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
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...
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...
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.
Energy Technology Data Exchange (ETDEWEB)
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.
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...
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
Making electromagnetic wavelets
Energy Technology Data Exchange (ETDEWEB)
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.
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
Institute of Scientific and Technical Information of China (English)
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.
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
DEFF Research Database (Denmark)
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
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.
Institute of Scientific and Technical Information of China (English)
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.
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.
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
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...
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
Energy Technology Data Exchange (ETDEWEB)
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
Institute of Scientific and Technical Information of China (English)
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.
WAVELET ANALYSIS OF ABNORMAL ECGS
Directory of Open Access Journals (Sweden)
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.
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...
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
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.
WAVELET RATIONAL FILTERS AND REGULARITY ANALYSIS
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
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.
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
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.
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
Wavelet frames and their duals
DEFF Research Database (Denmark)
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
Institute of Scientific and Technical Information of China (English)
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.
Morlet Wavelets in Quantum Mechanics
Directory of Open Access Journals (Sweden)
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.
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 Based Image Denoising Technique
Directory of Open Access Journals (Sweden)
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.
Local Extrema of Periodic Function's Wavelet Transform
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Four-Point Wavelets and Their Applications
Institute of Scientific and Technical Information of China (English)
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.
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
Institute of Scientific and Technical Information of China (English)
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
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.
Iris Recognition Using Wavelet
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.
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 ...
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...
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
Directory of Open Access Journals (Sweden)
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.
A wavelet phase filter for emission tomography
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
TRANSMISSION LINE FAULT ANALYSIS USING WAVELET THEORY
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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.
Analisis Perbandingan Kompresi Haar Wavelet Transform dengan Embedded Zerotree Wavelet pada Citra
Directory of Open Access Journals (Sweden)
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
Complex Wavelet Transform-Based Face Recognition
Directory of Open Access Journals (Sweden)
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.
Wavelet Transforms using VTK-m
Energy Technology Data Exchange (ETDEWEB)
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.
Orthogonal Matrix-Valued Wavelet Packets
Institute of Scientific and Technical Information of China (English)
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.
Wavelets for Sparse Representation of Music
DEFF Research Database (Denmark)
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
DEFF Research Database (Denmark)
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
Directory of Open Access Journals (Sweden)
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.
Wavelet Representation of Contour Sets
Energy Technology Data Exchange (ETDEWEB)
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.
Complex Wavelet Based Modulation Analysis
DEFF Research Database (Denmark)
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...
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
Institute of Scientific and Technical Information of China (English)
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
Directory of Open Access Journals (Sweden)
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.
Wavelet filtering of chaotic data
Directory of Open Access Journals (Sweden)
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.
An Overview on Wavelet Software Packages
Institute of Scientific and Technical Information of China (English)
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.
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.
Implementing wavelet transform with SAW elements
Institute of Scientific and Technical Information of China (English)
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.
Wavelet Transform and its Application to CBIR
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
Modeling Network Traffic in Wavelet Domain
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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.
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.
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
Institute of Scientific and Technical Information of China (English)
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
DEFF Research Database (Denmark)
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
DEFF Research Database (Denmark)
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
DEFF Research Database (Denmark)
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
Institute of Scientific and Technical Information of China (English)
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.
Multiple descriptions based wavelet image coding
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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.
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.
The lifting scheme of 4-channel orthogonal wavelet transforms
Institute of Scientific and Technical Information of China (English)
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.
THEORY AND APPLICATION OF WAVELET ANALYSIS INSTRUMENT LIBRARY
Institute of Scientific and Technical Information of China (English)
BO Lin; QIN Shuren; LIU Xiaofeng
2006-01-01
Some new theory and algorithms on wavelet analysis are proposed, including continuous wavelet transform (CWT), discrete wavelet transform (DWT), wavelet package transform (WPT),wavelet denosing and mother wavelet selection, etc. Using the component-based hierarchy mode, the platform for virtual instrument (Ⅵ) is constructed, and the functions such as data sampling, data analysis and data present, etc are provided. Subsequently, the wavelet analysis library is designed and developed. The library consists of expert system, experienced database, development platform and abundant wavelet analysis functional module, which together implement general and special wavelet analysis in the field of mechanical engineering, energy source, transportation and biomedicine, etc.Finally, the wavelet analysis virtual instrument library is applied to detect fault called engine knock.Experimental result indicates that the wavelet analysis virtual instrument library can efficiently solve the engineering problem such as detecting engine knock.
A new wavelet-based thin plate element using B-spline wavelet on the interval
Jiawei, Xiang; Xuefeng, Chen; Zhengjia, He; Yinghong, Zhang
2008-01-01
By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.
BIVARIATE REAL-VALUED ORTHOGONAL PERIODIC WAVELETS
Institute of Scientific and Technical Information of China (English)
Qiang Li; Xuezhang Liang
2005-01-01
In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corresponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in practical computation. Moreover, the relation between periodic wavelets and Fourier series is also discussed.
Application of wavelets in speech processing
Farouk, Mohamed Hesham
2014-01-01
This book provides a survey on wide-spread of employing wavelets analysis in different applications of speech processing. The author examines development and research in different application of speech processing. The book also summarizes the state of the art research on wavelet in speech processing.
APPLICATION OF WAVELET TRANSFORM IN STRUCTURAL OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
It is very common in structural optimization that the optima lie at or in the vicinities of the singular points of feasible domain. Therefore it is very reasonable to introduce wavelet transform that is advantageous in singularity detection. The principle and algorithm of the application of wavelet transform in structural optimization are discussed The feasibility is demonstrated by some typical examples.
Infinite matrices, wavelet coefficients and frames
Directory of Open Access Journals (Sweden)
N. A. Sheikh
2004-01-01
Full Text Available We study the action of A on f∈L2(ℝ and on its wavelet coefficients, where A=(almjklmjk is a double infinite matrix. We find the frame condition for A-transform of f∈L2(ℝ whose wavelet series expansion is known.
3D steerable wavelets in practice.
Chenouard, Nicolas; Unser, Michael
2012-11-01
We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.
Improvements of embedded zerotree wavelet (EZW) coding
Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay
1995-04-01
In this research, we investigate several improvements of embedded zerotree wavelet (EZW) coding. Several topics addressed include: the choice of wavelet transforms and boundary conditions, the use of arithmetic coder and arithmetic context and the design of encoding order for effective embedding. The superior performance of our improvements is demonstrated with extensive experimental results.
Realization of Wavelet Transform Using SAW Devices
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Based on the characteristics of surface acoustic wave(SAW) devices, the theory for realizing wavelet transform (WT) by SAW is deduced. Simulated experiment shows that the method of implementing WT using SAW devices has virtues of high speed and utility and is compatible with digital technique. It is important to implement wavelet transform.
The fast wavelet X-ray transform
R.A. Zuidwijk; P.M. de Zeeuw (Paul)
1999-01-01
textabstractThe wavelet X-ray transform computes one-dimensional wavelet transforms along lines in Euclidian space in order to perform a directional time-scale analysis of functions in several variables. A fast algorithm is proposed which executes this transformation starting with values given on a
Status of pattern recognition with wavelet analysis
Institute of Scientific and Technical Information of China (English)
Yuanyan TANG
2008-01-01
Pattern recognition has become one of the fastest growing research topics in the fields of computer science and electrical and electronic engineering in the recent years.Advanced research and development in pattern recognition have found numerous applications in such areas as artificial intelligence,information security,biometrics,military science and technology,finance and economics,weather forecast,image processing,communication,biomedical engineering,document processing,robot vision,transportation,and endless other areas,with many encouraging results.The achievement of pattern recognition is most likely to benefit from some new developments of theoretical mathematics including wavelet analysis.This paper aims at a brief survey of pattern recognition with the wavelet theory.It contains the following respects:analysis and detection of singularities with wavelets;wavelet descriptors for shapes of the objects;invariant representation of patterns;handwritten and printed character recognition;texture analysis and classification;image indexing and retrieval;classification and clustering;document analysis with wavelets;iris pattern recognition;face recognition using wavelet transform;hand gestures classification;character processing with B-spline wavelet transform;wavelet-based image fusion,and others.
Irregular wavelet frames on L2(Rn)
Institute of Scientific and Technical Information of China (English)
YANG Deyun; ZHOU Xingwei
2005-01-01
In this paper, we present the conditions on dilation parameter {sj }j that ensure a discrete irregular wavelet system {Snj/2ψ(sj·-bk)}j∈(Z),k∈(Z)n to be a frame on L2(Rn),and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.
Wavelet transform element of SAW type
Institute of Scientific and Technical Information of China (English)
LU Wenke; ZHU Changchun; LIU Qinghong; LIU Junhua
2005-01-01
This paper proposes to use substrate materials of small electromechanical coupling coefficient k2 (such as X-112YLiTaO3) to manufacture wavelet transform element of SAW type so as to reduce finger reflections, i.e. to reduce the error of wavelet transform element of SAW type. And it is concluded that the smaller the center frequency of the transmitting IDT of wavelet type, the smaller the error. We suggest to choose substrate material with electromechanical coupling coefficient smaller than that of X-112Y LiTaO3 in the manufacture of the transmitting IDTs of wavelet type and the receiving IDTs at center frequencies above 100MHZ, so as to reduce the errors of the transmitting IDTs of wavelet type and the receiving IDTs at center frequencies above 100MHZ.
Video Watermark Using Multiresolution Wavelet Decomposition
Institute of Scientific and Technical Information of China (English)
WANG Feng-bi; HUANG Jun-cai; WANG Bin; SHE Kun; ZHOU Ming-tian
2005-01-01
A novel technique for the video watermarking based on the discrete wavelet transform (DWT) is present. The intra frames of video are transformed to three gray image firstly, and then the 2th-level discrete wavelet decomposition of the gray images is computed, with which the watermark W is embedded simultaneously into and invert wavelet transform is done to obtain the gray images which contain the secret information. Change the intra frames of video based on the three gray images to make the intra frame contain the secret information. While extracting the secret information, the intra frames are transformed to three gray image, 2th-level discrete wavelet transform is done to the gray images, and the watermark W' is distilled from the wavelet coefficients of the three gray images. The test results show the superior performance of the technique and potential for the watermarking of video.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
Seamless multiresolution isosurfaces using wavelets
Energy Technology Data Exchange (ETDEWEB)
Udeshi, T.; Hudson, R.; Papka, M. E.
2000-04-11
Data sets that are being produced by today's simulations, such as the ones generated by DOE's ASCI program, are too large for real-time exploration and visualization. Therefore, new methods of visualizing these data sets need to be investigated. The authors present a method that combines isosurface representations of different resolutions into a seamless solution, virtually free of cracks and overlaps. The solution combines existing isosurface generation algorithms and wavelet theory to produce a real-time solution to multiple-resolution isosurfaces.
Wavelets and the lifting scheme
DEFF Research Database (Denmark)
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 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....
Representation of 1/f signal with wavelet bases
Institute of Scientific and Technical Information of China (English)
刘峰; 刘贵忠; 张茁生
2000-01-01
The representation of 1/f signal with wavelet transformation is explored. It is shown that a class of 1/f signal can be represented via wavelet synthetic formula and that a statistically self-similar property of signals may be characterized by the correlation functions of wavelet coefficients in the wavelet domain.
SAMPLING PRINCIPLE AND TECHNOLOGY IN WAVELET ANALYSIS FOR SIGNALS
Institute of Scientific and Technical Information of China (English)
1998-01-01
Sampling principle and characteristics and edge effect of orthogonal wavelet transform of signals are researched. Two samples of signals and wavelet bases must be taken in wavelet transform. In the second sample sampling interval or sampling length in different frequency range will be automatically adjusted. Wavelet transform can detect singular points. Both ends of signals are singular points. Edge effect is not avoidable.
Relations Between Wavelet Network and Feedforward Neural Network
Institute of Scientific and Technical Information of China (English)
刘志刚; 何正友; 钱清泉
2002-01-01
A comparison of construction forms and base functions is made between feedforward neural network and wavelet network. The relations between them are studied from the constructions of wavelet functions or dilation functions in wavelet network by different activation functions in feedforward neural network. It is concluded that some wavelet function is equal to the linear combination of several neurons in feedforward neural network.
Detection of ultrasound contrast agent microbubble with constructed bubble wavelet
Institute of Scientific and Technical Information of China (English)
LI Bin; WAN Mingxi
2005-01-01
To detect the echo irradiated by microbubble out from the signal reflected by surrounding tissues, a mother wavelet named bubble wavelet according to the modified Herring oscillation equation was constructed and then applied to the original ultrasound radio frequency signal to perform the wavelet transformation. The transformed wavelet coefficients were extracted by selected threshold values to differentiate the echo of microbubble from signal of surround tissues. The effect of bubble wavelet was compared with other three commonly used mother wavelets by computer simulation and phantom experiment. The results demonstrated that there existed a highly correlation between the bubble wavelet and the experimental echo irradiated by microbubble because bubble wavelet had represented the dynamics of microbubble in advance. Furthermore, the wavelet transform results showed a better signal-noise-ratio and a sharper contrast between the echo of microbubble and the signal of surrounding tissues. Finally,constructing an overall mother wavelet library can improve the applicability and robustness of this detection method.
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.
NOVEL ADAPTIVE MULTIUSER DETECTIONALGORITHM BASED ON WAVELET TRANSFORM
Institute of Scientific and Technical Information of China (English)
ZHANGXiao-fei; XUDa-zhuan; YANGBei
2004-01-01
The wavelet transform-based adaptive multiuser detection algorithm is presented. The novel adaptive multiuser detection algorithm uses the wavelet transform for the preprocessing, and wavelet-transformed signal uses LMS algorithm to implement the adaptive multiuser detection. The algorithm makes use of wavelet transform to divide the wavelet space, which shows that the wavelet transform has a better decorrelation ability and leads to better convergence. White noise can be wiped off under the wavelet transform according to different characteristics of signal and white noise under the wavelet transform. Theoretical analyses and simulations demonstrate that the algorithm converges faster than the conventional adaptive multiuser detection algorithm, and has the better performance. Simulation results reveal that the algorithm convergence relates to the wavelet base, and show that the algorithm convergence gets better with the increasing of regularity for the same series of the wavelet base. Finally the algorithm shows that it can be easily implemented.
Image coding with geometric wavelets.
Alani, Dror; Averbuch, Amir; Dekel, Shai
2007-01-01
This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
Leistedt, B
2012-01-01
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact harmonic transform on the radial line using damped Laguerre polynomials and develop a corresponding quadrature rule. Combined with the spherical harmonic transform, this approach leads to a sampling theorem on the ball and a novel three-dimensional decomposition which we call the Fourier-Laguerre transform. We relate this new transform to the well-known Fourier-Bessel decomposition and show that band-limitness in the Fourier-Laguerre basis is a sufficient condition to compute the Fourier-Bessel decomposition exactly. We then construct the flaglet transform on the ball through a harmonic tiling, which is exact thanks to the exactness of the Fourier-Laguerre transform (from which the name flaglets is coined). The corresponding wavelet kernels have compact localisation properties in real and harmonic space and their angular aperture is i...
