratio (SNR), mean square error (MSE) and information entropy (H) were taken to assess the effects of denoising when using wavelet threshold noise filtering method for determining the best wavelet basis and wavelet decomposition level. Some samples with different concentrations and H3 B03 (blank) were chosen to retest this instrument to verify its stability. The results show that: the best denoising result was obtained with the coif3 wavelet basis at the decomposition level of 3 when using the wavelet transform method. The determination coefficient (R2) range of the instrument is 0.990-0.996, indicating that a high degree of linearity was found between the contents of heavy metals in soil and each X-ray fluorescence spectral characteristic peak intensity with the instrument measurement within the range (0-1,500 mg · kg(-1)). After retesting and calculating, the results indicate that all the detection limits of the instrument are below the soil standards at national level. The accuracy of the model has been effectively improved, and the instrument also shows good precision with the practical application of wavelet transform to the establishment and improvement of X-ray fluorescence spectrometer detection model. Thus the instrument can be applied in on-site rapid screening of heavy metal in contaminated soil.
RFI Mitigation in Microwave Radiometry Using Wavelets
José Miguel Tarongí
2009-09-01
Full Text Available The performance of microwave radiometers can be seriously degraded by the presence of radio-frequency interference (RFI. Spurious signals and harmonics from lower frequency bands, spread-spectrum signals overlapping the “protected” band of operation, or out-of-band emissions not properly rejected by the pre-detection filters due to the finite rejection modify the detected power and the estimated antenna temperature from which the geophysical parameters will be retrieved. In recent years, techniques to detect the presence of RFI have been developed. They include time- and/or frequency domain analyses, or statistical analysis of the received signal which, in the absence of RFI, must be a zero-mean Gaussian process. Current mitigation techniques are mostly based on blanking in the time and/or frequency domains where RFI has been detected. However, in some geographical areas, RFI is so persistent in time that is not possible to acquire RFI-free radiometric data. In other applications such as sea surface salinity retrieval, where the sensitivity of the brightness temperature to salinity is weak, small amounts of RFI are also very difficult to detect and mitigate. In this work a wavelet-based technique is proposed to mitigate RFI (cancel RFI as much as possible. The interfering signal is estimated by using the powerful denoising capabilities of the wavelet transform. The estimated RFI signal is then subtracted from the received signal and a “cleaned” noise signal is obtained, from which the power is estimated later. The algorithm performance as a function of the threshold type, and the threshold selection method, the decomposition level, the wavelet type and the interferenceto-noise ratio is presented. Computational requirements are evaluated in terms of quantization levels, number of operations, memory requirements (sequence length. Even though they are high for today’s technology, the algorithms presented can be applied to recorded data
Recent advances in wavelet technology
Wells, R. O., Jr.
1994-01-01
Wavelet research has been developing rapidly over the past five years, and in particular in the academic world there has been significant activity at numerous universities. In the industrial world, there has been developments at Aware, Inc., Lockheed, Martin-Marietta, TRW, Kodak, Exxon, and many others. The government agencies supporting wavelet research and development include ARPA, ONR, AFOSR, NASA, and many other agencies. The recent literature in the past five years includes a recent book which is an index of citations in the past decade on this subject, and it contains over 1,000 references and abstracts.
Wavelet Analysis for Molecular Dynamics
2015-06-01
2480. 4. Ismail AE, Rutledge GC, Stephanopoulos G. Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. I. Freely...accelerated Monte Carlo. II. Self-avoiding chains. J Chem Phys. 2005;122:234902. 6. Coifman R, Maggioni M. Diffusion wavelets. Appl Comput Harm Anal...INFORMATION CTR DTIC OCA 2 (PDF) DIRECTOR US ARMY RESEARCH LAB RDRL CIO LL IMAL HRA MAIL & RECORDS MGMT 1 (PDF) GOVT PRINTG OFC A MALHOTRA 1 (PDF) DIR USARL RDRL WML B B RICE 21 INTENTIONALLY LEFT BLANK. 22
WAVELET ANALYSIS OF MODULATED SIGNALS
Hu Jianwei; Yang Shaoquan
2006-01-01
The relationship between Haar wavelet decomposition coefficients and modulated signal parameters is discussed. A new modulation classification method is presented. The new method uses the amplitude,frequency and phase information derived from Haar wavelet decomposition as feature vectors to distinguish the modulation types of M-ary Frequency-Shift Keying (MFSK), M-ary Phase-Shift Keying (MPSK) and Quadrature Amplitude Modulation (QAM) modulation types. A parallel combined classifier is designed based on these feature vectors. The overall successful recognition rate of 92.4% can be achieved even at a low Signal-to-Noise Ratio (SNR) of 5dB.
A CMOS Morlet Wavelet Generator
A. I. Bautista-Castillo
2017-04-01
Full Text Available The design and characterization of a CMOS circuit for Morlet wavelet generation is introduced. With the proposed Morlet wavelet circuit, it is possible to reach a~low power consumption, improve standard deviation (σ control and also have a small form factor. A prototype in a double poly, three metal layers, 0.5 µm CMOS process from MOSIS foundry was carried out in order to verify the functionality of the proposal. However, the design methodology can be extended to different CMOS processes. According to the performance exhibited by the circuit, may be useful in many different signal processing tasks such as nonlinear time-variant systems.
Optimization of integrated polarization filters
Gagnon, Denis; Déziel, Jean-Luc; Dubé, Louis J
2014-01-01
This study reports on the design of small footprint, integrated polarization filters based on engineered photonic lattices. Using a rods-in-air lattice as a basis for a TE filter and a holes-in-slab lattice for the analogous TM filter, we are able to maximize the degree of polarization of the output beams up to 98 % with a transmission efficiency greater than 75 %. The proposed designs allow not only for logical polarization filtering, but can also be tailored to output an arbitrary transverse beam profile. The lattice configurations are found using a recently proposed parallel tabu search algorithm for combinatorial optimization problems in integrated photonics.
An Overview on Wavelet Software Packages
无
2001-01-01
Wavelet analysis provides very powerful problem-solving tools foranalyzing, en coding, compressing, reconstructing, and modeling signals and images. The amount of wavelets-related software has been constantly multiplying. Many wavelet ana lysis tools are widely available. This overview represents a significant survey for many currently available packages. It will be of great benefit to engineers and researchers for using the toolkits and developing new software. The beginner to learning wavelets can also get a great help from the review. If you browse a round at some of the Internet sites listed in the reference of this paper, you m ay find more plentiful wavelet resources.