Peak Detection Using Wavelet Transform
Directory of Open Access Journals (Sweden)
Omar Daoud
2014-07-01
Full Text Available A new work based-wavelet transform is designed to o vercome one of the main drawbacks that found in the present new technologies. Orthogonal Frequency Divi sion Multiplexing (OFDMis proposed in the literature to enhance the multimedia resolution. Ho wever, the high peak power (PAPR values will obstr uct such achievements. Therefore, a new proposition is found in this work, making use of the wavelet transforms methods, and it is divided into three ma in stages; de-noising stage, thresholding stage and then the replacement stage. In order to check the system stages validity; a mat hematical model has been built and its checked afte r using a MATLAB simulation. A simulated bit error ra te (BER achievement will be compared with our previously published work, where an enhancement fro m 8×10 -1 to be 5×10 -1 is achieved. Moreover, these results will be compared to the work found in the l iterature, where we have accomplished around 27% PAPR extra reduction. As a result, the BER performance has been improved for the same bandwidth occupancy. Moreover and due to the de-noise stage, the verification rate ha s been improved to reach 81%. This is in addition t o the noise immunity enhancement.
Discrete wavelet transformations an elementary approach with applications
Van Fleet, Patrick
2008-01-01
An "applications first" approach to discrete wavelet transformations. Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising. The book begins with a cursory look at wavelet transformation development and illustrates its
Detecting the BAO using Discrete Wavelet Packets
Garcia, Noel Anthony; Wu, Yunyun; Kadowaki, Kevin; Pando, Jesus
2017-01-01
We use wavelet packets to investigate the clustering of matter on galactic scales in search of the Baryon Acoustic Oscillations. We do so in two ways. We develop a wavelet packet approach to measure the power spectrum and apply this method to the CMASS galaxy catalogue from the Sloan Digital Sky Survey (SDSS). We compare the resulting power spectrum to published BOSS results by measuring a parameter β that compares our wavelet detected oscillations to the results from the SDSS collaboration. We find that β=1 indicating that our wavelet packet methods are detecting the BAO at a similar level as traditional Fourier techniques. We then use wavelet packets to decompose, denoise, and then reconstruct the galaxy density field. Using this denoised field, we compute the standard two-point correlation function. We are able to successfully detect the BAO at r ≈ 105 h-1 Mpc in line with previous SDSS results. We conclude that wavelet packets do reproduce the results of the key clustering statistics computed by other means. The wavelet packets show distinct advantages in suppressing high frequency noise and in keeping information localized.
Application of the cross wavelet transform and wavelet coherence to geophysical time series
Directory of Open Access Journals (Sweden)
A. Grinsted
2004-01-01
Full Text Available Many scientists have made use of the wavelet method in analyzing time series, often using popular free software. However, at present there are no similar easy to use wavelet packages for analyzing two time series together. We discuss the cross wavelet transform and wavelet coherence for examining relationships in time frequency space between two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relationships and test mechanistic models of physical relationships between the time series. As an example of typical data where such analyses have proven useful, we apply the methods to the Arctic Oscillation index and the Baltic maximum sea ice extent record. Monte Carlo methods are used to assess the statistical significance against red noise backgrounds. A software package has been developed that allows users to perform the cross wavelet transform and wavelet coherence (www.pol.ac.uk/home/research/waveletcoherence/.
Tan, Liying; Ma, Jing; Wang, Guangming
2005-12-01
The image formation and the point-spread function of an optical system are analyzed by use of the wavelet basis function. The image described by a wavelet is no longer an indivisible whole image. It is, rather, a complex image consisting of many wavelet subimages, which come from the changes of different parameters (scale) a and c, and parameters b and d show the positions of wavelet subimages under different scales. A Gaussian frequency-modulated complex-valued wavelet function is introduced to express the point-spread function of an optical system and used to describe the image formation. The analysis, in allusion to the situation of illumination with a monochromatic plain light wave, shows that using the theory of wavelet optics to describe the image formation of an optical system is feasible.
Applications of a fast, continuous wavelet transform
Energy Technology Data Exchange (ETDEWEB)
Dress, W.B.
1997-02-01
A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.
Yu's Wavelet-a New Wavelet Used to Improve Resolution in Seismic Data Processing
Institute of Scientific and Technical Information of China (English)
Fan Weicui; Liu Jiren
1996-01-01
@@ Yu Shoupeng, a senior geophysicist in Bureau of Geophysical Prospecting (BGP) of China National Petroleum Corporation (CNPC) announced his new researched result - a broad band Ricker wavelet in Science and Technology Fair of (Geophysical Research Institute)GRI early this year. For his result, Yu,Shoupeng was rewarded with First Prize of GRI and all participants of the fair were impressed very much by his work. The new wavelet was named as Yu's wavelet.
Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice
Atkinson, Bruce W; Geronimo, Jeffrey S; Hardin, Douglas P
2011-01-01
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden-mean. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor $\\tau$.
IDENTIFICATION OF CRACKED ROTOR BY WAVELET TRANSFORM
Institute of Scientific and Technical Information of China (English)
邹剑; 陈进; 蒲亚鹏
2002-01-01
The dynamic equation of cracked rotor in rotational frame was modelled, the numerical simulation solutions of the cracked rotor and the uncracked rotor were obtained. By the wavelet transform, the time-frequency properties of the cracked rotor and the uncracked rotor were discussed, the difference of the time-frequency properties between the cracked rotor and the uncracked rotor was compared. A new detection algorithm using wavelet transform to identify crack was proposed. The experiments verify the availability and validity of the wavelet transform in identification of crack.
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
Transparent Image Watermarking in the Wavelet Domain
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Digital watermarking has been proposed as a viable solution to protect the copyright of multime-dia data in a networked environment, since it makes possible to embed identification codes into a digital docu-ment. This paper proposes a new scheme for image watermarking in which a watermark is embedded in a se-lected set of wavelet transform coefficients. To ensure the watermark invisibility with high robustness, a bi-nary pseudo-random sequence is embedded into significant wavelet coefficients by exploiting Embedded Ze-rotree Wavelet (EZW) coding algorithm. Experimental results show the effectiveness of this technique.
Wavelet-based multispectral face recognition
Institute of Scientific and Technical Information of China (English)
LIU Dian-ting; ZHOU Xiao-dan; WANG Cheng-wen
2008-01-01
This paper proposes a novel wavelet-based face recognition method using thermal infrared (1R) and visible-light face images. The method applies the combination of Gabor and the Fisherfaces method to the reconstructed IR and visible images derived from wavelet frequency subbands. Our objective is to search for the subbands that are insensitive to the variation in expression and in illumination. The classification performance is improved by combining the multispectal information coming from the subbands that attain individually low equal error rate. Experimental results on Notre Dame face database show that the proposed wavelet-based algorithm outperforms previous multispectral images fusion method as well as monospectral method.
Wavelet Analytical Forecasting Method of Water Consumption
Institute of Scientific and Technical Information of China (English)
刘洪波; 张宏伟
2004-01-01
A new method of short-term forecasting for water consumption in municipal supply water networks based on wavelet transformation is introduced. By wavelet decomposing commonly used in the signal field, water consumption per hour is decomposed into many series. Trend item, cycle item and random item are separated from the original time series in this way.Then by analyzing, building a model, forecasting every series and composing the results, the forecasting value of the original consumption is received. Simulation results show that this forecasting method is faster and more accurate, of which the error is less than 20%,indicating that the wavelet analytical method is practicable.
Wavelet Neural Networks for Adaptive Equalization
Institute of Scientific and Technical Information of China (English)
JIANGMinghu; DENGBeixing; GIELENGeorges; ZHANGBo
2003-01-01
A structure based on the Wavelet neural networks (WNNs) is proposed for nonlinear channel equalization in a digital communication system. The construction algorithm of the Minimum error probability (MEP) is presented and applied as a performance criterion to update the parameter matrix of wavelet networks. Our experimental results show that performance of the proposed wavelet networks based on equalizer can significantly improve the neural modeling accuracy, perform quite well in compensating the nonlinear distortion introduced by the channel, and outperform the conventional neural networks in signal to noise ratio and channel non-llnearity.
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.
Perturbation of Wavelet and Gabor Frames
Institute of Scientific and Technical Information of China (English)
Ivana Carrizo; Sergio Favier
2003-01-01
In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically,we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.
Directory of Open Access Journals (Sweden)
K. Vijayarekha
2012-12-01
Full Text Available The aim of this study is to classify the citrus fruit images based on the external defect using the features extracted in the spectral domain (transform based and to compare the performance of each of the feature set. Automatic classification of agricultural produce by machine vision technology plays a very important role as it improves the quality of grading. Multi resolution analysis using wavelets yields better results for pattern recognition and object classification. This study details about an image processing method applied for classifying three external surface defects of citrus fruit using wavelet transforms based features and an artificial neural network. The Discrete Wavelet Transform (DWT, Stationary Wavelet Transform (SWT and Wavelet Packet Transform (WPT features viz. mean and standard deviation of the details and approximations were extracted from citrus fruit images and used for classifying the defects. The DWT and SWT features were extracted from 40x40 sub-windows of the fruit image. The WPT features were extracted from the full fruit image of size 640x480. The classification results pertaining to the three wavelet transforms are reported and discussed.
Electric Equipment Diagnosis based on Wavelet Analysis
Directory of Open Access Journals (Sweden)
Stavitsky Sergey A.
2016-01-01
Full Text Available Due to electric equipment development and complication it is necessary to have a precise and intense diagnosis. Nowadays there are two basic ways of diagnosis: analog signal processing and digital signal processing. The latter is more preferable. The basic ways of digital signal processing (Fourier transform and Fast Fourier transform include one of the modern methods based on wavelet transform. This research is dedicated to analyzing characteristic features and advantages of wavelet transform. This article shows the ways of using wavelet analysis and the process of test signal converting. In order to carry out this analysis, computer software Mathcad was used and 2D wavelet spectrum for a complex function was created.
Multiuser detector based on wavelet networks
Institute of Scientific and Technical Information of China (English)
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.
Matching a wavelet to ECG signal.
Takla, George F; Nair, Bala G; Loparo, Kenneth A
2006-01-01
In this paper we develop an approach to synthesize a wavelet that matches the ECG signal. Matching a wavelet to a signal of interest has potential advantages in extracting signal features with greater accuracy, particularly when the signal is contaminated with noise. The approach that we have taken is based on the theoretical work done by Chapa and Rao. We have applied their technique to a noise-free ECG signal representing one cardiac cycle. Results indicate that a matched wavelet, that was able to capture the broad ECG features, could be obtained. Such a wavelet could be used to extract ECG features such as QRS complexes and P&T waves with greater accuracy.
Multiple descriptions based wavelet image coding
Institute of Scientific and Technical Information of China (English)
CHEN Hai-lin(陈海林); YANG Yu-hang(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 a receiver 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.
Wavelet based approach for facial expression recognition
Directory of Open Access Journals (Sweden)
Zaenal Abidin
2015-03-01
Full Text Available Facial expression recognition is one of the most active fields of research. Many facial expression recognition methods have been developed and implemented. Neural networks (NNs have capability to undertake such pattern recognition tasks. The key factor of the use of NN is based on its characteristics. It is capable in conducting learning and generalizing, non-linear mapping, and parallel computation. Backpropagation neural networks (BPNNs are the approach methods that mostly used. In this study, BPNNs were used as classifier to categorize facial expression images into seven-class of expressions which are anger, disgust, fear, happiness, sadness, neutral and surprise. For the purpose of feature extraction tasks, three discrete wavelet transforms were used to decompose images, namely Haar wavelet, Daubechies (4 wavelet and Coiflet (1 wavelet. To analyze the proposed method, a facial expression recognition system was built. The proposed method was tested on static images from JAFFE database.
Wavelet-based acoustic recognition of aircraft
Energy Technology Data Exchange (ETDEWEB)
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.
A Novel Fractal Wavelet Image Compression Approach
Institute of Scientific and Technical Information of China (English)
SONG Chun-lin; FENG Rui; LIU Fu-qiang; CHEN Xi
2007-01-01
By investigating the limitation of existing wavelet tree based image compression methods, we propose a novel wavelet fractal image compression method in this paper. Briefly, the initial errors are appointed given the different levels of importance accorded the frequency sublevel band wavelet coefficients. Higher frequency sublevel bands would lead to larger initial errors. As a result, the sizes of sublevel blocks and super blocks would be changed according to the initial errors. The matching sizes between sublevel blocks and super blocks would be changed according to the permitted errors and compression rates. Systematic analyses are performed and the experimental results demonstrate that the proposed method provides a satisfactory performance with a clearly increasing rate of compression and speed of encoding without reducing SNR and the quality of decoded images. Simulation results show that our method is superior to the traditional wavelet tree based methods of fractal image compression.
Wavelet Analysis for Acoustic Phased Array
Kozlov, Inna; Zlotnick, Zvi
2003-03-01
Wavelet spectrum analysis is known to be one of the most powerful tools for exploring quasistationary signals. In this paper we use wavelet technique to develop a new Direction Finding (DF) Algorithm for the Acoustic Phased Array (APA) systems. Utilising multi-scale analysis of libraries of wavelets allows us to work with frequency bands instead of individual frequency of an acoustic source. These frequency bands could be regarded as features extracted from quasistationary signals emitted by a noisy object. For detection, tracing and identification of a sound source in a noisy environment we develop smart algorithm. The essential part of this algorithm is a special interacting procedure of the above-mentioned DF-algorithm and the wavelet-based Identification (ID) algorithm developed in [4]. Significant improvement of the basic properties of a receiving APA pattern is achieved.
Nonparametric Transient Classification using Adaptive Wavelets
Varughese, Melvin M; Stephanou, Michael; Bassett, Bruce A
2015-01-01
Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind ...
Scalets, wavelets and (complex) turning point quantization
Handy, C. R.; Brooks, H. A.
2001-05-01
Despite the many successes of wavelet analysis in image and signal processing, the incorporation of continuous wavelet transform theory within quantum mechanics has lacked a compelling, first principles, motivating analytical framework, until now. For arbitrary one-dimensional rational fraction Hamiltonians, we develop a simple, unified formalism, which clearly underscores the complementary, and mutually interdependent, role played by moment quantization theory (i.e. via scalets, as defined herein) and wavelets. This analysis involves no approximation of the Hamiltonian within the (equivalent) wavelet space, and emphasizes the importance of (complex) multiple turning point contributions in the quantization process. We apply the method to three illustrative examples. These include the (double-well) quartic anharmonic oscillator potential problem, V(x) = Z2x2 + gx4, the quartic potential, V(x) = x4, and the very interesting and significant non-Hermitian potential V(x) = -(ix)3, recently studied by Bender and Boettcher.
Discrete multiscale wavelet shrinkage and integrodifferential equations
Didas, S.; Steidl, G.; Weickert, J.
2008-04-01
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.
Coherent states, wavelets, and their generalizations
Ali, Syed Twareque; Gazeau, Jean-Pierre
2014-01-01
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altoget...
Wavelets theory and applications for manufacturing
Gao, Robert X
2011-01-01
With the aim of facilitating signal processing in manufacturing, this book presents a systematic description of the fundamentals on wavelet transform and the ways of applying it to the condition monitoring and health diagnosis of rotating machine components.
Applications of a fast continuous wavelet transform
Dress, William B.
1997-04-01
A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice
Wavelet transform based watermark for digital images.
Xia, X G; Boncelet, C; Arce, G
1998-12-07
In this paper, we introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to proposed methods to some common image distortions, such as the wavelet transform based image compression, image rescaling/stretching and image halftoning. Moreover, the method is hierarchical.
Niederhauser's model for epilepsy and wavelet methods
Trevino, J P; Moran, J L; Murguia, J S; Rosu, H C
2006-01-01
Wavelets and wavelet transforms (WT) could be a very useful tool to analyze electroencephalogram (EEG) signals. To illustrate the WT method we make use of a simple electric circuit model introduced by Niederhauser, which is used to produce EEG-like signals, particularly during an epileptic seizure. The original model is modified to resemble the 10-20 derivation of the EEG measurements. WT is used to study the main features of these signals
Wavelet adaptation for automatic voice disorders sorting.
Erfanian Saeedi, Nafise; Almasganj, Farshad
2013-07-01
Early diagnosis of voice disorders and abnormalities by means of digital speech processing is a subject of interest for many researchers. Various methods are introduced in the literature, some of which are able to extensively discriminate pathological voices from normal ones. Voice disorders sorting, on the other hand, has received less attention due to the complexity of the problem. Although, previous publications show satisfactory results in classifying one type of disordered voice from normal cases, or two different types of abnormalities from each other, no comprehensive approach for automatic sorting of vocal abnormalities has been offered yet. In this paper, a solution for this problem is suggested. We create a powerful wavelet feature extraction approach, in which, instead of standard wavelets, adaptive wavelets are generated and applied to the voice signals. Orthogonal wavelets are parameterized via lattice structure and then, the optimal parameters are investigated through an iterative process, using the genetic algorithm (GA). GA is guided by the classifier results. Based on the generated wavelet, a wavelet-filterbank is constructed and the voice signals are decomposed to compute eight energy-based features. A support vector machine (SVM) then classifies the signals using the extracted features. Experimental results show that six various types of vocal disorders: paralysis, nodules, polyps, edema, spasmodic dysphonia and keratosis are fully sorted via the proposed method. This could be a successful step toward sorting a larger number of abnormalities associated with the vocal system. Copyright © 2013 Elsevier Ltd. All rights reserved.
Optimal wavelet denoising for smart biomonitor systems
Messer, Sheila R.; Agzarian, John; Abbott, Derek
2001-03-01
Future smart-systems promise many benefits for biomedical diagnostics. The ideal is for simple portable systems that display and interpret information from smart integrated probes or MEMS-based devices. In this paper, we will discuss a step towards this vision with a heart bio-monitor case study. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. In our example of heartbeat analysis, phonocardiograms (PCGs) have many advantages in that they may be replayed and analysed for spectral and frequency information. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. Wavelets can be employed to denoise the PCG. The signal is decomposed by a discrete wavelet transform. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert Transform to heart sound analysis are discussed.
Some Problems on the Global Wavelet Spectrum
Institute of Scientific and Technical Information of China (English)
WU Shu; LIU Qinyu
2005-01-01
In order to test the validity of the global wavelet spectrum - a new period analysis method based on wavelet analysis, we carried out some simple experiments. In our experiments we used idealized time series and real Ni(~n)o 3 sea surface temperature (SST) for testing purposes. First we combined different signals which have the same power but different periods into some new time series. Then we calculated the global wavelet spectra and Fourier power spectra for the testing time series. The testing results revealed that on some occasions the global wavelet spectrum tends to amplify the relative power of longer periods. By making comparisons with the results obtained by the traditional Fourier power spectrum, we demonstrated that on an occasion when the global wavelet spectrum does not work the Fourier power spectrum can be used to achieve the right results. Hence it is recommended that when making period analysis with the global wavelet spectrum one needs to do further tests to confirm their results.
Application of wavelet transform in runoff sequence analysis
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A wavelet transform is applied to runoff analysis to obtain the composition of the runoff sequence and to forecast future runoff. An observed runoff sequence is firstly decomposed and reconstructed by wavelet transform and its expanding tendency is derived. Then, the runoff sequence is forecasted by the back propagation artificial neural networks (BPANN) and by a wavelet transform combined with BPANN. The earlier researches seldom involve the problem of how to choose wavelet function, which is important and cannot be ignored when the wavelet transform is used. With application of the developed approach to the analysis of runoff sequence, several kinds of wavelet functions have been tested.
WAVELET KERNEL SUPPORT VECTOR MACHINES FOR SPARSE APPROXIMATION
Institute of Scientific and Technical Information of China (English)
Tong Yubing; Yang Dongkai; Zhang Qishan
2006-01-01
Wavelet, a powerful tool for signal processing, can be used to approximate the target function. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with better sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target funciton with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation experiment show the feasibility and validity of wavelet kernel support vector machines.
Combustion instability detection using the wavelet detail of pressure fluctuations
Institute of Scientific and Technical Information of China (English)
Junjie JI; Yonghao LUO
2008-01-01
A combustion instability detection method that uses the wavelet detail of combustion pressure fluctuations is put forward. To confirm this method, combustion pressure fluctuations in a stoker boiler are recorded at stable and unstable combustion with a pressure transducer. Daubechies one-order wavelet is chosen to obtain the wavelet details for comparison. It shows that the wavelet approximation indicates the general pressure change in the furnace, and the wavelet detail magnitude is consistent with the intensity of turbulence and combustion noise. The magnitude of the wavelet detail is nearly constant when the combustion is stable, however, it will fluctuate much when the combustion is unstable.
Wavelets as q-bits and q-bit states as wavelets
Steblinski, Pawel; Blachowicz, Tomasz
2009-01-01
In this short report it is argued that by the use of wavelets formalism it is possible to describe the q-bit state. The wavelet formalism address the real-valued physical signals, for example, obtained during typical physical measurements.
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.
Wavelet-aided pavement distress image processing
Zhou, Jian; Huang, Peisen S.; Chiang, Fu-Pen
2003-11-01
A wavelet-based pavement distress detection and evaluation method is proposed. This method consists of two main parts, real-time processing for distress detection and offline processing for distress evaluation. The real-time processing part includes wavelet transform, distress detection and isolation, and image compression and noise reduction. When a pavement image is decomposed into different frequency subbands by wavelet transform, the distresses, which are usually irregular in shape, appear as high-amplitude wavelet coefficients in the high-frequency details subbands, while the background appears in the low-frequency approximation subband. Two statistical parameters, high-amplitude wavelet coefficient percentage (HAWCP) and high-frequency energy percentage (HFEP), are established and used as criteria for real-time distress detection and distress image isolation. For compression of isolated distress images, a modified EZW (Embedded Zerotrees of Wavelet coding) is developed, which can simultaneously compress the images and reduce the noise. The compressed data are saved to the hard drive for further analysis and evaluation. The offline processing includes distress classification, distress quantification, and reconstruction of the original image for distress segmentation, distress mapping, and maintenance decision-making. The compressed data are first loaded and decoded to obtain wavelet coefficients. Then Radon transform is then applied and the parameters related to the peaks in the Radon domain are used for distress classification. For distress quantification, a norm is defined that can be used as an index for evaluating the severity and extent of the distress. Compared to visual or manual inspection, the proposed method has the advantages of being objective, high-speed, safe, automated, and applicable to different types of pavements and distresses.
Multiresolution wavelet-ANN model for significant wave height forecasting.
Digital Repository Service at National Institute of Oceanography (India)
Deka, P.C.; Mandal, S.; Prahlada, R.
Hybrid wavelet artificial neural network (WLNN) has been applied in the present study to forecast significant wave heights (Hs). Here Discrete Wavelet Transformation is used to preprocess the time series data (Hs) prior to Artificial Neural Network...
TESTING FOR OUTLIERS IN TIME SERIES USING WAVELETS
Institute of Scientific and Technical Information of China (English)
ZHANG Tong; ZHANG Xibin; ZHANG Shiying
2003-01-01
One remarkable feature of wavelet decomposition is that the wavelet coefficients are localized, and any singularity in the input signals can only affect the wavelet coefficients at the point near the singularity. The localized property of the wavelet coefficients allows us to identify the singularities in the input signals by studying the wavelet coefficients at different resolution levels. This paper considers wavelet-based approaches for the detection of outliers in time series. Outliers are high-frequency phenomena which are associated with the wavelet coefficients with large absolute values at different resolution levels. On the basis of the first-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a time series. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributed as a X12. Empirical examples are presented to demonstrate the application of the proposed diagnostic.
Wavelet transforms as solutions of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Zweig, G.
1997-10-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuous wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.
A Remark on the Mallat Pyramidal Algorithm of Wavelet Analysis
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
The exact relationships between the lenthgs of scale sequences and wavelet sequences in the Mallat pyramidal algorithm for computing wavelet trans-form coefficients are obtained,and the maximum possible scale of arbitrary discrete signal is derived.
Wavelet Subspaces Invariant Under Groups of Translation Operators
Indian Academy of Sciences (India)
Biswaranjan Behera; Shobha Madan
2003-05-01
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty.
Wavelets associated with Hankel transform and their Weyl transforms
Institute of Scientific and Technical Information of China (English)
PENG; Lizhong; MA; Ruiqin
2004-01-01
The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.
Wavelet based Non LSB Steganography
Directory of Open Access Journals (Sweden)
H S Manjunatha Reddy
2011-11-01
Full Text Available Steganography is the methods of communicating secrete information hidden in the cover object. The messages hidden in a host data are digital image, video or audio files, etc, and then transmitted secretly to the destination. In this paper we propose Wavelet based Non LSB Steganography (WNLS. The cover image is segmented into 4*4 cells and DWT/IWT is applied on each cell. The 2*2 cell of HH band of DWT/IWT are considered and manipulated with payload bit pairs using identity matrix to generate stego image. The key is used to extract payload bit pairs at the destination. It is observed that the PSNR values are better in the case of IWT compare to DWT for all image formats. The algorithm can’t be detected by existing steganalysis techniques such as chi-square and pair of values techniques. The PSNR values are high in the case of raw images compared to formatted images.
Wavelet view on renormalization group
Altaisky, M V
2016-01-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier described in {\\em Phys.Rev.D} 81(2010)125003, 88(2013)025015, is finite by construction. The space of scale-dependent functions $\\{ \\phi_a(x) \\}$ is more relevant to physical reality than the space of square-integrable functions $\\mathrm{L}^2(R^d)$, because, due to the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than point. The effective action $\\Gamma_{(A)}$ of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet -- an "aperture function" of a measuring device used to produce the snapshot of a field $\\phi$ at the point $x$ with the resolution $a$. The standard RG results for $\\phi^4$ model are reproduced.
Nuclear data compression and reconstruction via discrete wavelet transform
Energy Technology Data Exchange (ETDEWEB)
Park, Young Ryong; Cho, Nam Zin [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1997-12-31
Discrete Wavelet Transforms (DWTs) are recent mathematics, and begin to be used in various fields. The wavelet transform can be used to compress the signal and image due to its inherent properties. We applied the wavelet transform compression and reconstruction to the neutron cross section data. Numerical tests illustrate that the signal compression using wavelet is very effective to reduce the data saving spaces. 7 refs., 4 figs., 3 tabs. (Author)
Discovering the Merit of the Wavelet Transform for Object Classification
2004-03-01
key steps in object recognition. Typically, geometric primitives are extracted from an image using local analysis. However, the wavelet transform provides...network. This thesis examines the benefits of the wavelet transform as a preprocessor to a neural network for object recognition. Scaling of the...benefits of the wavelet transform , the effects of the various post-wavelet scaling functions, and the best neural network topology for this research. This is done by analyzing the system s performance on CAD models.
The convolution theorem for two-dimensional continuous wavelet transform
Institute of Scientific and Technical Information of China (English)
ZHANG CHI
2013-01-01
In this paper , application of two -dimensional continuous wavelet transform to image processes is studied. We first show that the convolution and correlation of two continuous wavelets satisfy the required admissibility and regularity conditions ,and then we derive the convolution and correlation theorem for two-dimensional continuous wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for two -dimensional continuous wavelet transform to perform image restoration in the presence of additive noise.
OPTICAL REALIZATION OF WAVELET TRANSFORM WITH A SINGLE LENS
Institute of Scientific and Technical Information of China (English)
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.
RESEARCH OF WAVELET TRANSFORM INSTRUMENT SYSTEM FOR SIGNAL ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
After brief describing the principle of wavelet transform (WT) of signals, a new signals analysis system based on wavelet transform is introduced. The design and development of the instrument of wavelet transform are described. A number of practical uses of this system demonstrate that wavelet transform system is specially functional in identifying and processing impulse, singular and nonsmooth signals,so that it should be evaluated the most advanced signal analyzing system.
Parameterization and algebraic structure of 3-band orthogonal wavelet systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, a complete parameterization for the 3-band compact wavelet systems is presented. Using the parametric result, a program of the filterbank design is completed, which can give not only the filterbanks but also the graphs of all possible scaling functions and their corresponding wavelets. Especially some symmetric wavelets with small supports are given. Finally an algebraic structure for this kind of wavelet systems is characterized.
Generalizing Lifted Tensor-Product Wavelets to Irregular Polygonal Domains
Energy Technology Data Exchange (ETDEWEB)
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2002-04-11
We present a new construction approach for symmetric lifted B-spline wavelets on irregular polygonal control meshes defining two-manifold topologies. Polygonal control meshes are recursively refined by stationary subdivision rules and converge to piecewise polynomial limit surfaces. At every subdivision level, our wavelet transforms provide an efficient way to add geometric details that are expanded from wavelet coefficients. Both wavelet decomposition and reconstruction operations are based on local lifting steps and have linear-time complexity.
Wavelet Variance Analysis of EEG Based on Window Function
Institute of Scientific and Technical Information of China (English)
ZHENG Yuan-zhuang; YOU Rong-yi
2014-01-01
A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram (EEG).The ex-prienmental results show that the wavelet energy of epileptic EEGs are more discrete than normal EEGs, and the variation of wavelet variance is different between epileptic and normal EEGs with the increase of time-window width. Furthermore, it is found that the wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normal EEGs.
Construction of a class of Daubechies type wavelet bases
Energy Technology Data Exchange (ETDEWEB)
Li Dengfeng [Institute of Applied Mathematics, School of Mathematics and Information Sciences Henan University, Kaifeng 475001 (China); Wu Guochang [College of Information, Henan University of Finance and Economics, Zhengzhou 450002 (China)], E-mail: archang-0111@163.com
2009-10-15
Extensive work has been done in the theory and the construction of compactly supported orthonormal wavelet bases of L{sup 2}(R). Some of the most distinguished work was done by Daubechies, who constructed a whole family of such wavelet bases. In this paper, we construct a class of orthonormal wavelet bases by using the principle of Daubechies, and investigate the length of support and the regularity of these wavelet bases.
Wavelet-Based Denoising Attack on Image Watermarking
Institute of Scientific and Technical Information of China (English)
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.
Embedded wavelet video coding with error concealment
Chang, Pao-Chi; Chen, Hsiao-Ching; Lu, Ta-Te
2000-04-01
We present an error-concealed embedded wavelet (ECEW) video coding system for transmission over Internet or wireless networks. This system consists of two types of frames: intra (I) frames and inter, or predicted (P), frames. Inter frames are constructed by the residual frames formed by variable block-size multiresolution motion estimation (MRME). Motion vectors are compressed by arithmetic coding. The image data of intra frames and residual frames are coded by error-resilient embedded zerotree wavelet (ER-EZW) coding. The ER-EZW coding partitions the wavelet coefficients into several groups and each group is coded independently. Therefore, the error propagation effect resulting from an error is only confined in a group. In EZW coding any single error may result in a totally undecodable bitstream. To further reduce the error damage, we use the error concealment at the decoding end. In intra frames, the erroneous wavelet coefficients are replaced by neighbors. In inter frames, erroneous blocks of wavelet coefficients are replaced by data from the previous frame. Simulations show that the performance of ECEW is superior to ECEW without error concealment by 7 to approximately 8 dB at the error-rate of 10-3 in intra frames. The improvement still has 2 to approximately 3 dB at a higher error-rate of 10-2 in inter frames.