Page, Ralph H.; Doty, Patrick F.
2017-08-01
The various technologies presented herein relate to a tiled filter array that can be used in connection with performance of spatial sampling of optical signals. The filter array comprises filter tiles, wherein a first plurality of filter tiles are formed from a first material, the first material being configured such that only photons having wavelengths in a first wavelength band pass therethrough. A second plurality of filter tiles is formed from a second material, the second material being configured such that only photons having wavelengths in a second wavelength band pass therethrough. The first plurality of filter tiles and the second plurality of filter tiles can be interspersed to form the filter array comprising an alternating arrangement of first filter tiles and second filter tiles.
Efficient Reversible Watermarking Using Differential Expansible Integer Wavelet Transform
Sanjay Patel
2016-07-01
Full Text Available Digital watermarking has been utilized widely to claim the ownership and to protect images from alternation. Reversible watermarking is having great importance as it provided original image and the embedded logo without any loss. This paper proposed reversible watermarking algorithm using integer wavelet transform to satisfy the reversibility requirement. Further difference expansion based lifting scheme is used to make algorithm fast. To show the robustness of algorithm, various attacks like noise, rotating/scaling an image and filtering to the watermarked image is employed. The extraction of original image against such attacks is quantified in terms of peak signal to noise ratio (PSNR
Directional spin wavelets on the sphere
McEwen, Jason D; Büttner, Martin; Peiris, Hiranya V; Wiaux, Yves
2015-01-01
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the sphere that is able to probe the directional intensity of spin signals. Furthermore, directional spin scale-discretised wavelets support the exact synthesis of a signal on the sphere from its wavelet coefficients and satisfy excellent localisation and uncorrelation properties. Consequently, directional spin scale-discretised wavelets are likely to be of use in a wide range of applications and in particular for the analysis of the polarisation of the cosmic microwave background (CMB). We develop new algorithms to compute (scalar and spin) forward and inverse wavelet transforms exactly and efficiently for very large data-sets containing tens of millions of samples on the sphere. By leveraging a novel sampling theorem on the rotation group developed in a companion article, only hal...
Denoising and robust nonlinear wavelet analysis
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-03-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.
Multi-spectral image fusion method based on two channels non-separable wavelets
LIU Bin; PENG JiaXiong
2008-01-01
A construction method of two channels non-separable wavelets filter bank which dilation matrix is [1, 1; 1, -1] and its application in the fusion of multi-spectral image are presented. Many 4x4 filter banks are designed. The multi-spectral image fusion algorithm based on this kind of wavelet is proposed. Using this filter bank, multi-resolution wavelet decomposition of the intensity of multi-spectral image and panchromatic image is performed, and the two low-frequency components of the intensity and the panchromatic image are merged by using a tradeoff parameter. The experiment results show that this method is good in the preservation of spectral quality and high spatial resolution information. Its performance in preserving spectral quality and high spatial information is better than the fusion method based on DWFT and IHS. When the parameter t is closed to 1, the fused image can obtain rich spectral information from the original MS image. The amount of computation reduced to only half of the fusion method based on four channels wavelet transform.
Implementation of the 2-D Wavelet Transform into FPGA for Image
León, M.; Barba, L.; Vargas, L.; Torres, C. O.
2011-01-01
This paper presents a hardware system implementation of the of discrete wavelet transform algoritm in two dimensions for FPGA, using the Daubechies filter family of order 2 (db2). The decomposition algorithm of this transform is designed and simulated with the Hardware Description Language VHDL and is implemented in a programmable logic device (FPGA) XC3S1200E reference, Spartan IIIE family, by Xilinx, take advantage the parallels properties of these gives us and speeds processing that can reach them. The architecture is evaluated using images input of different sizes. This implementation is done with the aim of developing a future images encryption hardware system using wavelet transform for security information.
Min Wang; Zhen Li; Xiangjun Duan; Wei Li
2015-01-01
This paper proposes an image denoising method, using the wavelet transform and the singular value decomposition (SVD), with the enhancement of the directional features. First, use the single-level discrete 2D wavelet transform to decompose the noised image into the low-frequency image part and the high-frequency parts (the horizontal, vertical, and diagonal parts), with the edge extracted and retained to avoid edge loss. Then, use the SVD to filter the noise of the high-frequency parts with i...
Peak alignment using wavelet pattern matching and differential evolution.
Zhang, Zhi-Min; Chen, Shan; Liang, Yi-Zeng
2011-01-30
Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).
Adaptive wavelet transform algorithm for image compression applications
Pogrebnyak, Oleksiy B.; Manrique Ramirez, Pablo
2003-11-01
A new algorithm of locally adaptive wavelet transform is presented. The algorithm implements the integer-to-integer lifting scheme. It performs an adaptation of the wavelet function at the prediction stage to the local image data activity. The proposed algorithm is based on the generalized framework for the lifting scheme that permits to obtain easily different wavelet coefficients in the case of the (N~,N) lifting. It is proposed to perform the hard switching between (2, 4) and (4, 4) lifting filter outputs according to an estimate of the local data activity. When the data activity is high, i.e., in the vicinity of edges, the (4, 4) lifting is performed. Otherwise, in the plain areas, the (2,4) decomposition coefficients are calculated. The calculations are rather simples that permit the implementation of the designed algorithm in fixed point DSP processors. The proposed adaptive transform possesses the perfect restoration of the processed data and possesses good energy compactation. The designed algorithm was tested on different images. The proposed adaptive transform algorithm can be used for image/signal lossless compression.
On the Fourier and Wavelet Analysis of Coronal Time Series
Auchère, F.; Froment, C.; Bocchialini, K.; Buchlin, E.; Solomon, J.
2016-07-01
Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provides a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.
On the construction of invertible filter banks on the 2-sphere.
Yeo, Boon Thye Thomas; Ou, Wanmei; Golland, Polina
2008-03-01
The theories of signal sampling, filter banks, wavelets, and "overcomplete wavelets" are well established for the Euclidean spaces and are widely used in the processing and analysis of images. While recent advances have extended some filtering methods to spherical images, many key challenges remain. In this paper, we develop theoretical conditions for the invertibility of filter banks under continuous spherical convolution. Furthermore, we present an analogue of the Papoulis generalized sampling theorem on the 2-Sphere. We use the theoretical results to establish a general framework for the design of invertible filter banks on the sphere and demonstrate the approach with examples of self-invertible spherical wavelets and steerable pyramids. We conclude by examining the use of a self-invertible spherical steerable pyramid in a denoising experiment and discussing the computational complexity of the filtering framework.
An Image Denoising Framework with Multi-resolution Bilateral Filtering and Normal Shrink Approach
Shivani Sharma
2014-02-01
Full Text Available In this study, an image denoising algorithm is presented, which takes into account wavelet thresholding and bilateral filtering in transform domain. The proposed algorithm gives an extension of the bilateral filter i.e., multiresolution bilateral filter, in which bilateral filtering is applied to the approximation sub bands and normal shrink is used for thresholding the wavelet coefficients of the detail sub bands of an image decomposed using a wavelet filter bank up to 2-level of decomposition. The algorithm is tested against ultrasound image of gall bladder corrupted by different types of noise namely, gaussian, speckle, poisson and impulse. The result shows that with increase in decomposition levels the proposed method is effective in eliminating noise but gives overly smoothed image. The algorithm outperforms with speckle and poisson noise at 2- level decomposition in terms of PSNR.
Numerical simulation of large fabric filter
Kovařík Petr
2012-04-01
Full Text Available Fabric filters are used in the wide range of industrial technologies for cleaning of incoming or exhaust gases. To achieve maximal efficiency of the discrete phase separation and long lifetime of the filter hoses, it is necessary to ensure uniform load on filter surface and to avoid impacts of heavy particles with high velocities to the filter hoses. The paper deals with numerical simulation of two phase flow field in a large fabric filter. The filter is composed of six chambers with approx. 1600 filter hoses in total. The model was simplified to one half of the filter, the filter hoses walls were substituted by porous zones. The model settings were based on experimental data, especially on the filter pressure drop. Unsteady simulations with different turbulence models were done. Flow field together with particles trajectories were analyzed. The results were compared with experimental observations.
Numerical simulation of large fabric filter
Sedláček, Jan; Kovařík, Petr
2012-04-01
Fabric filters are used in the wide range of industrial technologies for cleaning of incoming or exhaust gases. To achieve maximal efficiency of the discrete phase separation and long lifetime of the filter hoses, it is necessary to ensure uniform load on filter surface and to avoid impacts of heavy particles with high velocities to the filter hoses. The paper deals with numerical simulation of two phase flow field in a large fabric filter. The filter is composed of six chambers with approx. 1600 filter hoses in total. The model was simplified to one half of the filter, the filter hoses walls were substituted by porous zones. The model settings were based on experimental data, especially on the filter pressure drop. Unsteady simulations with different turbulence models were done. Flow field together with particles trajectories were analyzed. The results were compared with experimental observations.
Implementing wavelet transform with SAW elements
LU; Wenke(卢文科); ZHU; Changchun(朱长纯); LIU; Junhua(刘君华); LIU; Qinghong(刘清洪)
2003-01-01
In the design of the finger-overlap envelope according to the envelope of wavelet function, it is concluded that the pulse-response function of the interdigital transducer (IDT) for surface acoustic wave (SAW) is identical to the wavelet function. SAW type of the wavelet-transform element is manufactured. A new method of using two wavelet-transform elements to manufacture the reconstruction element of the wavelet transform is proposed. The sources of the element error are analyzed, and the methods for reducing the error are put forward. SAW type of the wavelet transformation element and its reconstruction element have the following three characteristics: (i) the implementing methods of the wavelet transform element and its reconstruction element are simple, and free of complicated mathematical algorithms of the wavelet transform; (ii) because one of SAW element is fast, the response velocities of SAW type of the wavelet transform element and its reconstruction element are also fast; (iii) the costs of the wavelet transform element and its reconstruction element are low, so the elements may be manufactured in a large quantity.
EEG Signal Denoising and Feature Extraction Using Wavelet Transform in Brain Computer Interface
WU Ting; YAN Guo-zheng; YANG Bang-hua; SUN Hong
2007-01-01
Electroencephalogram (EEG) signal preprocessing is one of the most important techniques in brain computer interface (BCI). The target is to increase signal-to-noise ratio and make it more favorable for feature extraction and pattern recognition. Wavelet transform is a method of multi-resolution time-frequency analysis, it can decompose the mixed signals which consist of different frequencies into different frequency band. EEG signal is analyzed and denoised using wavelet transform. Moreover, wavelet transform can be used for EEG feature extraction. The energies of specific sub-bands and corresponding decomposition coefficients which have maximal separability according to the Fisher distance criterion are selected as features. The eigenvector for classification is obtained by combining the effective features from different channels. The performance is evaluated by separability and pattern recognition accuracy using the data set of BCI 2003 Competition, the final classification results have proved the effectiveness of this technology for EEG denoising and feature extraction.
Md. Rafiqul Islam
2012-05-01
Full Text Available Fingerprint analysis plays a crucial role in crucial legal matters such as investigation of crime and security system. Due to the large number and size of fingerprint images, data compression has to be applied to reduce the storage and communication bandwidth requirements of those images. To do this, there are many types of wavelet has been used for fingerprint image compression. In this paper we haveused Coiflet-Type wavelets and our aim is to determine the most appropriate Coiflet-Type wavelet for better compression of a digitized fingerprint image and to achieve our goal Retain Energy (RE and Number of Zeros (NZ in percentage is determined for different Coiflet-Type wavelets at different threshold values at the fixed decomposition level 3 using wavelet and wavelet packet transform. We have used 8-bit grayscale left thumb digitized fingerprint image of size 480×400 as a test image.
Wavelet-based texture analysis of EEG signal for prediction of epileptic seizure
Petrosian, Arthur A.; Homan, Richard; Pemmaraju, Suryalakshmi; Mitra, Sunanda
1995-09-01
Electroencephalographic (EEG) signal texture content analysis has been proposed for early warning of an epileptic seizure. This approach was evaluated by investigating the interrelationship between texture features and basic signal informational characteristics, such as Kolmogorov complexity and fractal dimension. The comparison of several traditional techniques, including higher-order FIR digital filtering, chaos, autoregressive and FFT time- frequency analysis was also carried out on the same epileptic EEG recording. The purpose of this study is to investigate whether wavelet transform can be used to further enhance the developed methods for prediction of epileptic seizures. The combined consideration of texture and entropy characteristics extracted from subsignals decomposed by wavelet transform are explored for that purpose. Yet, the novel neuro-fuzzy clustering algorithm is performed on wavelet coefficients to segment given EEG recording into different stages prior to an actual seizure onset.