GPS Receiver Performance Inspection by Wavelet Transform
Institute of Scientific and Technical Information of China (English)
Xia Lin-yuan; Liu Jing-nan; Lu Liang-xi
2003-01-01
As a powerful analysis tool and the result of contemporary mathematics development, wavelet transform has shown its promising application potentials through the research in the paper. Three aspects regarding GPS receiver performance is tackled: cycle slip detection, receiver noise analysis and receiver channel bias inspection. Wavelet decomposition for double differential observation has demonstrated that this multi-level transform can reveal cycle slips as small as 0.5 cycles without any pre-adjustment processes or satellite orbit information, it can therefore be regarded as a 'geometry free' method. Based on property assumption of receiver noise, signal of noise serial is obtained at the high frequency scale in wavelet decomposition layers. This kind of noise influence on GPSb aseline result can be effectively eliminated by reconstruction process during wavelet reconstruction. Through observed data analysis, the transform has detected a kind of receiver channel bias that has not been completely removed by processing unit of GPS receiver during clock offset resetting operation. Thus the wavelet approach can be employed as a kind of system diagnosis in a generalized point of view.
Wavelet based detection of manatee vocalizations
Gur, Berke M.; Niezrecki, Christopher
2005-04-01
The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.
Wavelet applied to computer vision in astrophysics
Bijaoui, Albert; Slezak, Eric; Traina, Myriam
2004-02-01
Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.
Directory of Open Access Journals (Sweden)
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.
A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions
Directory of Open Access Journals (Sweden)
Seyed Hossein Mahdavi
2015-01-01
Full Text Available Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet.
Singularity Detection of Signals Based on their Wavelet Transform
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper introduces a multiresolution decomposition of signals based on their wavelet transform. The different behaviors of the wavelet transform between the signal and the noise are compared. An algorithm of singularity detection and processing in signals is proposed by the modulus maximum of the wavelet transform.
The Discrete, Orthogonal Wavelet Transform, A Protective Approach.
1995-09-01
completely determined by the collection of functions onto which it projects. The wavelet transform projects onto a set of functions which satisfy a...simple linear relationship between different levels of dilation. The properties of the wavelet transform are determined by the coefficients of this linear...relationship. This thesis examines the connections between the wavelet transform properties and the linear relationship coefficients. (AN)
Convergence of Wavelet Expansions in the Orlicz Space
Institute of Scientific and Technical Information of China (English)
Chang Mei TAN
2011-01-01
In this paper we study the convergence in norm and pointwise convergence of wavelet expansion in the Orlicz spaces, and prove that, under certain conditions on the wavelet, the wavelet expansion converges in the Orlicz-norm and also converges almost everywhere.
On extensions of wavelet systems to dual pairs of frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2015-01-01
It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems are generated by the multiscale setup with trigonometric...
Further Result of Sideways Heat Equation and Wavelets
Institute of Scientific and Technical Information of China (English)
傅初黎; 邱春雨; 朱佑彬
2001-01-01
@@"Sideways heat equation and wavelets" written by Teresa Reginska[1] is one of the earliest important literatures about solving ill-posed problem by using wavelet regularization. In this paper a new approach of wavelet regularization for the following sideways heat equation[2] in the quarter plane (t≥0, x≥0) has been considered:
A Characterization of Generalized Frame MRAs Deriving Orthonormal Wavelets
Institute of Scientific and Technical Information of China (English)
Zhi Hua ZHANG
2006-01-01
In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA (GFMRA). In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a general approach to the constructions of non-MRA wavelets. Finally we present two examples to illustrate the theory.
Stationarizing two classes of nonstationary processes by wavelet
Institute of Scientific and Technical Information of China (English)
TANG Hong-min; XIE Zhong-jie
2006-01-01
The main purpose of this paper is to discuss the stationarity of two classes of nonstationary processes after wavelet transformations.Owing to the fact that the wavelet transformation possesses localization and implicit differencing property,the authors show that after wavelet transformation,the fractionally differenced process and the harmonizable periodically correlated process may be changed into stationary processes.
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.
Predictive depth coding of wavelet transformed images
Lehtinen, Joonas
1999-10-01
In this paper, a new prediction based method, predictive depth coding, for lossy wavelet image compression is presented. It compresses a wavelet pyramid composition by predicting the number of significant bits in each wavelet coefficient quantized by the universal scalar quantization and then by coding the prediction error with arithmetic coding. The adaptively found linear prediction context covers spatial neighbors of the coefficient to be predicted and the corresponding coefficients on lower scale and in the different orientation pyramids. In addition to the number of significant bits, the sign and the bits of non-zero coefficients are coded. The compression method is tested with a standard set of images and the results are compared with SFQ, SPIHT, EZW and context based algorithms. Even though the algorithm is very simple and it does not require any extra memory, the compression results are relatively good.
Wavelet Digital Watermarking with Unsupervised Learning
Institute of Scientific and Technical Information of China (English)
SHEKun; HUANGJuncai; ZHOUMingtian
2005-01-01
In this paper a novel technique for the digital watermarking of still color images based on the concept of color space transform, wavelet fusion and image denoising is presented. Our algorithm transforms R, G, B colorspace to R′, G′, B′ color space firstly, which constructs three grey images, then computes the 2nd-level discretewavelet decomposition of the three grey images. Embedding watermark fuses a grey image (watermark) with each of the three images' wavelet coefficients, then transforms R′, G′, B′ color space to R, G, B color space to obtain thewatermarked color image. When extracting watermark, at first two grey images X1, X2 from the two of three wavelet coefficients is distilled, then Independent component analyses (ICA) is used to denoise and get grey image (watermark) W. The results of our test show the superior performance of the technique and the great potential of the watermarking of photographic imagery.
Spatial Verification Using Wavelet Transforms: A Review
Weniger, Michael; Friederichs, Petra
2016-01-01
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last five years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields such as feature detection, image fusion, texture analysis, or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tab the full potential of wavelet analysis, we revise the stat...
Comparison of fast discrete wavelet transform algorithms
Institute of Scientific and Technical Information of China (English)
MENG Shu-ping; TIAN Feng-chun; XU Xin
2005-01-01
This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short-length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.
Denoising CT Images using wavelet transform
Directory of Open Access Journals (Sweden)
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.
Wavelet Analysis of Space Solar Telescope Images
Institute of Scientific and Technical Information of China (English)
Xi-An Zhu; Sheng-Zhen Jin; Jing-Yu Wang; Shu-Nian Ning
2003-01-01
The scientific satellite SST (Space Solar Telescope) is an important research project strongly supported by the Chinese Academy of Sciences. Every day,SST acquires 50 GB of data (after processing) but only 10GB can be transmitted to the ground because of limited time of satellite passage and limited channel volume.Therefore, the data must be compressed before transmission. Wavelets analysis is a new technique developed over the last 10 years, with great potential of application.We start with a brief introduction to the essential principles of wavelet analysis,and then describe the main idea of embedded zerotree wavelet coding, used for compressing the SST images. The results show that this coding is adequate for the job.
Lifting scheme of symmetric tight wavelets frames
Institute of Scientific and Technical Information of China (English)
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.
Partially coherent imaging and spatial coherence wavelets
Castaneda, R
2003-01-01
A description of spatially partially coherent imaging based on the propagation of second order spatial coherence wavelets and marginal power spectra (Wigner distribution functions) is presented. In this dynamics, the spatial coherence wavelets will be affected by the system through its elementary transfer function. The consistency of the model with the both extreme cases of full coherent and incoherent imaging was proved. In the last case we obtained the classical concept of optical transfer function as a simple integral of the elementary transfer function. Furthermore, the elementary incoherent response function was introduced as the Fourier transform of the elementary transfer function. It describes the propagation of spatial coherence wavelets form each object point to each image point through a specific point on the pupil planes. The point spread function of the system was obtained by a simple integral of the elementary incoherent response function.
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.
Fingerprint verification based on wavelet subbands
Huang, Ke; Aviyente, Selin
2004-08-01
Fingerprint verification has been deployed in a variety of security applications. Traditional minutiae detection based verification algorithms do not utilize the rich discriminatory texture structure of fingerprint images. Furthermore, minutiae detection requires substantial improvement of image quality and is thus error-prone. In this paper, we propose an algorithm for fingerprint verification using the statistics of subbands from wavelet analysis. One important feature for each frequency subband is the distribution of the wavelet coefficients, which can be modeled with a Generalized Gaussian Density (GGD) function. A fingerprint verification algorithm that combines the GGD parameters from different subbands is proposed to match two fingerprints. The verification algorithm in this paper is tested on a set of 1,200 fingerprint images. Experimental results indicate that wavelet analysis provides useful features for the task of fingerprint verification.
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.
Wavelet Scattering Regression of Quantum Chemical Energies
Hirn, Matthew; Poilvert, Nicolas
2016-01-01
We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is represented by an electronic density function. A multiscale invariant dictionary is calculated with wavelet scattering invariants. It cascades a first wavelet transform which separates scales, with a second wavelet transform which computes interactions across scales. Sparse scattering regressions give state of the art results over two databases of organic planar molecules. On these databases, the regression error is of the order of the error produced by DFT codes, but at a fraction of the computational cost.
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.
Characterization and simulation of gunfire with wavelets
Energy Technology Data Exchange (ETDEWEB)
Smallwood, D.O.
1998-09-01
Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The response of a structure to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The methods all used some form of the discrete fourier transform. The current paper will explore a simpler method to describe the nonstationary random process in terms of a wavelet transform. As was done previously, the gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. The wavelet transform is performed on each of these records. The mean and standard deviation of the resulting wavelet coefficients describe the composite characteristics of the entire waveform. It is shown that the distribution of the wavelet coefficients is approximately Gaussian with a nonzero mean and that the standard deviation of the coefficients at different times and levels are approximately independent. The gunfire is simulated by generating realizations of records of a single-round firing by computing the inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously discussed gunfire record. The individual realizations are then assembled into a realization of a time history of many rounds firing. A second-order correction of the probability density function (pdf) is accomplished with a zero memory nonlinear (ZMNL) function. The method is straightforward, easy to implement, and produces a simulated record very much like the original measured gunfire record.
Signal extrapolation based on wavelet representation
Xia, Xiang-Gen; Kuo, C.-C. Jay; Zhang, Zhen
1993-11-01
The Papoulis-Gerchberg (PG) algorithm is well known for band-limited signal extrapolation. We consider the generalization of the PG algorithm to signals in the wavelet subspaces in this research. The uniqueness of the extrapolation for continuous-time signals is examined, and sufficient conditions on signals and wavelet bases for the generalized PG (GPG) algorithm to converge are given. We also propose a discrete GPG algorithm for discrete-time signal extrapolation, and investigate its convergence. Numerical examples are given to illustrate the performance of the discrete GPG algorithm.
Wavelet methods in mathematical analysis and engineering
Damlamian, Alain
2010-01-01
This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a stateoftheart in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented.
Scalable still image coding based on wavelet
Yan, Yang; Zhang, Zhengbing
2005-02-01
The scalable image coding is an important objective of the future image coding technologies. In this paper, we present a kind of scalable image coding scheme based on wavelet transform. This method uses the famous EZW (Embedded Zero tree Wavelet) algorithm; we give a high-quality encoding to the ROI (region of interest) of the original image and a rough encoding to the rest. This method is applied well in limited memory space condition, and we encode the region of background according to the memory capacity. In this way, we can store the encoded image in limited memory space easily without losing its main information. Simulation results show it is effective.
New Algorithm For Calculating Wavelet Transforms
Directory of Open Access Journals (Sweden)
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.
ON CONVERGENCE OF WAVELET PACKET EXPANSIONS
Institute of Scientific and Technical Information of China (English)
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.
Improved System Identification Approach Using Wavelet Networks
Institute of Scientific and Technical Information of China (English)
石宏理; 蔡远利; 邱祖廉
2005-01-01
A new approach is proposed to improve the general identification algorithm of multidimensional systems using wavelet networks. The general algorithm involves mapping vector input into its norm to avoid problem of dimensionality in construction multidimensional wavelet basis functions. Thus, the basis functions are spherically symmetric without direction selectivity. In order to restore the direction selectivity, the improved approach weights the input variables before mapping it into a scalar form. The weights can be obtained using universal optimization algorithms. Generally, only local optimal weights are obtained. Even so, performance of identification can be improved.
Use of wavelet in specifying optics
Institute of Scientific and Technical Information of China (English)
Zhi Yang; Yifan Dai; Guilin Wang
2007-01-01
Using power spectral density (PSD) function to specify large aperture optical components' quality of laser system is universal. But it cannot provide effective guidance to eliminate certain frequency segment error.In order to solve this problem, two-dimensional discrete wavelet transform (2D-DWT) is used to separate frequency segment error and detect the corresponding region of certain frequency segment error, which is used as feedback to a machining process. The experimental results show that the corresponding region of certain frequency segment can be found and machining can be guided effectively by using wavelet.
Numerical Algorithms Based on Biorthogonal Wavelets
Ponenti, Pj.; Liandrat, J.
1996-01-01
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
Gaussian Functions, Γ-Functions and Wavelets
Institute of Scientific and Technical Information of China (English)
蔡涛; 许天周
2003-01-01
The relations between Gaussian function and Γ-function is revealed first at one-dimensional situation. Then, the Fourier transformation of n-dimensional Gaussian function is deduced by a lemma. Following the train of thought in one-dimensional situation, the relation between n-dimensional Gaussian function and Γ-function is given. By these, the possibility of arbitrary derivative of an n-dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ-function as well as in finding high-dimensional mother wavelets.
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
Quantization of wavelet packet audio coding
Institute of Scientific and Technical Information of China (English)
Tan Jianguo; Zhang Wenjun; Liu Peilin
2006-01-01
The method of quantization noise control of audio coding in the wavelet domain is proposed. Using the inverse Discrete Fourier Transform (DFT), it converts the masking threshold coming from MPEG psycho-acoustic model in the frequency domain to the signal in the time domain; the Discrete Wavelet Packet Transform (DWPT) is performed; the energy in each subband is regarded as the maximum allowed quantization noise energy. The experimental result shows that the proposed method can attain the nearly transparent audio quality below 64kbps for the most testing audio signals.
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
Solution of wave-like equation based on Haar wavelet
Directory of Open Access Journals (Sweden)
Naresh Berwal
2012-11-01
Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.
The Lifting Scheme Based on the Second Generation Wavelets
Institute of Scientific and Technical Information of China (English)
FENG Hui; GUO Lanying; XIAO Jinsheng
2006-01-01
The lifting scheme is a custom-design construction of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform, which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.
Mass spectrometry cancer data classification using wavelets and genetic algorithm.
Nguyen, Thanh; Nahavandi, Saeid; Creighton, Douglas; Khosravi, Abbas
2015-12-21
This paper introduces a hybrid feature extraction method applied to mass spectrometry (MS) data for cancer classification. Haar wavelets are employed to transform MS data into orthogonal wavelet coefficients. The most prominent discriminant wavelets are then selected by genetic algorithm (GA) to form feature sets. The combination of wavelets and GA yields highly distinct feature sets that serve as inputs to classification algorithms. Experimental results show the robustness and significant dominance of the wavelet-GA against competitive methods. The proposed method therefore can be applied to cancer classification models that are useful as real clinical decision support systems for medical practitioners.
A primer on wavelets and their scientific applications
Walker, James S
2008-01-01
In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments, this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications. Ingeniously relying o
Wavelet Neural Network Based Traffic Prediction for Next Generation Network
Institute of Scientific and Technical Information of China (English)
Zhao Qigang; Li Qunzhan; He Zhengyou
2005-01-01
By using netflow traffic collecting technology, some traffic data for analysis are collected from a next generation network (NGN) operator. To build a wavelet basis neural network (NN), the Sigmoid function is replaced with the wavelet in NN. Then the wavelet multiresolution analysis method is used to decompose the traffic signal, and the decomposed component sequences are employed to train the NN. By using the methods, an NGN traffic prediction model is built to predict one day's traffic. The experimental results show that the traffic prediction method of wavelet NN is more accurate than that without using wavelet in the NGN traffic forecasting.
Low-power Analog VLSI Implementation of Wavelet Transform
Institute of Scientific and Technical Information of China (English)
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.
OPEN-LOOP FOG SIGNAL TESTING AND WAVELET ELIMINATING NOISE
Institute of Scientific and Technical Information of China (English)
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.
Han, Bin
2003-06-01
Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d×d dilation matrix M, we demonstrate in a constructive way that we can construct compactly supported tight M-wavelet frames and orthonormal M-wavelet bases in of exponential decay, which are derived from compactly supported M-refinable functions, such that they can have both arbitrarily high smoothness and any preassigned order of vanishing moments. This paper improves several results in Battle (Comm. Math. Phys. 110 (1987) 601), Bownik (J. Fourier Anal. Appl. 7(2001) 489), Gröchenig and Ron (Proc. Amer. Math. Soc. 126 (1998) 1101), Lemarie (J. Math. Pures Appl. 67 (1988) 227), and Strichartz (Constr. Approx. 9 (1993) 327).
Dyadic Bivariate Wavelet Multipliers in L2(R2)
Institute of Scientific and Technical Information of China (English)
Zhong Yan LI; Xian Liang SHI
2011-01-01
The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA|＝2)wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium(1998)and Li Z.,et al.(2010).But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation.matrix with the absolute value of determinant not 2 in L2(R2).In this paper,we choose 2I2＝(0202)as the dilation matrix and consider the 2I2-dilation multivariate wavelet Ψ＝{ψ1,ψ2,ψ3}(which is called a dyadic bivariate wavelet)multipliers.Here we call a measurable function family f＝{f1,f2,f3}a dyadic bivariate wavelet multiplier if Ψ1＝{F-1(f1ψ1),F-1(f2ψ2),F-1(f3ψ3)} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Ψ={ψ1,ψ2,ψ3},where(f)and,F-1 denote the Fourier transform and the inverse transform of function f respectively.We study dyadic bivariate wavelet multipliers,and give some conditions for dyadic bivariate wavelet multipliers.We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.
A Comparative Study of Wavelet Thresholding for Image Denoising
Directory of Open Access Journals (Sweden)
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.
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.
Denoising and robust non-linear wavelet analysis
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-04-01
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 resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, 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.
Comparison of Satellite Image Enhancement Techniques in Wavelet Domain
Directory of Open Access Journals (Sweden)
K. Narasimhan
2012-12-01
Full Text Available In this study, a comparison of various existing satellite image resolution enhancement techniques in wavelet domain is done. Each method is analysed quantitatively and visually. There are various wavelet domain based methods such as Wavelet Zero Padding, Dual Tree-Complex Wavelet Transform, Discrete Wavelet Transform, Cycle Spinning and Undecimated Wavelet Transform. On the basis of analysis, the most efficient method is proposed. The algorithms take the low resolution image as the input image and then wavelet transformation using daubechies (db3 is used to decompose the input image into different sub band images containing high and low frequency component. Then these subband images along with the input image are interpolated followed by combining all these images to generate a new resolution enhanced image by an inverse process.
Performance Evaluation of Wavelet Based on Human Visual System
Institute of Scientific and Technical Information of China (English)
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.
RESEARCH OF PROBLEMS ON REALIZING DIRECT ALGORITHM OF WAVELET TRANSFORM
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Direct algorithm of wavelet transform (WT) is the numerical algorithm obtained from the integral formula of WT by directly digitization.Some problems on realizing the algorithm are studied.Some conclusions on the direct algorithm of discrete wavelet transform (DWT), such as discrete convolution operation formula of wavelet coefficients and wavelet components, sampling principle and technology to wavelets, deciding method for scale range of wavelets, measures to solve edge effect problem, etc, are obtained.The realization of direct algorithm of continuous wavelet transform (CWT) is also studied.The computing cost of direct algorithm and Mallat algorithm of DWT are still studied, and the computing formulae are obtained.These works are beneficial to deeply understand WT and Mallat algorithm.Examples in the end show that direct algorithm can also be applied widely.
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.
Application of wavelet transform to seismic data; Wavelet henkan no jishin tansa eno tekiyo
Energy Technology Data Exchange (ETDEWEB)
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.
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
Conductance calculations with a wavelet basis set
DEFF Research Database (Denmark)
Thygesen, Kristian Sommer; Bollinger, Mikkel; Jacobsen, Karsten Wedel
2003-01-01
. The linear-response conductance is calculated from the Green's function which is represented in terms of a system-independent basis set containing wavelets with compact support. This allows us to rigorously separate the central region from the contacts and to test for convergence in a systematic way...
Cosmic Ray elimination using the Wavelet Transform
Orozco-Aguilera, M. T.; Cruz, J.; Altamirano, L.; Serrano, A.
2009-11-01
In this work, we present a method for the automatic cosmic ray elimination in a single CCD exposure using the Wavelet Transform. The proposed method can eliminate cosmic rays of any shape or size. With this method we can eliminate over 95% of cosmic rays in a spectral image.
Parallel adaptive wavelet collocation method for PDEs
Energy Technology Data Exchange (ETDEWEB)
Nejadmalayeri, Alireza, E-mail: Alireza.Nejadmalayeri@gmail.com [FortiVenti Inc., Suite 404, 999 Canada Place, Vancouver, BC, V6C 3E2 (Canada); Vezolainen, Alexei, E-mail: Alexei.Vezolainen@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States); Brown-Dymkoski, Eric, E-mail: Eric.Browndymkoski@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States); Vasilyev, Oleg V., E-mail: Oleg.Vasilyev@Colorado.edu [Department of Mechanical Engineering, University of Colorado Boulder, UCB 427, Boulder, CO 80309 (United States)
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
Spatial verification using wavelet transforms: a review
Weniger, Michael; Kapp, Florian; Friederichs, Petra
2017-01-01
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last five years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields such as feature detection, image fusion, texture analysis, or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tab the full potential of wavelet analysis, we revise the state-of-the art in one- and two-dimensional wavelet analysis and its application with emphasis on spatial verification. We further use a technique developed for texture analysis in the context of high-resolution quantitative precipitation forecasts, which is able to assess structural characteristics of the precipitation fields and allows efficient clustering of ensemble data.
Wave Forecasting Using Neuro Wavelet Technique
Directory of Open Access Journals (Sweden)
Pradnya Dixit
2014-12-01
Full Text Available In the present work a hybrid Neuro-Wavelet Technique is used for forecasting waves up to 6 hr, 12 hr, 18 hr and 24 hr in advance using hourly measured significant wave heights at an NDBC station 41004 near the east coast of USA. The NW Technique is employed by combining two methods, Discrete Wavelet Transform and Artificial Neural Networks. The hourly data of previously measured significant wave heights spanning over 2 years from 2010 and 2011 is used to calibrate and test the models. The discrete wavelet transform of NWT analyzes frequency of signal with respect to time at different scales. It decomposes time series into low (approximate and high (detail frequency components. The decomposition of approximate can be carried out up to desired multiple levels in order to provide more detail and approximate components which provides relatively smooth varying amplitude series. The neural network is trained with decorrelated approximate and detail wavelet coefficients. The outputs of networks during testing are reconstructed back using inverse DWT. The results were judged by drawing the wave plots, scatter plots and other error measures. The developed models show reasonable accuracy in prediction of significant wave heights from 6 to 24 hours. To compare the results traditional ANN models were also developed at the same location using the same data and for same time interval.
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.
Characterization and Simulation of Gunfire with Wavelets
Directory of Open Access Journals (Sweden)
David O. Smallwood
1999-01-01
Full Text Available Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The structural response to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The current paper will explore a method to describe the nonstationary random process using a wavelet transform. The gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. A wavelet transform is performed on each of these records. The gunfire is simulated by generating realizations of records of a single-round firing by computing an inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously analyzed gunfire record. The individual records are assembled into a realization of many rounds firing. A second-order correction of the probability density function is accomplished with a zero memory nonlinear function. The method is straightforward, easy to implement, and produces a simulated record much like the measured gunfire record.
Building nonredundant adaptive wavelets by update lifting
Heijmans, H.J.A.M.; Pesquet-Popescu, B.; Piella, G.
2002-01-01
Adaptive wavelet decompositions appear useful in various applications in image and video processing, such as image analysis, compression, feature extraction, denoising and deconvolution, or optic flow estimation. For such tasks it may be important that the multiresolution representations take into a
COSMIC RAY ELIMINATION USING THE WAVELET TRANSFORM
Directory of Open Access Journals (Sweden)
M. T. Orozco-Aguilera
2009-01-01
Full Text Available In this work, we present a method for the automatic cosmic ray elimination in a single CCD exposure using the Wavelet Transform. The proposed method can eliminate cosmic rays of any shape or size. With this method we can eliminate over 95% of cosmic rays in a spectral image.
Wavelet fractal character of overlapping signal
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A new method based on the combining of the wavelet theory with the fractal theory and named wavelet fractal peak position method (WFPPM) is introduced to extract the number of the components and the relevant peak positions from overlapping signals in chemistry. The overlapping signal is first transformed into continuous wavelet transform value of time domain in certain dilation range via continuous wavelet transform (CWT), and then changed into capacity dimensions (Dc). The number of the components and the relevant positions of overlapping peaks can be identified easily according to the change of Dc. An investigation concerning the influence of different dilation ranges on the peak positions extracted by WFPPM is also provided. Studies show that WFPPM is and efficient tool for extracting the peak positions and identifying the number of peaks from unresolved signals, even wht\\en this kind of overlapping is significantly serious. Relative errors of less than 1.0% in peak are found when WFPPM is used in the processing of the cadmium(Ⅱ)-indium(Ⅲ) mixture system. The analytical results demonstrate that the desired peak positions can be extracted conveniently, accurately and rapidly from and unresolved signal via WFPPM. Tremendous developing and applications based on currently reported WFPPM in extracting overlapping signals would be expected in the near futrue.
IRREGULAR WAVELET FRAMES AND GABOR FRAMES
Institute of Scientific and Technical Information of China (English)
Ole Christensen; Sergio Favier; Felipe Zó
2001-01-01
Given g ∈ L2 (R), we consider irregular wavelet systems of theform {λ g(λj x-kb) }j z. kz, where λj ＞0 and b＞0. Sufficient conditions for the wavelet system to constitute a frame for L2(R) are given. For a class of functions g ∈ L 2 (R) we prove that certain growth conditions on {λj} will lead to frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system {exib(j,x)g(x-λh)}jzn,kz to be a frame.CLC Number：O17 Document ID：AAuthor Resume：Ole Christensen;E-mail: Ole. Christensen@mat. dtu. dk Sergio Favier and Felipe Zó ;e-mails : sfavier@unsl. edu. ar fzo@unsl. edu. ar References：[1]Casaza,P.G. and Christensen,O.,Weyl-Heisenberg Frames for Subspaces of L2(R),Proc.Amer. Math. Soc. ,129(2001),145-154.[2]Casazza,P.G. and Christensen,O. ,Classifying Certain Irregular Gabor Frames,preprint[2]001.[3]Christensen,O. and Lindner,A. ,Lower Bounds for Finite Wavelet and Gabor Systems,Appr. Theory and Appl.,17(2001),17-31.[4]Chui,C.K. and Shi,X. ,Inequalities of Litdewood-Paley Type for Frames and Wavelets,SIAM J. Math. Anal. ,24:1(1993),263-277.[5]Daubechies,I. ,Ten Lectures on Wavelets,SIAM,Philadelphia,1992.[6]Favier,S. and Zalik,R. ,On the Stability of Frames and Riesz Bases,Appl. Comp. Ham.Anal. ,2(1995),160-173.[7]Feichtinger,H.G. and Strohmer,T. ,(Eds.),Gabor Analysis and Algorithms : Theory and Applications,Birkhauser,1998.[8]Heil,C.E. and Walnut,D.F. ,Continuous and Discrete Wavelet Transforms,SIAM Review,31:4(1989),628-666.[9]Sun,W. and Zhou,X. ,Irregular Wavelet Frames,Science in China (Series A),43:2(2000),122-127.Manuscript Received：2001年7月10日Manuscript Revised：2001年7月23日Published：2001年9月1日
Directory of Open Access Journals (Sweden)
Jikai Chen
2016-12-01
Full Text Available In a power system, the analysis of transient signals is the theoretical basis of fault diagnosis and transient protection theory. Shannon wavelet entropy (SWE and Shannon wavelet packet entropy (SWPE are powerful mathematics tools for transient signal analysis. Combined with the recent achievements regarding SWE and SWPE, their applications are summarized in feature extraction of transient signals and transient fault recognition. For wavelet aliasing at adjacent scale of wavelet decomposition, the impact of wavelet aliasing is analyzed for feature extraction accuracy of SWE and SWPE, and their differences are compared. Meanwhile, the analyses mentioned are verified by partial discharge (PD feature extraction of power cable. Finally, some new ideas and further researches are proposed in the wavelet entropy mechanism, operation speed and how to overcome wavelet aliasing.
Novel Adaptive Beamforming Algorithm Based on Wavelet Packet Transform
Institute of Scientific and Technical Information of China (English)
Zhang Xiaofei; Xu Dazhuan
2005-01-01
An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packet theory to adaptive beamforming, a wavelet packet transform-based adaptive beamforming algorithm (WP-ABF) is proposed . This WP-ABF algorithm uses wavelet packet transform as the preprocessing, and the wavelet packet transformed signal uses least mean square algorithm to implement the adaptive beamforming. White noise can be wiped off under wavelet packet transform according to the different characteristics of signal and white under the wavelet packet transform. Theoretical analysis and simulations demonstrate that the proposed WP-ABF algorithm converges faster than the conventional adaptive beamforming algorithm and the wavelet transform-based beamforming algorithm. Simulation results also reveal that the convergence of the algorithm relates closely to the wavelet base and series; that is, the algorithm convergence gets better with the increasing of series, and for the same series of wavelet base the convergence gets better with the increasing of regularity.
Directory of Open Access Journals (Sweden)
Akimov Pavel Alekseevich
2012-10-01
Full Text Available Part 1 of this paper represents an introduction into the multi-resolution wavelet analysis. The wavelet-based analysis is an exciting new problem-solving tool used by mathematicians, scientists and engineers. In the paper, the authors try to present the fundamental elements of the multi-resolution wavelet analysis in a way that is accessible to an engineer, a scientist and an applied mathematician both as a theoretical approach and as a potential practical method of solving problems (particularly, boundary problems of structural mechanics and mathematical physics. The main goal of the contemporary wavelet research is to generate a set of basic functions (or general expansion functions and transformations that will provide an informative, efficient and useful description of a function or a signal. Another central idea is that of multi-resolution whereby decomposition of a signal represents the resolution of the detail. The multi-resolution decomposition seems to separate components of a signal in a way that is superior to most other methods of analysis, processing or compression. Due to the ability of the discrete wavelet transformation technique to decompose a signal at different independent scaling levels and to do it in a very flexible way, wavelets can be named "the microscopes of mathematics". Indeed, the use of the wavelet analysis and wavelet transformations requires a new point of view and a new method of interpreting representations.