Afeyan, Bedros; Starck, Jean Luc; Cuneo, Michael
2012-01-01
We introduce wavelets, curvelets and multiresolution analysis techniques to assess the symmetry of X ray driven imploding shells in ICF targets. After denoising X ray backlighting produced images, we determine the Shell Thickness Averaged Radius (STAR) of maximum density, r*(N, {\\theta}), where N is the percentage of the shell thickness over which to average. The non-uniformities of r*(N, {\\theta}) are quantified by a Legendre polynomial decomposition in angle, {\\theta}. Undecimated wavelet decompositions outperform decimated ones in denoising and both are surpassed by the curvelet transform. In each case, hard thresholding based on noise modeling is used. We have also applied combined wavelet and curvelet filter techniques with variational minimization as a way to select the significant coefficients. Gains are minimal over curvelets alone in the images we have analyzed.
TEXTURE BASED LAND COVER CLASSIFICATION ALGORITHM USING GABOR WAVELET AND ANFIS CLASSIFIER
S. Jenicka
2016-05-01
Full Text Available Texture features play a predominant role in land cover classification of remotely sensed images. In this study, for extracting texture features from data intensive remotely sensed image, Gabor wavelet has been used. Gabor wavelet transform filters frequency components of an image through decomposition and produces useful features. For classification of fuzzy land cover patterns in the remotely sensed image, Adaptive Neuro Fuzzy Inference System (ANFIS has been used. The strength of ANFIS classifier is that it combines the merits of fuzzy logic and neural network. Hence in this article, land cover classification of remotely sensed image has been performed using Gabor wavelet and ANFIS classifier. The classification accuracy of the classified image obtained is found to be 92.8%.
Area and Throughput Trade-Offs in the Design of Pipelined Discrete Wavelet Transform Architectures
Silva, Sandro V
2011-01-01
The JPEG2000 standard defines the discrete wavelet transform (DWT) as a linear space-to-frequency transform of the image domain in an irreversible compression. This irreversible discrete wavelet transform is implemented by FIR filter using 9/7 Daubechies coefficients or a lifting scheme of factorizated coefficients from 9/7 Daubechies coefficients. This work investigates the tradeoffs between area, power and data throughput (or operating frequency) of several implementations of the Discrete Wavelet Transform using the lifting scheme in various pipeline designs. This paper shows the results of five different architectures synthesized and simulated in FPGAs. It concludes that the descriptions with pipelined operators provide the best area-power-operating frequency trade-off over non-pipelined operators descriptions. Those descriptions require around 40% more hardware to increase the maximum operating frequency up to 100% and reduce power consumption to less than 50%. Starting from behavioral HDL descriptions pr...
CW-THz image contrast enhancement using wavelet transform and Retinex
Chen, Lin; Zhang, Min; Hu, Qi-fan; Huang, Ying-Xue; Liang, Hua-Wei
2015-10-01
To enhance continuous wave terahertz (CW-THz) scanning images contrast and denoising, a method based on wavelet transform and Retinex theory was proposed. In this paper, the factors affecting the quality of CW-THz images were analysed. Second, an approach of combination of the discrete wavelet transform (DWT) and a designed nonlinear function in wavelet domain for the purpose of contrast enhancing was applied. Then, we combine the Retinex algorithm for further contrast enhancement. To evaluate the effectiveness of the proposed method in qualitative and quantitative, it was compared with the adaptive histogram equalization method, the homomorphic filtering method and the SSR(Single-Scale-Retinex) method. Experimental results demonstrated that the presented algorithm can effectively enhance the contrast of CW-THZ image and obtain better visual effect.
Weng, Jiawen; Zhong, Jingang; Hu, Cuiying
2009-06-20
We describe a numerical reconstruction technique for digital holography by means of the two-dimensional Gabor wavelet transform (2D-GWT). Applying the 2D-GWT to digital holography, the object wave can be reconstructed by calculating the wavelet coefficients of the hologram at the peak of the 2D-GWT automatically. At the same time the effect of the zero-order diffraction image and the twin image are eliminated without spatial filtering. Comparing the numerical reconstruction of a holographic image by the analysis of the one-dimensional Gabor wavelet transform (1D-GWT) with the 2D-GWT, we show that the 2D-GWT method is superior to the 1D-GWT method, especially when the fringes of the hologram are not just along the y direction. The theory and the results of a simulation and experiments are shown.
Janusz Brzozowski
2014-05-01
Full Text Available The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result: If L is a regular language of quotient complexity n and G is the subgroup of permutations in the transition semigroup T of the minimal DFA of L, then L is maximally atomic if and only if G is transitive on k-subsets of 1,...,n for 0 <= k <= n and T contains a transformation of rank n-1.
Optimization of integer wavelet transforms based on difference correlation structures.
Li, Hongliang; Liu, Guizhong; Zhang, Zhongwei
2005-11-01
In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.
Classification of multiple diseases based on wavelet features
Nalini Bodasingi
2017-03-01
Full Text Available This study presents an efficient disease classification approach based on medical images. The approach is more efficient as it reduces the computational complexity. The implementation uses only two wavelet filters in selecting the texture features as compared with five filters used in the earlier research works. The computed average and energy features are fed to feed-forward neural network (FFNN and support vector machine (SVM classifiers. The SVM is proved as a better classifier than the FFNN for all the three diseases related to skin, breast and retina with an improved accuracies of 89%, 92% and 100%, respectively. Also, a graphical user interface is developed useful for various disease classification based on the whole dataset of size 100.
Andersen, Klaus Ejner
1985-01-01
Guinea pig maximization tests (GPMT) with chlorocresol were performed to ascertain whether the sensitization rate was affected by minor changes in the Freund's complete adjuvant (FCA) emulsion used. Three types of emulsion were evaluated: the oil phase was mixed with propylene glycol, saline with...... to the saline/oil emulsion. Placing of the challenge patches affected the response, as simultaneous chlorocresol challenge on the flank located 2 cm closer to the abdomen than the usual challenge site gave decreased reactions....
Zak, Michail
2008-01-01
A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).