Indian Academy of Sciences (India)
Mourad Talbi
2014-08-01
In this paper, we propose a new technique of Electrocardiogram (ECG) signal de-noising based on thresholding of the coefficients obtained from the application of the Forward Wavelet Transform Translation Invariant (FWT_TI) to each Bionic Wavelet coefficient. The De-noise De-noised ECG is obtained from the application of the inverse of BWT (BWT−1) to the de-noise de-noised bionic wavelet coefficients. For evaluating this new proposed de-noising technique, we have compared it to a thresholding technique in the FWT_TI domain. Preliminary tests of the application of the two de-noising techniques were constructed on a number of ECG signals taken from MIT-BIH database. The obtained results from Signal to Noise Ratio (SNR) and Mean Square Error (MSE) computations showed that our proposed de-noising technique outperforms the second technique. We have also compared the proposed technique to the thresholding technique in the bionic wavelet domain and this comparison was performed by SNR improvement computing. The obtained results from this evaluation showed that the proposed technique also outperforms the de-noising technique based on bionic wavelet coefficients thresholding.
Synthesis of Vibration Waves Based on Wavelet Technology
Directory of Open Access Journals (Sweden)
L.H. Zou
2012-01-01
Full Text Available A novel method to generate time series of vibration waves is proposed in the paper. Considering the frequency band energy as the criterion, synthesis formulas for fluctuating wind pressure and earthquake ground motion are developed in terms of Daubechies wavelet and Harr wavelet respectively. The wavelet reconstruction method is applicable to both stationary and non-stationary process simulation. Theoretically, for non-stationary (such as seismic process synthesis, it has a better non-stationarity in time-frequency domain than the traditional trigonometric series. Influence of wavelet delamination number and wavelet function type is also analyzed. Numerical results show that the synthesis of vibration waves based on wavelet reconstruction method contains main components of vibration, and can reflect the main properties of practical vibrations.
Based on the Wavelet Function of Power Network Fault Location
Directory of Open Access Journals (Sweden)
Fan YU
2013-04-01
Full Text Available In order to improve the measurement accuracy, in the traditional measuring method based on, by avoiding wave speed influence on fault location of transmission line method, and compares it with the combination of wavelet transform. This article selects dBN wavelet and three B spline wavelet contrast, compared them with new methods, through the Xi'an City Power Supply Bureau of the actual fault data validation. The results show that, with3 B spline wavelet and the new method combined with the location results are closer to the actual distance, its accuracy is higher than that of db3wavelet transform and a new method derived from the results, the error is far less than the db3 wavelet function, location is satisfactory.
Development of Wavelet Image Compression Technique to Particle Image Velocimetry
Institute of Scientific and Technical Information of China (English)
HuiLi
2000-01-01
In order to reduce the noise in the images and the physical storage,the wavelet-based image compression technique was applied to PIV processing in this paper,To study the effect of the wavelet bases,the standard PIV images were compressed by some known wavelet families,Daubechies,Coifman and Baylkin families with various compression ratios.It was found that a higher order wavelet base provided good compression performance for compressing PIV images,The error analysis of velocity field obtained indicated that the high compression ratio even up to 64:1,can be realized without losing significant flow information in PIV processing.The wavelet compression technique of PIV was applied to the experimental images of jet flow and showed excellent performance,A reduced number of erroneous vectors can be realized by varying compression ratio.It can say that the wavelet image compression technique is very effective in PIV system.
Comparative study of wavelet denoising in myoelectric control applications.
Sharma, Tanu; Veer, Karan
2016-01-01
Here, the wavelet analysis has been investigated to improve the quality of myoelectric signal before use in prosthetic design. Effective Surface Electromyogram (SEMG) signals were estimated by first decomposing the obtained signal using wavelet transform and then analysing the decomposed coefficients by threshold methods. With the appropriate choice of wavelet, it is possible to reduce interference noise effectively in the SEMG signal. However, the most effective wavelet for SEMG denoising is chosen by calculating the root mean square value and signal power values. The combined results of root mean square value and signal power shows that wavelet db4 performs the best denoising among the wavelets. Furthermore, time domain and frequency domain methods were applied for SEMG signal analysis to investigate the effect of muscle-force contraction on the signal. It was found that, during sustained contractions, the mean frequency (MNF) and median frequency (MDF) increase as muscle force levels increase.
Fingerprint spoof detection using wavelet based local binary pattern
Kumpituck, Supawan; Li, Dongju; Kunieda, Hiroaki; Isshiki, Tsuyoshi
2017-02-01
In this work, a fingerprint spoof detection method using an extended feature, namely Wavelet-based Local Binary Pattern (Wavelet-LBP) is introduced. Conventional wavelet-based methods calculate wavelet energy of sub-band images as the feature for discrimination while we propose to use Local Binary Pattern (LBP) operation to capture the local appearance of the sub-band images instead. The fingerprint image is firstly decomposed by two-dimensional discrete wavelet transform (2D-DWT), and then LBP is applied on the derived wavelet sub-band images. Furthermore, the extracted features are used to train Support Vector Machine (SVM) classifier to create the model for classifying the fingerprint images into genuine and spoof. Experiments that has been done on Fingerprint Liveness Detection Competition (LivDet) datasets show the improvement of the fingerprint spoof detection by using the proposed feature.
Research on ghost imaging method based on wavelet transform
Li, Mengying; He, Ruiqing; Chen, Qian; Gu, Guohua; Zhang, Wenwen
2017-09-01
We present an algorithm of extracting the wavelet coefficients of object based on ghost imaging (GI) system. Through modification of the projected random patterns by using a series of templates, wavelet transform GI (WTGI) can directly measure the high frequency components of wavelet coefficients without needing the original image. In this study, we theoretically and experimentally perform the high frequency components of wavelet coefficients detection with an arrow and a letter A based on GI and WTGI. Comparing with the traditional method, the use of the algorithm proposed in this paper can significantly improve the quality of the image of wavelet coefficients in both cases. The special advantages of GI will make the wavelet coefficient detection based on WTGI very valuable in real applications.
Group-normalized processing of complex wavelet packets
Institute of Scientific and Technical Information of China (English)
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
Fast Adaptive Wavelet for Remote Sensing Image Compression
Institute of Scientific and Technical Information of China (English)
Bo Li; Run-Hai Jiao; Yuan-Cheng Li
2007-01-01
Remote sensing images are hard to achieve high compression ratio because of their rich texture. By analyzing the influence of wavelet properties on image compression, this paper proposes wavelet construction rules and builds a new biorthogonal wavelet construction model with parameters. The model parameters are optimized by using genetic algorithm and adopting energy compaction as the optimization object function. In addition, in order to resolve the computation complexity problem of online construction, according to the image classification rule proposed in this paper we construct wavelets for different classes of images and implement the fast adaptive wavelet selection algorithm (FAWS). Experimental results show wavelet bases of FAWS gain better compression performance than Daubechies9/7.
FPGA Implementations of Bireciprocal Lattice Wave Discrete Wavelet Filter Banks
Directory of Open Access Journals (Sweden)
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.
Localisation of directional scale-discretised wavelets on the sphere
McEwen, Jason D; Wiaux, Yves
2015-01-01
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at about the same time) but relax the axisymmetric property of needlets so that directional signal content can be probed. Needlets have been shown to satisfy important quasi-exponential localisation and asymptotic uncorrelation properties. We show that these properties also hold for directional scale-discretised wavelets on the sphere and derive similar localisation and uncorrelation bounds in both the scalar and spin settings. Scale-discretised wavelets can thus be considered as directional needlets.
Frame Wavelets with Compact Supports for L2(Rn)
Institute of Scientific and Technical Information of China (English)
De Yun YANG; Xing Wei ZHOU; Zhu Zhi YUAN
2007-01-01
The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n×n real expansive matrix A, the frame-sets with respect to A are a family of sets in Rn. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry
An introduction to random vibrations, spectral & wavelet analysis
Newland, D E
2005-01-01
One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms.Starting with an introduction to probability distributions and averages, the text examines joint probability distributions, ensemble averages, and correlation; Fourier analysis; spectral density and excitation response relation
Embedded wavelet packet transform technique for texture compression
Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay
1995-09-01
A highly efficient texture compression scheme is proposed in this research. With this scheme, energy compaction of texture images is first achieved by the wavelet packet transform, and an embedding approach is then adopted for the coding of the wavelet packet transform coefficients. By comparing the proposed algorithm with the JPEG standard, FBI wavelet/scalar quantization standard and the EZW scheme with extensive experimental results, we observe a significant improvement in the rate-distortion performance and visual quality.
A Novel Digital Audio Watermarking Scheme in the Wavelet Domain
Institute of Scientific and Technical Information of China (English)
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.
Hybrid Coding of Image Sequences by Using Wavelet Transform
Directory of Open Access Journals (Sweden)
M. Surin
2000-04-01
Full Text Available In this paper, a new method of hybrid coding of image sequences byusing wavelet transform is proposed. The basic MPEG scheme with DCT hasbeen modificated in sense of replacement DCT by wavelet transform. Inthe proposed method, the motion estimation and compensation are usedfor motion vectors calculation and different frame between currentframe and compensated frame is coded by using wavelet transform. Someexperimental results of image sequences coding by using a new methodare presented.
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...
Mean size formula of wavelet subdivision tree on Heisenberg group
Institute of Scientific and Technical Information of China (English)
WANG Guo-mao
2008-01-01
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.
MOVING TARGETS PATTERN RECOGNITION BASED ON THE WAVELET NEURAL NETWORK
Institute of Scientific and Technical Information of China (English)
Ge Guangying; Chen Lili; Xu Jianjian
2005-01-01
Based on pattern recognition theory and neural network technology, moving objects automatic detection and classification method integrating advanced wavelet analysis are discussed in detail. An algorithm of moving targets pattern recognition on the combination of inter-frame difference and wavelet neural network is presented. The experimental results indicate that the designed BP wavelet network using this algorithm can recognize and classify moving targets rapidly and effectively.
Construction of compactly supported orthonormal wavelets with beautiful structure
Institute of Scientific and Technical Information of China (English)
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.
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
Wavelet and Blend maps for texture synthesis
Directory of Open Access Journals (Sweden)
Du Jin-Lian
2011-04-01
Full Text Available blending is now a popular technology for large realtime texture synthesis .Nevertheless, creating blend map during rendering is time and computation consuming work. In this paper, we exploited a method to create a kind of blend tile which can be tile together seamlessly. Note that blend map is in fact a kind of image, which is Markov Random Field, contains multiresolution signals, while wavelet is a powerful way to process multiresolution signals, we use wavelet to process the traditional blend tile. After our processing steps, the result blend tile become smooth and suitable for tiling, with no important features lost. Using this kind blend tile, many computation resources for computing blend map during texture synthesizing is saved. The experimental results shows that our method may successfully process many traditional blend tiles.
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.
Image compression algorithm using wavelet transform
Cadena, Luis; Cadena, Franklin; Simonov, Konstantin; Zotin, Alexander; Okhotnikov, Grigory
2016-09-01
Within the multi-resolution analysis, the study of the image compression algorithm using the Haar wavelet has been performed. We have studied the dependence of the image quality on the compression ratio. Also, the variation of the compression level of the studied image has been obtained. It is shown that the compression ratio in the range of 8-10 is optimal for environmental monitoring. Under these conditions the compression level is in the range of 1.7 - 4.2, depending on the type of images. It is shown that the algorithm used is more convenient and has more advantages than Winrar. The Haar wavelet algorithm has improved the method of signal and image processing.
Wavelet domain hidden markovian bayesian document segmentation
Institute of Scientific and Technical Information of China (English)
Sun Junxi; Xiao Changyan; Zhang Su; Chen Yazhu
2005-01-01
A novel algorithm for Bayesian document segmentation is proposed based on the wavelet domain hidden Markov tree (HMT) model. Once the parameters of model are known, according to the sequential maximum a posterior probability (SMAP) rule, firstly, the likelihood probability of HMT model for each pattern is computed from fine to coarse procedure. Then, the interscale state transition probability is solved using Expectation Maximum (EM) algorithm based on hybrid-quadtree and multiscale context information is fused from coarse to fine procedure. In order to get pixellevel segmentation, the redundant wavelet domain Gaussian mixture model (GMM) is employed to formulate pixel-level statistical property. The experiment results show that the proposed scheme is feasible and robust.
Wavelet-Based Monitoring for Biosurveillance
Directory of Open Access Journals (Sweden)
Galit Shmueli
2013-07-01
Full Text Available Biosurveillance, focused on the early detection of disease outbreaks, relies on classical statistical control charts for detecting disease outbreaks. However, such methods are not always suitable in this context. Assumptions of normality, independence and stationarity are typically violated in syndromic data. Furthermore, outbreak signatures are typically of unknown patterns and, therefore, call for general detectors. We propose wavelet-based methods, which make less assumptions and are suitable for detecting abnormalities of unknown form. Wavelets have been widely used for data denoising and compression, but little work has been published on using them for monitoring. We discuss monitoring-based issues and illustrate them using data on military clinic visits in the USA.
Wavelet analysis of the impedance cardiogram waveforms
Podtaev, S.; Stepanov, R.; Dumler, A.; Chugainov, S.; Tziberkin, K.
2012-12-01
Impedance cardiography has been used for diagnosing atrial and ventricular dysfunctions, valve disorders, aortic stenosis, and vascular diseases. Almost all the applications of impedance cardiography require determination of some of the characteristic points of the ICG waveform. The ICG waveform has a set of characteristic points known as A, B, E ((dZ/dt)max) X, Y, O and Z. These points are related to distinct physiological events in the cardiac cycle. Objective of this work is an approbation of a new method of processing and interpretation of the impedance cardiogram waveforms using wavelet analysis. A method of computer thoracic tetrapolar polyrheocardiography is used for hemodynamic registrations. Use of original wavelet differentiation algorithm allows combining filtration and calculation of the derivatives of rheocardiogram. The proposed approach can be used in clinical practice for early diagnostics of cardiovascular system remodelling in the course of different pathologies.
Wavelets and their applications past and future
Coifman, Ronald R.
2009-04-01
As this is a conference on mathematical tools for defense, I would like to dedicate this talk to the memory of Louis Auslander, who through his insights and visionary leadership, brought powerful new mathematics into DARPA, he has provided the main impetus to the development and insertion of wavelet based processing in defense. My goal here is to describe the evolution of a stream of ideas in Harmonic Analysis, ideas which in the past have been mostly applied for the analysis and extraction of information from physical data, and which now are increasingly applied to organize and extract information and knowledge from any set of digital documents, from text to music to questionnaires. This form of signal processing on digital data, is part of the future of wavelet analysis.
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.
Detecting Impulses in Mechanical Signals by Wavelets
Directory of Open Access Journals (Sweden)
Yang W-X
2004-01-01
Full Text Available The presence of periodical or nonperiodical impulses in vibration signals often indicates the occurrence of machine faults. This knowledge is applied to the fault diagnosis of such machines as engines, gearboxes, rolling element bearings, and so on. The development of an effective impulse detection technique is necessary and significant for evaluating the working condition of these machines, diagnosing their malfunctions, and keeping them running normally over prolong periods. With the aid of wavelet transforms, a wavelet-based envelope analysis method is proposed. In order to suppress any undesired information and highlight the features of interest, an improved soft threshold method has been designed so that the inspected signal is analyzed in a more exact way. Furthermore, an impulse detection technique is developed based on the aforementioned methods. The effectiveness of the proposed technique on the extraction of impulsive features of mechanical signals has been proved by both simulated and practical experiments.