Modeling Network Traffic in Wavelet Domain
Sheng Ma
2004-12-01
Full Text Available This work discovers that although network traffic has the complicated short- and long-range temporal dependence, the corresponding wavelet coefficients are no longer long-range dependent. Therefore, a "short-range" dependent process can be used to model network traffic in the wavelet domain. Both independent and Markov models are investigated. Theoretical analysis shows that the independent wavelet model is sufficiently accurate in terms of the buffer overflow probability for Fractional Gaussian Noise traffic. Any model, which captures additional correlations in the wavelet domain, only improves the performance marginally. The independent wavelet model is then used as a unified approach to model network traffic including VBR MPEG video and Ethernet data. The computational complexity is O(N for developing such wavelet models and generating synthesized traffic of length N, which is among the lowest attained.
Watermarking for Multimedia Security Using Complex Wavelets
Alastair Ian Thompson
2010-10-01
Full Text Available This paper investigates the application of complex wavelet transforms to the field of digital data hiding. Complex wavelets offer improved directional selectivity and shift invariance over their discretely sampled counterparts allowing for better adaptation of watermark distortions to the host media. Two methods of deriving visual models for the watermarking system are adapted to the complex wavelet transforms and their performances are compared. To produce improved capacity a spread transform embedding algorithm is devised, this combines the robustness of spread spectrum methods with the high capacity of quantization based methods. Using established information theoretic methods, limits of watermark capacity are derived that demonstrate the superiority of complex wavelets over discretely sampled wavelets. Finally results for the algorithm against commonly used attacks demonstrate its robustness and the improved performance offered by complex wavelet transforms.
On the wavelet optimized finite difference method
Jameson, Leland
1994-01-01
When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.
Cross wavelet analysis: significance testing and pitfalls
D. Maraun
2004-01-01
Full Text Available In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs.
Visualization of a Turbulent Jet Using Wavelets
Hui LI
2001-01-01
An application of multiresolution image analysis to turbulence was investigated in this paper, in order to visualize the coherent structure and the most essential scales governing turbulence. The digital imaging photograph of jet slice was decomposed by two-dimensional discrete wavelet transform based on Daubechies, Coifman and Baylkin bases. The best choice of orthogonal wavelet basis for analyzing the image of the turbulent structures was first discussed. It is found that these orthonormal wavelet families with index N＜10 were inappropriate for multiresolution image analysis of turbulent flow. The multiresolution images of turbulent structures were very similar when using the wavelet basis with the higher index number, even though wavelet bases are different functions. From the image components in orthogonal wavelet spaces with different scales, the further evident of the multi-scale structures in jet can be observed, and the edges of the vortices at different resolutions or scales and the coherent structure can be easily extracted.
Background Subtraction Based on Three-Dimensional Discrete Wavelet Transform.
Han, Guang; Wang, Jinkuan; Cai, Xi
2016-03-30
Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques.
Analysis of Acoustic Emission Signals using WaveletTransformation Technique
S.V. Subba Rao
2008-07-01
Full Text Available Acoustic emission (AE monitoring is carried out during proof pressure testing of pressurevessels to find the occurrence of any crack growth-related phenomenon. While carrying out AEmonitoring, it is often found that the background noise is very high. Along with the noise, thesignal includes various phenomena related to crack growth, rubbing of fasteners, leaks, etc. Dueto the presence of noise, it becomes difficult to identify signature of the original signals related to the above phenomenon. Through various filtering/ thresholding techniques, it was found that the original signals were getting filtered out along with noise. Wavelet transformation technique is found to be more appropriate to analyse the AE signals under such situations. Wavelet transformation technique is used to de-noise the AE data. The de-noised signal is classified to identify a signature based on the type of phenomena.Defence Science Journal, 2008, 58(4, pp.559-564, DOI:http://dx.doi.org/10.14429/dsj.58.1677
Spatial model of lifting scheme in wavelet transforms and image compression
Wu, Yu; Li, Gang; Wang, Guoyin
2002-03-01
Wavelet transforms via lifting scheme are called the second-generation wavelet transforms. However, in some lifting schemes the coefficients are transformed using mathematical method from the first-generation wavelets, so the filters with better performance using in lifting are limited. The spatial structures of lifting scheme are also simple. For example, the classical lifting scheme, predicting-updating, is two-stage, and most researchers simply adopt this structure. In addition, in most design results the lifting filters are not only hard to get and also fixed. In our former work, we had presented a new three-stage lifting scheme, predicting-updating-adapting, and the results of filter design are no more fixed. In this paper, we continue to research the spatial model of lifting scheme. A group of general multi-stage lifting schemes are achieved and designed. All lifting filters are designed in spatial domain and proper mathematical methods are selected. Our designed coefficients are flexible and can be adjusted according to different data. We give the mathematical design details in this paper. Finally, all designed model of lifting are used in image compression and satisfactory results are achieved.
2001-10-25
We evaluate a combined discrete wavelet transform (DWT) and wavelet packet algorithm to improve the homogeneity of magnetic resonance imaging when a...image and uses this information to normalize the image intensity variations. Estimation of the coil sensitivity profile based on the wavelet transform of
Embedded Zero -Tree Wavelet Based Image Steganography
Vijendra Rai; Jaishree Jain; Ajay Kr. Yadav; Sheshmani Yadav
2012-01-01
Image steganography using Discrete Wavelet Transform can attain very good results as compared to traditional methods, in this paper we discuss a method to embed digital watermark based on modifying frequency coefficient in discrete wavelet transform (DWT) domain. This method uses the embedded zero-tree (EZW) algorithm to insert a watermark in discrete wavelet transform domain. EZW is an effective image compression algorithm, having property that image in the bit stream are generated in order...
Wavelet transform of neural spike trains
Kim, Youngtae; Jung, Min Whan; Kim, Yunbok
2000-02-01
Wavelet transform of neural spike trains recorded with a tetrode in the rat primary somatosensory cortex is described. Continuous wavelet transform (CWT) of the spike train clearly shows singularities hidden in the noisy or chaotic spike trains. A multiresolution analysis of the spike train is also carried out using discrete wavelet transform (DWT) for denoising and approximating at different time scales. Results suggest that this multiscale shape analysis can be a useful tool for classifying the spike trains.
A Class of Bidimensional FMRA Wavelet Frames
Yun Zhang LI
2006-01-01
This paper addresses the construction of wavelet frame from a frame multiresolution analysis (FMRA) associated with a dilation matrix of determinant ±2. The dilation matrices of determinant ±2 can be classified as six classes according to integral similarity. In this paper, for four classes of them, the construction of wavelet frame from an FMRA is obtained, and, as examples, Shannon type wavelet frames are constructed, which have an independent value for their optimality in some sense.