Remote sensing image compression method based on lift scheme wavelet transform
Tao, Hongjiu; Tang, Xinjian; Liu, Jian; Tian, Jinwen
2003-06-01
Based on lifting scheme and the construction theorem of the integer Haar wavelet and biorthogonal wavelet, we propose a new integer wavelet transform construct method on the basis of lift scheme after introduciton of constructing specific-demand biorthogonal wavelet transform using Harr wavelet and Lazy wavelet. In this paper, we represent the method and algorithm of the lifting scheme, and we also give mathematical formulation on this method and experimental results as well.
Wavelet features in motion data classification
Szczesna, Agnieszka; Świtoński, Adam; Słupik, Janusz; Josiński, Henryk; Wojciechowski, Konrad
2016-06-01
The paper deals with the problem of motion data classification based on result of multiresolution analysis implemented in form of quaternion lifting scheme. Scheme processes directly on time series of rotations coded in form of unit quaternion signal. In the work new features derived from wavelet energy and entropy are proposed. To validate the approach gait database containing data of 30 different humans is used. The obtained results are satisfactory. The classification has over than 91% accuracy.
Wavelet transform approach to video compression
Li, Jin; Cheng, Po-Yuen; Kuo, C.-C. Jay
1995-04-01
In this research, we propose a video compression scheme that uses the boundary-control vectors to represent the motion field and the embedded zerotree wavelet (EZW) to compress the displacement frame difference. When compared to the DCT-based MPEG, the proposed new scheme achieves a better compression performance in terms of the MSE (mean square error) value and visual perception for the same given bit rate.
Some Contributions to Wavelet Based Image Coding
2000-07-01
MSE or PSNR. However, it is noted that JZW does not implement the embedded property as in EZW and SPIHT and that the embedded property can be...achieved by passing the JND quantized wavelet coefficients to EZW or SPIHT. It is noted that the lowest frequency (the coarsest scale) band (LL band) is the...other higher frequency subbands can be efficiently encoded using our zero-tree encoding scheme which is derived from EZW and [improved version of EZW by
Global motion estimation with Gabor wavelet transform
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A novel algorithm of global motion estimation is proposed. First, through Gabor wavelet transform (GWT), a kind of energy distribution of image is obtained and checkpoints are selected according to a probability decision approach proposed. Then, the initialized motion vectors are obtained via a hierarchal block-matching based on these checkpoints.Finally, by employing a 3-parameter motion model, precise parameters of global motion are found. From the experiment, the algorithm is reliable and robust.
Progressive Wavelet Correlation for Image Recognition
Stojanovic, Igor
2013-01-01
An algorithm for recognition and retrieval of image from image collection is developed. Basis of the algorithm is the progressive wavelet correlation. The final result is the recognition and retrieval of the wanted image, if it is in the image collection. Instructions for the choice of correlation threshold value for obtaining desired results are defined. The areas where the algorithm can be applied are also discussed. To increase efficiency is presented two phases solution. The first phase u...
Wavelet Analysis of Fractionally Integrated Processes
Mark J. Jensen
1994-01-01
In this paper we apply wavelet analysis to the class of fractionally integrated processes to show that this class is a member of the $1/f$ family of processes as defined by Wornell (1993) and to produce an alternative method of estimating the fractional differencing parameter. Currently the method by Geweke and Porter-Hudak (1983) is used most often to estimate and test the fractional differencing parameter. The GPH approach, however, has been shown to have poor statistical properties and suf...
A NOTE ON FINITE ELEMENT WAVELETS
Institute of Scientific and Technical Information of China (English)
谌秋辉; 陈翰麟
2001-01-01
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These coefficients are very important for the properties of wavelets, such as vanishing moments and regularity.
Wavelet description of the Glottal Gap
Gómez Vilda, Pedro; Nieto Lluis, Victor; Rodellar Biarge, M. Victoria; Martínez Olalla, Rafael; Muñoz Mulas, Cristina Elena; Álvarez Marquina, Agustin; Mazaira Fernández, Luis Miguel; Scola Yurrita, Bartolomé; Ramírez Calvo, Carlos; Poletti Serafini,Daniel
2013-01-01
The Glottal Source correlates reconstructed from the phonated parts of voice may render interesting information with applicability in different fields. One of them is defective closure (gap) detection. Through the paper the background to explain the physical foundations of defective gap are reviewed. A possible method to estimate defective gap is also presented based on a Wavelet Description of the Glottal Source. The method is validated using results from the analysis of a gender-balanced sp...
Wavelet Denoising and Surface Electromyography Analysis
Hussain, M.S.; Md. Mamun
2012-01-01
In this research, Surface Electromyography (SEMG) signal analysis from the right rectus femoris muscle is performed during walk. Wavelet Transform (WT) has been applied for removing noise from the surface SEMG. Gaussianity tests are conducted to understand changes in muscle contraction and to quantify the effectiveness of the noise removal process. Results show that the proposed method can effectively remove noise from the raw SEMG signals for further analysis.
Wavelet representation of the nuclear dynamics
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The study of transport phenomena in nuclear matter is addressed in a new approach named DYWAN, based on the projection methods of statistical physics and on the mathematical theory of wavelets. Strongly compressed representations of the nuclear systems are obtained with an accurate description of the wave functions and of their antisymmetrization. The results of the approach are illustrated for the ground state description as well as for the dissipative dynamics of nuclei at intermediate energies. (K.A.). 52 refs.
Abnormal traffic flow data detection based on wavelet analysis
Directory of Open Access Journals (Sweden)
Xiao Qian
2016-01-01
Full Text Available In view of the traffic flow data of non-stationary, the abnormal data detection is difficult.proposed basing on the wavelet analysis and least squares method of abnormal traffic flow data detection in this paper.First using wavelet analysis to make the traffic flow data of high frequency and low frequency component and separation, and then, combined with least square method to find abnormal points in the reconstructed signal data.Wavelet analysis and least square method, the simulation results show that using wavelet analysis of abnormal traffic flow data detection, effectively reduce the detection results of misjudgment rate and false negative rate.
Polynomial Representations for a Wavelet Model of Interest Rates
Directory of Open Access Journals (Sweden)
Dennis G. Llemit
2015-12-01
Full Text Available In this paper, we approximate a non – polynomial function which promises to be an essential tool in interest rates forecasting in the Philippines. We provide two numerical schemes in order to generate polynomial functions that approximate a new wavelet which is a modification of Morlet and Mexican Hat wavelets. The first is the Polynomial Least Squares method which approximates the underlying wavelet according to desired numerical errors. The second is the Chebyshev Polynomial approximation which generates the required function through a sequence of recursive and orthogonal polynomial functions. We seek to determine the lowest order polynomial representations of this wavelet corresponding to a set of error thresholds.
Reproducing wavelet kernel method in nonlinear system identification
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; XU Xiao-ming; CAI Yun-ze
2008-01-01
By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identifica-tion scheme using wavelet support vector machines ( WSVM ) estimator is proposed for nonlinear dynamic sys-tems. The good approximating properties of wavelet kernel function enhance the generalization ability of the pro-posed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays
1994-02-01
AD-A276 963 1111111111 I NAWCWPNS TP 8185 Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays OTIC by ELECTE Dr. Gary Hewer MAR 151994 and...REPORT TYPE AND DATES COVERED IFebruary 1994 Final; 199 ,L TTLE ND SBTILE LFUNDNG UBER Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays...nonlinearity 71,(w) = sgn(w)(IwI-t). with threshold t to each empirical sample value w in the wavelet transform d scales. After thresholding the wavelet
A Novel Algorithm for Robust Audio Watermarking in Wavelet Domain
Institute of Scientific and Technical Information of China (English)
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.
Watermarking on 3D mesh based on spherical wavelet transform
Institute of Scientific and Technical Information of China (English)
金剑秋; 戴敏雅; 鲍虎军; 彭群生
2004-01-01
In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.
Nonlinear wavelet estimation of regression function with random desigm
Institute of Scientific and Technical Information of China (English)
张双林; 郑忠国
1999-01-01
The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov space Bp,q? is proved under quite genera] assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.
Application of spline wavelet transform in differential of electroanalytical signal
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet transform has both the property of denoising and that of differential. As a result, the relation between the spline wavelet transform and the differential was studied in theory. Experimental results show that the spline wavelet transform can well be applied to the differential of the electroanalytical signal. Compared with other kinds of wavelet transform, the spline wavelet trans-form has a characteristic of differential. Compared with the digital differential and simulative differential with electronic circuit, the spline wavelet transform not only can carry out denoising and differential for a signal, but also has the ad-vantages of simple operation and small quantity of calcula-tion, because step length, RC constant and other kinds of parameters need not be selected. Compared with Alexander Kai-man Leung's differential method, the differential method with spline wavelet transform has the characteristic that the differential order is not dependent on the number of data points in the original signal.
Triangular Wavelets: An Isotropic Image Representation with Hexagonal Symmetry
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
The Wavelet Property of the Geomagnetic Anomaly Signal
Institute of Scientific and Technical Information of China (English)
JiangfaLIN; GangWANG
1997-01-01
In this study,wavelet analysis is utilized to analyze the geomagnetic signals for oil-gas exploration,in order to show the relation between the wavelet property of the geomagnetic signals and the underground treasure.At firest,the global geomagentic anomaly signal in the oil exploration is given.Then.with the wavelet theory the geomagnetic signals of an oil-gas field is analyzed.The preliminary wavelet analysis shows that the underground oil-gas location can be determined with the help of its regional high frequency signal distributions.
[Wavelet entropy analysis of spontaneous EEG signals in Alzheimer's disease].
Zhang, Meiyun; Zhang, Benshu; Chen, Ying
2014-08-01
Wavelet entropy is a quantitative index to describe the complexity of signals. Continuous wavelet transform method was employed to analyze the spontaneous electroencephalogram (EEG) signals of mild, moderate and severe Alzheimer's disease (AD) patients and normal elderly control people in this study. Wavelet power spectrums of EEG signals were calculated based on wavelet coefficients. Wavelet entropies of mild, moderate and severe AD patients were compared with those of normal controls. The correlation analysis between wavelet entropy and MMSE score was carried out. There existed significant difference on wavelet entropy among mild, moderate, severe AD patients and normal controls (Pentropy for mild, moderate, severe AD patients was significantly lower than that for normal controls, which was related to the narrow distribution of their wavelet power spectrums. The statistical difference was significant (Pentropy of EEG and the MMSE score were significantly correlated (r= 0. 601-0. 799, Pentropy is a quantitative indicator describing the complexity of EEG signals. Wavelet entropy is likely to be an electrophysiological index for AD diagnosis and severity assessment.
Wavelet modulation: An alternative modulation with low energy consumption
Chafii, Marwa; Palicot, Jacques; Gribonval, Rémi
2017-02-01
This paper presents wavelet modulation, based on the discrete wavelet transform, as an alternative modulation with low energy consumption. The transmitted signal has low envelope variations, which induces a good efficiency for the power amplifier. Wavelet modulation is analyzed and compared for different wavelet families with orthogonal frequency division multiplexing (OFDM) in terms of peak-to-average power ratio (PAPR), power spectral density (PSD) properties, and the impact of the power amplifier on the spectral regrowth. The performance in terms of bit error rate and complexity of implementation are also evaluated, and several trade-offs are characterized. xml:lang="fr"
Image denoising with the dual-tree complex wavelet transform
Yaseen, Alauldeen S.; Pavlova, Olga N.; Pavlov, Alexey N.; Hramov, Alexander E.
2016-04-01
The purpose of this study is to compare image denoising techniques based on real and complex wavelet-transforms. Possibilities provided by the classical discrete wavelet transform (DWT) with hard and soft thresholding are considered, and influences of the wavelet basis and image resizing are discussed. The quality of image denoising for the standard 2-D DWT and the dual-tree complex wavelet transform (DT-CWT) is studied. It is shown that DT-CWT outperforms 2-D DWT at the appropriate selection of the threshold level.
Wavelet Transform Modulus Maxima-Based Robust Digital Image Watermarking in Wavelet Domain
Institute of Scientific and Technical Information of China (English)
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.
Energy Technology Data Exchange (ETDEWEB)
Ives, R.W.; Kiser, C.; Magotra, N.
1998-10-27
While many synthetic aperture radar (SAR) applications use only detected imagery, dramatic improvements in resolution and employment of algorithms requiring complex-valued SAR imagery suggest the need for compression of complex data. Here, we investigate the benefits of using complex- valued wavelets on complex SAR imagery in the embedded zerotree wavelet compression algorithm, compared to using real-valued wavelets applied separately to the real and imaginary components. This compression is applied at low ratios (4:1-12:1) for high fidelity output. The complex spatial correlation metric is used to numerically evaluate quality. Numerical results are tabulated and original and decompressed imagery are presented as well as correlation maps to allow visual comparisons.
Comparison on Integer Wavelet Transforms in Spherical Wavelet Based Image Based Relighting
Institute of Scientific and Technical Information of China (English)
WANGZe; LEEYin; LEUNGChising; WONGTientsin; ZHUYisheng
2003-01-01
To provide a good quality rendering in the Image based relighting (IBL) system, tremendous reference images under various illumination conditions are needed. Therefore data compression is essential to enable interactive action. And the rendering speed is another crucial consideration for real applications. Based on Spherical wavelet transform (SWT), this paper presents a quick representation method with Integer wavelet transform (IWT) for the IBL system. It focuses on comparison on different IWTs with the Embedded zerotree wavelet (EZW) used in the IBL system. The whole compression procedure contains two major compression steps. Firstly, SWT is applied to consider the correlation among different reference images. Secondly, the SW transformed images are compressed with IWT based image compression approach. Two IWTs are used and good results are showed in the simulations.
Wavelets in Recognition of Bird Sounds
Directory of Open Access Journals (Sweden)
Selin Arja
2007-01-01
Full Text Available This paper presents a novel method to recognize inharmonic and transient bird sounds efficiently. The recognition algorithm consists of feature extraction using wavelet decomposition and recognition using either supervised or unsupervised classifier. The proposed method was tested on sounds of eight bird species of which five species have inharmonic sounds and three reference species have harmonic sounds. Inharmonic sounds are not well matched to the conventional spectral analysis methods, because the spectral domain does not include any visible trajectories that computer can track and identify. Thus, the wavelet analysis was selected due to its ability to preserve both frequency and temporal information, and its ability to analyze signals which contain discontinuities and sharp spikes. The shift invariant feature vectors calculated from the wavelet coefficients were used as inputs of two neural networks: the unsupervised self-organizing map (SOM and the supervised multilayer perceptron (MLP. The results were encouraging: the SOM network recognized 78% and the MLP network 96% of the test sounds correctly.
Denoising solar radiation data using coiflet wavelets
Energy Technology Data Exchange (ETDEWEB)
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.
Inversion of receiver function by wavelet transformation
Institute of Scientific and Technical Information of China (English)
吴庆举; 田小波; 张乃铃; 李桂银; 曾融生
2003-01-01
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low tohigh scale, with the inversion result for low order receiver function as the initial model for high order. Aneighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on theinitial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal andupper mantle velocity with high resolution.
Analysis of phonocardiogram signals using wavelet transform.