Wavelets and the lifting scheme
la Cour-Harbo, Anders; Jensen, Arne
2012-01-01
The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge of li...... of linear algebra and signal processing will suffice. The lifting based definition is equivalent to the usual filer bank based definition of the DWT. The article does not discuss applications in any detail. The reader is referred to other articles in this collection.......The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge...
Wavelets and the lifting scheme
la Cour-Harbo, Anders; Jensen, Arne
2009-01-01
The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge of li...... of linear algebra and signal processing will suffice. The lifting based definition is equivalent to the usual filer bank based definition of the DWT. The article does not discuss applications in any detail. The reader is referred to other articles in this collection.......The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge...
Wavelets and the Lifting Scheme
la Cour-Harbo, Anders; Jensen, Arne
The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge of li...... of linear algebra and signal processing will suffice. The lifting based definition is equivalent to the usual filer bank based definition of the DWT. The article does not discuss applications in any detail. The reader is referred to other articles in this collection.......The objective of this article is to give a concise introduction to the discrete wavelet transform (DWT) based on a technique called lifting. The lifting technique allows one to give an elementary, but rigorous, definition of the DWT, with modest requirements on the reader. A basic knowledge...
Wavelet analysis of epileptic spikes
Latka, M; Kozik, A; West, B J; Latka, Miroslaw; Was, Ziemowit; Kozik, Andrzej; West, Bruce J.
2003-01-01
Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.
Tree wavelet approximations with applications
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
Wavelet analysis of epileptic spikes
Latka, Miroslaw; Was, Ziemowit; Kozik, Andrzej; West, Bruce J.
2003-05-01
Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.
Deasy, Joseph O; Wickerhauser, M Victor; Picard, Mathieu
2002-10-01
The Monte Carlo dose calculation method works by simulating individual energetic photons or electrons as they traverse a digital representation of the patient anatomy. However, Monte Carlo results fluctuate until a large number of particles are simulated. We propose wavelet threshold de-noising as a postprocessing step to accelerate convergence of Monte Carlo dose calculations. A sampled rough function (such as Monte Carlo noise) gives wavelet transform coefficients which are more nearly equal in amplitude than those of a sampled smooth function. Wavelet hard-threshold de-noising sets to zero those wavelet coefficients which fall below a threshold; the image is then reconstructed. We implemented the computationally efficient 9,7-biorthogonal filters in the C language. Transform results were averaged over transform origin selections to reduce artifacts. A method for selecting best threshold values is described. The algorithm requires about 336 floating point arithmetic operations per dose grid point. We applied wavelet threshold de-noising to two two-dimensional dose distributions: a dose distribution generated by 10 MeV electrons incident on a water phantom with a step-heterogeneity, and a slice from a lung heterogeneity phantom. Dose distributions were simulated using the Integrated Tiger Series Monte Carlo code. We studied threshold selection, resulting dose image smoothness, and resulting dose image accuracy as a function of the number of source particles. For both phantoms, with a suitable value of the threshold parameter, voxel-to-voxel noise was suppressed with little introduction of bias. The roughness of wavelet de-noised dose distributions (according to a Laplacian metric) was nearly independent of the number of source electrons, though the accuracy of the de-noised dose image improved with increasing numbers of source electrons. We conclude that wavelet shrinkage de-noising is a promising method for effectively accelerating Monte Carlo dose calculations
Wavelet-based calculation of cerebral angiographic data from time-resolved CT perfusion acquisitions
Havla, Lukas; Dietrich, Olaf [Ludwig-Maximilians-University Hospital Munich, Josef-Lissner-Laboratory for Biomedical Imaging, Institute for Clinical Radiology, Munich (Germany); Thierfelder, Kolja M.; Beyer, Sebastian E.; Sommer, Wieland H. [Ludwig-Maximilians-University Hospital Munich, Institute for Clinical Radiology, Munich (Germany)
2015-08-15
To evaluate a new approach for reconstructing angiographic images by application of wavelet transforms on CT perfusion data. Fifteen consecutive patients with suspected stroke were examined with a multi-detector CT acquiring 32 dynamic phases (∇t = 1.5s) of 99 slices (total slab thickness 99mm) at 80kV/200mAs. Thirty-five mL of iomeprol-350 was injected (flow rate = 4.5mL/s). Angiographic datasets were calculated after initial rigid-body motion correction using (a) temporally filtered maximum intensity projections (tMIP) and (b) the wavelet transform (Paul wavelet, order 1) of each voxel time course. The maximum of the wavelet-power-spectrum was defined as the angiographic signal intensity. The contrast-to-noise ratio (CNR) of 18 different vessel segments was quantified and two blinded readers rated the images qualitatively using 5pt Likert scales. The CNR for the wavelet angiography (501.8 ± 433.0) was significantly higher than for the tMIP approach (55.7 ± 29.7, Wilcoxon test p < 0.00001). Image quality was rated to be significantly higher (p < 0.001) for the wavelet angiography with median scores of 4/4 (reader 1/reader 2) than the tMIP (scores of 3/3). The proposed calculation approach for angiography data using temporal wavelet transforms of intracranial CT perfusion datasets provides higher vascular contrast and intrinsic removal of non-enhancing structures such as bone. (orig.)
Anderson, Brian D O
2005-01-01
This graduate-level text augments and extends beyond undergraduate studies of signal processing, particularly in regard to communication systems and digital filtering theory. Vital for students in the fields of control and communications, its contents are also relevant to students in such diverse areas as statistics, economics, bioengineering, and operations research.Topics include filtering, linear systems, and estimation; the discrete-time Kalman filter; time-invariant filters; properties of Kalman filters; computational aspects; and smoothing of discrete-time signals. Additional subjects e
Multiple descriptions based wavelet image coding
陈海林; 杨宇航
2004-01-01
We present a simple and efficient scheme that combines multiple descriptions coding with wavelet transform under JPEG2000 image coding architecture. To reduce packet losses, controlled amounts of redundancy are added to the wavelet transform coefficients to produce multiple descriptions of wavelet coefficients during the compression process to produce multiple descriptions bit-stream of a compressed image. Even if areceiver gets only parts of descriptions (other descriptions being lost), it can still reconstruct image with acceptable quality. Specifically, the scheme uses not only high-performance wavelet transform to improve compression efficiency, but also multiple descriptions technique to enhance the robustness of the compressed image that is transmitted through unreliable network channels.
Power System Transients Analysis by Wavelet Transforms
陈维荣; 宋永华; 赵蔚
2002-01-01
In contrast to Fourier transform, wavelet transform is especially suitable for transient analysis because of its time-frequency characteristics with automatically-adjusted window lengths. Research shows that wavelet transform is one of the most powerful tools for power system transient analysis. The basic ideas of wavelet transform are presented in the paper together with several power system applications. It is clear that wavelet transform has some clear advantages over other transforms in detecting, analyzing, and identifying various types of power system transients.
Wavelet analysis and its applications an introduction
Yajnik, Archit
2013-01-01
"Wavelet analysis and its applications: an introduction" demonstrates the consequences of Fourier analysis and introduces the concept of wavelet followed by applications lucidly. While dealing with one dimension signals, sometimes they are required to be oversampled. A novel technique of oversampling the digital signal is introduced in this book alongwith necessary illustrations. The technique of feature extraction in the development of optical character recognition software for any natural language alongwith wavelet based feature extraction technique is demonstrated using multiresolution analysis of wavelet in the book.
Wavelet-based prediction of oil prices
Yousefi, Shahriar [Econometric Group, Department of Economics, University of Southern Denmark, DK-5230 Odense M (Denmark); Weinreich, Ilona [Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhr Campus, D-53424 Remagen (Germany)]. E-mail: weinreich@rheinahrcampus.de; Reinarz, Dominik [Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhr Campus, D-53424 Remagen (Germany)
2005-07-01
This paper illustrates an application of wavelets as a possible vehicle for investigating the issue of market efficiency in futures markets for oil. The paper provides a short introduction to the wavelets and a few interesting wavelet-based contributions in economics and finance are briefly reviewed. A wavelet-based prediction procedure is introduced and market data on crude oil is used to provide forecasts over different forecasting horizons. The results are compared with data from futures markets for oil and the relative performance of this procedure is used to investigate whether futures markets are efficiently priced.
Entangled Husimi distribution and Complex Wavelet transformation
Hu, Li-yun
2009-01-01
Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.
Intelligent gearbox diagnosis methods based on SVM, wavelet lifting and RBR.
Gao, Lixin; Ren, Zhiqiang; Tang, Wenliang; Wang, Huaqing; Chen, Peng
2010-01-01
Given the problems in intelligent gearbox diagnosis methods, it is difficult to obtain the desired information and a large enough sample size to study; therefore, we propose the application of various methods for gearbox fault diagnosis, including wavelet lifting, a support vector machine (SVM) and rule-based reasoning (RBR). In a complex field environment, it is less likely for machines to have the same fault; moreover, the fault features can also vary. Therefore, a SVM could be used for the initial diagnosis. First, gearbox vibration signals were processed with wavelet packet decomposition, and the signal energy coefficients of each frequency band were extracted and used as input feature vectors in SVM for normal and faulty pattern recognition. Second, precision analysis using wavelet lifting could successfully filter out the noisy signals while maintaining the impulse characteristics of the fault; thus effectively extracting the fault frequency of the machine. Lastly, the knowledge base was built based on the field rules summarized by experts to identify the detailed fault type. Results have shown that SVM is a powerful tool to accomplish gearbox fault pattern recognition when the sample size is small, whereas the wavelet lifting scheme can effectively extract fault features, and rule-based reasoning can be used to identify the detailed fault type. Therefore, a method that combines SVM, wavelet lifting and rule-based reasoning ensures effective gearbox fault diagnosis.
A Study on the Performance of Wavelet OFDM in Power Line
Koga, Hisao; Kodama, Nobutaka
Recently, the demand of high speed network in home is increasing. Some Multicarrier Modulation (MCM) based systems use FFT OFDM, and some use a Wavelet OFDM in place of FFT OFDM. Wavelet transforms consist of an M-band transmultiplexers, which use filters of greater length than the rectangular windows used in FFT OFDM. The use of symbols of longer duration allows obtaining lower side-lobe levels with respect to FFT OFDM. Better stop-band attenuation results in both lower levels of inter-carrier interference (ICI) and greater robustness to narrowband interference. For the power line channel, we have chosen two channels measured by network analyzer. The root mean square (R.M.S.) delay spreads of Channels A and B are 0.22 [μsec] and 1.1 [μsec], respectively. In this paper, the PHY (Physical layer) data rates [Mbps] achievable by Wavelet OFDM over Channels A and B are shown for two different kinds of FEC. Then, the effects of ISI and ICI on Wavelet OFDM can be compensated by increasing the number of carriers. Finally, it is shown that Wavelet OFDM characteristic is better than that of FFT OFDM about PHY rates [Mbps] with the same channels.
Mean square error approximation for wavelet-based semiregular mesh compression.
Payan, Frédéric; Antonini, Marc
2006-01-01
The objective of this paper is to propose an efficient model-based bit allocation process optimizing the performances of a wavelet coder for semiregular meshes. More precisely, this process should compute the best quantizers for the wavelet coefficient subbands that minimize the reconstructed mean square error for one specific target bitrate. In order to design a fast and low complex allocation process, we propose an approximation of the reconstructed mean square error relative to the coding of semiregular mesh geometry. This error is expressed directly from the quantization errors of each coefficient subband. For that purpose, we have to take into account the influence of the wavelet filters on the quantized coefficients. Furthermore, we propose a specific approximation for wavelet transforms based on lifting schemes. Experimentally, we show that, in comparison with a "naive" approximation (depending on the subband levels), using the proposed approximation as distortion criterion during the model-based allocation process improves the performances of a wavelet-based coder for any model, any bitrate, and any lifting scheme.
The lifting scheme of 4-channel orthogonal wavelet transforms
PENG Lizhong; CHU Xiaoyong
2006-01-01
The 4-channel smooth wavelets with linear phase and orthogonality are designed from the 2-channel orthogonal wavelets with high transfer vanishing moments. Reversely, for simple lifting scheme of such 4-channel orthogonal wavelet transforms, a new 2-channel orthogonal wavelet associated with this 4-channel wavelet is constructed. The new 2-channel wavelet has at least the same number of vanishing moments as the associated 4-channel one. Finally, by combining the two such 2-channel wavelet systems, the lifting scheme of 4-channel orthogonal wavelet transform, which has simple structure and is easy to apply, is presented.
Steady-state sweep visual evoked potential processing denoised by wavelet transform
Weiderpass, Heinar A.; Yamamoto, Jorge F.; Salomão, Solange R.; Berezovsky, Adriana; Pereira, Josenilson M.; Sacai, Paula Y.; de Oliveira, José P.; Costa, Marcio A.; Burattini, Marcelo N.
2008-03-01
Visually evoked potential (VEP) is a very small electrical signal originated in the visual cortex in response to periodic visual stimulation. Sweep-VEP is a modified VEP procedure used to measure grating visual acuity in non-verbal and preverbal patients. This biopotential is buried in a large amount of electroencephalographic (EEG) noise and movement related artifact. The signal-to-noise ratio (SNR) plays a dominant role in determining both systematic and statistic errors. The purpose of this study is to present a method based on wavelet transform technique for filtering and extracting steady-state sweep-VEP. Counter-phase sine-wave luminance gratings modulated at 6 Hz were used as stimuli to determine sweep-VEP grating acuity thresholds. The amplitude and phase of the second-harmonic (12 Hz) pattern reversal response were analyzed using the fast Fourier transform after the wavelet filtering. The wavelet transform method was used to decompose the VEP signal into wavelet coefficients by a discrete wavelet analysis to determine which coefficients yield significant activity at the corresponding frequency. In a subsequent step only significant coefficients were considered and the remaining was set to zero allowing a reconstruction of the VEP signal. This procedure resulted in filtering out other frequencies that were considered noise. Numerical simulations and analyses of human VEP data showed that this method has provided higher SNR when compared with the classical recursive least squares (RLS) method. An additional advantage was a more appropriate phase analysis showing more realistic second-harmonic amplitude value during phase brake.
Three-dimensional wavelet transform and multiresolution surface reconstruction from volume data
Wang, Yun; Sloan, Kenneth R., Jr.
1995-04-01
Multiresolution surface reconstruction from volume data is very useful in medical imaging, data compression and multiresolution modeling. This paper presents a hierarchical structure for extracting multiresolution surfaces from volume data by using a 3-D wavelet transform. The hierarchical scheme is used to visualize different levels of detail of the surface and allows a user to explore different features of the surface at different scales. We use 3-D surface curvature as a smoothness condition to control the hierarchical level and the distance error between the reconstructed surface and the original data as the stopping criteria. A 3-D wavelet transform provides an appropriate hierarchical structure to build the volume pyramid. It can be constructed by the tensor products of 1-D wavelet transforms in three subspaces. We choose the symmetric and smoothing filters such as Haar, linear, pseudoCoiflet, cubic B-spline and their corresponding orthogonal wavelets to build the volume pyramid. The surface is reconstructed at each level of volume data by using the cell interpolation method. Some experimental results are shown through the comparison of the different filters based on the distance errors of the surfaces.
Wang, Xiaojun; Lai, Weidong
2011-08-01
In this paper, a combined method have been put forward for one ASTER detected image with the wavelet filter to attenuate the noise and the anisotropic diffusion PDE(Partial Differential Equation) for further recovering image contrast. The model is verified in different noising background, since the remote sensing image usually contains salt and pepper, Gaussian as well as speckle noise. Considered the features that noise existing in wavelet domain, the wavelet filter with Bayesian estimation threshold is applied for recovering image contrast from the blurring background. The proposed PDE are performing an anisotropic diffusion in the orthogonal direction, thus preserving the edges during further denoising process. Simulation indicates that the combined algorithm can more effectively recover the blurred image from speckle and Gauss noise background than the only wavelet denoising method, while the denoising effect is also distinct when the pepper-salt noise has low intensity. The combined algorithm proposed in this article can be integrated in remote sensing image analyzing to obtain higher accuracy for environmental interpretation and pattern recognition.
Yadav, Raj Bahadur; Gupta, Arun K.
2010-02-01
Segmentation in Magnetic resonance imaging (MRI) images is a widely studied problem, and techniques (supervised and unsupervised) are discussed in the literature. The basic approaches to image segmentation are based upon: (a) boundary representation, (b) regional characteristics and (c) a combination of boundary and region-based features. In this paper, we report classification of brain tissue based objects employing one of combination of boundary and region-based features as wavelet modified generic Fourier descriptor (WGFD) technique. This technique have been applied to a database consisting of 3 different class's tissues, each class consist of 50 shapes. The Euclidean distance has been calculated as a similarity measure parameter for tissue shape classification. The classification results have been carried out and it is inferred that WGFD performs for brain tissue classification. For brain tissue recognition, a simulation experiment employing hybrid correlator architecture has been carried out. We have used Wavelet modified maximum average correlation hight (MACH) filter for hybrid correlator. Mexican-hat wavelet has used to synthesize the wavelet MACH filter for simulation experiment.
Social group utility maximization
Gong, Xiaowen; Yang, Lei; Zhang, Junshan
2014-01-01
This SpringerBrief explains how to leverage mobile users' social relationships to improve the interactions of mobile devices in mobile networks. It develops a social group utility maximization (SGUM) framework that captures diverse social ties of mobile users and diverse physical coupling of mobile devices. Key topics include random access control, power control, spectrum access, and location privacy.This brief also investigates SGUM-based power control game and random access control game, for which it establishes the socially-aware Nash equilibrium (SNE). It then examines the critical SGUM-b
Brandes, U; Gaertler, M; Goerke, R; Hoefer, M; Nikoloski, Z; Wagner, D
2006-01-01
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.
Lattice Structure for Paraunitary Linear-phase Filter Banks with Accuracy
Hong Ying XIAO
2006-01-01
Multivariate filter banks with a polyphase matrix built by matrix factorization (lattice structure) were proposed to obtain orthonormal wavelet basis. On the basis of that, we propose a general method of constructing filter banks which ensure second and third accuracy of its corresponding scaling function. In the last part, examples with second and third accuracy are given.
Maximizing without difficulty: A modified maximizing scale and its correlates
Linda Lai
2010-01-01
This article presents several studies that replicate and extend previous research on maximizing. A modified scale for measuring individual maximizing tendency is introduced. The scale has adequate psychometric properties and reflects maximizers' aspirations for high standards and their preference for extensive alternative search, but not the decision difficulty aspect included in several previous studies. Based on this scale, maximizing is positively correlated with optimism, need for cogniti...