Meziani, F; Debbal, S M; Atbi, A
2012-08-01
Phonocardiograms (PCG) are recordings of the acoustic waves produced by the mechanical action of the heart. They generally consist of two kinds of acoustic vibrations: heart sounds and heart murmurs. Heart murmurs are often the first signs of pathological changes of the heart valves, and are usually found during auscultation in primary health care. Heart auscultation has been recognized for a long time as an important tool for the diagnosis of heart disease, although its accuracy is still insufficient to diagnose some heart diseases. It does not enable the analyst to obtain both qualitative and quantitative characteristics of the PCG signals. The efficiency of diagnosis can be improved considerably by using modern digital signal processing techniques. Therefore, these last can provide useful and valuable information on these signals. The aim of this study is to analyse PCG signals using wavelet transform. This analysis is based on an algorithm for the detection of heart sounds (the first and second sounds, S1 and S2) and heart murmurs using the PCG signal as the only source. The segmentation algorithm, which separates the components of the heart signal, is based on denoising by wavelet transform (DWT). This algorithm makes it possible to isolate individual sounds (S1 or S2) and murmurs. Thus, the analysis of various PCGs signals using wavelet transform can provide a wide range of statistical parameters related to the phonocardiogram signal.
Synchrosqueezed wavelet transform for damping identification
Mihalec, Marko; Slavič, Janko; Boltežar, Miha
2016-12-01
Synchrosqueezing is a procedure for improving the frequency localization of a continuous wavelet transform. This research focuses on using a synchrosqueezed wavelet transform (SWT) to determine the damping ratios of a vibrating system using a free-response signal. While synchrosqueezing is advantageous due to its localisation in the frequency, damping identification with the original SWT is not sufficiently accurate. Here, the synchrosqueezing was researched in detail, and it was found that an error in the frequency occurs as a result of the numerical calculation of the preliminary frequencies. If this error were to be compensated, a better damping identification would be expected. To minimize the frequency-shift error, three different strategies are investigated: the scale-dependent coefficient method, the shifted-coefficient method and the autocorrelated-frequency method. Furthermore, to improve the SWT, two synchrosqueezing criteria are introduced: the average SWT and the proportional SWT. Finally, the proposed modifications are tested against close modes and the noise in the signals. It was numerically and experimentally confirmed that the SWT with the proportional criterion offers better frequency localization and performs better than the continuous wavelet transform when tested against noisy signals.
Wavelet and statistical analysis for melanoma classification
Nimunkar, Amit; Dhawan, Atam P.; Relue, Patricia A.; Patwardhan, Sachin V.
2002-05-01
The present work focuses on spatial/frequency analysis of epiluminesence images of dysplastic nevus and melanoma. A three-level wavelet decomposition was performed on skin-lesion images to obtain coefficients in the wavelet domain. A total of 34 features were obtained by computing ratios of the mean, variance, energy and entropy of the wavelet coefficients along with the mean and standard deviation of image intensity. An unpaired t-test for a normal distribution based features and the Wilcoxon rank-sum test for non-normal distribution based features were performed for selecting statistically correlated features. For our data set, the statistical analysis of features reduced the feature set from 34 to 5 features. For classification, the discriminant functions were computed in the feature space using the Mahanalobis distance. ROC curves were generated and evaluated for false positive fraction from 0.1 to 0.4. Most of the discrimination functions provided a true positive rate for melanoma of 93% with a false positive rate up to 21%.
Structural Pounding Detection by Using Wavelet Scalogram
Directory of Open Access Journals (Sweden)
Shutao Xing
2012-01-01
Full Text Available Structural pounding can cause considerable damage and even lead to collapse of structures. Most research focuses on modeling, parameter investigation, and mitigation approaches. With the development of structural health monitoring, the on-line detection of pounding becomes possible. The detection of pounding can provide useful information of potential damage of structures. This paper proposed using wavelet scalograms of dynamic response to detect pounding and examined the feasibility of this method. Numerical investigations were performed on a pounding system that consisted of a damped single-degree-of-freedom (SDOF structure and a rigid barrier. Hertz contact model was used to simulate pounding behavior. The responses and pounding forces of the system under harmonic and earthquake excitations were numerically solved. The wavelet scalograms of acceleration responses were used to identify poundings. It was found that the scalograms can indicate the occurrence of pounding and occurrence time very well. The severity of the poundings was also approximately estimated. Experimental studies were carried out, in which shake table tests were conducted on a bridge model that underwent pounding between its different components during ground motion excitation. The wavelet scalograms of the bridge responses indicated pounding occurrence quite well. Hence the conclusions from the numerical studies were verified experimentally.
Pedestrian detection based on redundant wavelet transform
Huang, Lin; Ji, Liping; Hu, Ping; Yang, Tiejun
2016-10-01
Intelligent video surveillance is to analysis video or image sequences captured by a fixed or mobile surveillance camera, including moving object detection, segmentation and recognition. By using it, we can be notified immediately in an abnormal situation. Pedestrian detection plays an important role in an intelligent video surveillance system, and it is also a key technology in the field of intelligent vehicle. So pedestrian detection has very vital significance in traffic management optimization, security early warn and abnormal behavior detection. Generally, pedestrian detection can be summarized as: first to estimate moving areas; then to extract features of region of interest; finally to classify using a classifier. Redundant wavelet transform (RWT) overcomes the deficiency of shift variant of discrete wavelet transform, and it has better performance in motion estimation when compared to discrete wavelet transform. Addressing the problem of the detection of multi-pedestrian with different speed, we present an algorithm of pedestrian detection based on motion estimation using RWT, combining histogram of oriented gradients (HOG) and support vector machine (SVM). Firstly, three intensities of movement (IoM) are estimated using RWT and the corresponding areas are segmented. According to the different IoM, a region proposal (RP) is generated. Then, the features of a RP is extracted using HOG. Finally, the features are fed into a SVM trained by pedestrian databases and the final detection results are gained. Experiments show that the proposed algorithm can detect pedestrians accurately and efficiently.
MR Image Compression Based on Selection of Mother Wavelet and Lifting Based Wavelet
Directory of Open Access Journals (Sweden)
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 ”.
Denoising lidar signal by combining wavelet improved threshold with wavelet domain spatial filtering
Institute of Scientific and Technical Information of China (English)
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.
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.
EEG Signal Decomposition and Improved Spectral Analysis Using Wavelet Transform
2001-10-25
research and medical applications. Wavelet transform (WT) is a new multi-resolution time-frequency analysis method. WT possesses localization feature both... wavelet transform , the EEG signals are successfully decomposed and denoised. In this paper we also use a ’quasi-detrending’ method for classification of EEG
Wavelet-Coded OFDM for Next Generation Mobile Communications
DEFF Research Database (Denmark)
Cavalcante, Lucas Costa Pereira; Vegas Olmos, Juan José; Tafur Monroy, Idelfonso
2016-01-01
In this work, we evaluate the performance of Wavelet-Coding into offering robustness for OFDM signals against the combined effects of varying fading and noise bursts. Wavelet-Code enables high diversity gains with a low complex receiver, and, most notably, without compromising the system’s spectr...
On Generalized Carleson Operators of Periodic Wavelet Packet Expansions
Directory of Open Access Journals (Sweden)
Shyam Lal
2013-01-01
Full Text Available Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.
Wavelet methods in (financial) time-series processing
Struzik, Z.R.
2000-01-01
We briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the S&P index. In particular, we show how to uncover local the scaling (correlation) characteristics of the S&P index with the wavelet based effective H'older expone
Multiresolution signal decomposition schemes. Part 2: Morphological wavelets
H.J.A.M. Heijmans (Henk); J. Goutsias (John)
1999-01-01
htmlabstractIn its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens. The
A Fast Wavelet Multilevel Approach to Total Variation Image Denoising
Directory of Open Access Journals (Sweden)
Kossi Edoh
2009-09-01
Full Text Available In this paper we present an adaptive multilevel total variational (TV method for image denoising which utilizes TV partial differential equation (PDE models and exploits the multiresolution properties of wavelets. The adaptive multilevel TV method provides fast adaptive wavelet-based solvers for the TV model. Our approach employs a wavelet collocation method applied to the TV model using two-dimensional anisotropic tensor product of Daubechies wavelets. The algorithm inherently combines the denoising property of wavelet compression algorithms with that of the TV model, and produces results superior to each method when implemented alone. It exploits the edge preservation property of the TVmodel to reduce the oscillations that may be generated around the edges in wavelet compression. In contrast with previous work combining TV denoising with wavelet compression, the method presented in this paper treats the numerical solution in a novel waywhich decreases the computational cost associated with the solution of the TV model. We present a detailed description of our method and results which indicate that a combination of wavelet based denoising techniques with the TV model produces superior results, for afraction of the computational cost.
The application of modeling and prediction with MRA wavelet network
Institute of Scientific and Technical Information of China (English)
LU Shu-ping; YANG Xue-jing; ZHAO Xi-ren
2004-01-01
As there are lots of non-linear systems in the real engineering, it is very important to do more researches on the modeling and prediction of non-linear systems. Based on the multi-resolution analysis (MRA) of wavelet theory, this paper combined the wavelet theory with neural network and established a MRA wavelet network with the scaling function and wavelet function as its neurons. From the analysis in the frequency domain, the results indicated that MRA wavelet network was better than other wavelet networks in the ability of approaching to the signals. An essential research was carried out on modeling and prediction with MRA wavelet network in the non-linear system. Using the lengthwise sway data received from the experiment of ship model, a model of offline prediction was established and was applied to the short-time prediction of ship motion. The simulation results indicated that the forecasting model improved the prediction precision effectively, lengthened the forecasting time and had a better prediction results than that of AR linear model.The research indicates that it is feasible to use the MRA wavelet network in the short -time prediction of ship motion.
Invariant wavelet transform-based automatic target recognition
Sadovnik, Lev S.; Rashkovskiy, Oleg; Tebelev, Igor
1995-03-01
The authors' previous work (SPIE Vol. 2237) on scale-, rotation- and shift-invariant wavelet transform is extended to accommodate multiple objects in the scene and a nonuniform background. After background elimination and segmentation, a set of windows each containing a single object are analyzed based on an invariant wavelet feature extraction algorithm and neural network-based classifier.
Finite element wavelets for solving partial differential equations
Nguyen, Hoang
2005-01-01
This thesis deals with the application of wavelet bases for the numerical solution of operator equations, as boundary value problems and boundary integral equations. The use of suitable wavelet bases has the advantage that the arising stiffness matrices are well-conditioned uniformly in their sizes,
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
A fast and efficient hybrid fractal-wavelet image coder.
Iano, Yuzo; da Silva, Fernando Silvestre; Cruz, Ana Lúcia Mendes
2006-01-01
The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. Fast fractal encoding using Fisher's domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees (SPIHT) coding, on the remaining coefficients. Furthermore, image details and wavelet progressive transmission characteristics are maintained, no blocking effects from fractal techniques are introduced, and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme promotes an average of 94% reduction in encoding-decoding time comparing to the pure accelerated Fractal coding results. The simulations also compare the results to the SPIHT wavelet coding. In both cases, the new scheme improves the subjective quality of pictures for high-medium-low bitrates.
A Multiscale Wavelet Solver with O( n) Complexity
Williams, John R.; Amaratunga, Kevin
1995-11-01
In this paper, we use the biorthogonal wavelets recently constructed by Dahlke and Weinreich to implement a highly efficient procedure for solving a certain class of one-dimensional problems, (∂21/∂x21)u = f,I ɛ Z, I > 0. For these problems, the discrete biorthogonal wavelet transform allows us to set up a system of wavelet-Galerkin equations in which the scales are uncoupled, so that a true multiscale solution procedure may be formulated. We prove that the resulting stiffness matrix is in fact an almost perfectly diagonal matrix (the original aim of the construction was to achieve a block diagonal structure) and we show that this leads to an algorithm whose cost is O(n). We also present numerical results which demonstrate that the multiscale biorthogonal wavelet algorithm is superior to the more conventional single scale orthogonal wavelet approach both in terms of speed and in terms of convergence.
DIRECT DISPLACEMENT OF PARALLEL MECHANISM WITH WAVELET NETWORK
Institute of Scientific and Technical Information of China (English)
CHEN Weishan; CHEN Hua; LIU Junkao
2007-01-01
A new method solution for the direct displacement of parallel mechanism, wavelet network method, is proposed. Comparing with the classical analytical and numerical methods, this method can be extended to any parallel mechanism with any selected degree of freedom and configuration. A wavelet network suiting to approach multi-input and multi-output system is constructed. The network is optimized by analyzing the sparseness of input data and selecting the fitting wavelets by orthogonalization method according to the output data. Then it is applied to solve the direct displacement of a general six-degree-of-freedom parallel mechanism as a numerical example. For comparison purposes, a BP neural network is also used for this problem. Simulation results show that the wavelet network performs better than BP neural network. In addition, the wavelet network learns much faster than BP network.
Heart Rate Variability Analysis Using Threshold of Wavelet Package Coefficients
Kheder, G; Massoued, M Ben; Samet, M
2009-01-01
In this paper, a new efficient feature extraction method based on the adaptive threshold of wavelet package coefficients is presented. This paper especially deals with the assessment of autonomic nervous system using the background variation of the signal Heart Rate Variability HRV extracted from the wavelet package coefficients. The application of a wavelet package transform allows us to obtain a time-frequency representation of the signal, which provides better insight in the frequency distribution of the signal with time. A 6 level decomposition of HRV was achieved with db4 as mother wavelet, and the above two bands LF and HF were combined in 12 specialized frequencies sub-bands obtained in wavelet package transform. Features extracted from these coefficients can efficiently represent the characteristics of the original signal. ANOVA statistical test is used for the evaluation of proposed algorithm.
Combining Wavelet Transform and Hidden Markov Models for ECG Segmentation
Directory of Open Access Journals (Sweden)
Jérôme Boudy
2007-01-01
Full Text Available This work aims at providing new insights on the electrocardiogram (ECG segmentation problem using wavelets. The wavelet transform has been originally combined with a hidden Markov models (HMMs framework in order to carry out beat segmentation and classification. A group of five continuous wavelet functions commonly used in ECG analysis has been implemented and compared using the same framework. All experiments were realized on the QT database, which is composed of a representative number of ambulatory recordings of several individuals and is supplied with manual labels made by a physician. Our main contribution relies on the consistent set of experiments performed. Moreover, the results obtained in terms of beat segmentation and premature ventricular beat (PVC detection are comparable to others works reported in the literature, independently of the type of the wavelet. Finally, through an original concept of combining two wavelet functions in the segmentation stage, we achieve our best performances.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
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.
Implementation of Wavelet Networks in Nonlinear System Identification
Institute of Scientific and Technical Information of China (English)
李德强; 黄莎白
2002-01-01
Orthogonal Least Squares (OLS) is a general and powerful algorithm for solving the output layer weights of a wavelet network. In this paper, the Recursive Orthogonal Least Squares (ROLS) method is used to orthogonalize the wavelet regressors. With the result of ROLS method, it is possible to compute which wavelets are important, and which are redundant and can be eliminated from the wavelet network. A structure identification algorithm is carried out based on OLS for the reduction of network. Akaike 's Information Criterion (AIC) is introduced in the process of structure identification to seek a compromise between network complexity and accuracy. The final network models obtain acceptable accuracy with a relatively small number of significant wavelets. Numerical example is given to illustrate the effectiveness of the method mentioned above.
Wavelet approach to accelerator problems. 1: Polynomial dynamics
Energy Technology Data Exchange (ETDEWEB)
Fedorova, A.; Zeitlin, M. [Russian Academy of Sciences, St. Petersburg (Russian Federation). Inst. of Problems of Mechanical Engineering; Parsa, Z. [Brookhaven National Lab., Upton, NY (United States). Dept. of Physics
1997-05-01
This is the first part of a series of talks in which the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case they have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parameterized by solutions of two reduced algebraical problems, one is nonlinear and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. In this paper the authors consider the problem of calculation of orbital motion in storage rings. The key point in the solution of this problem is the use of the methods of wavelet analysis, relatively novel set of mathematical methods, which gives one a possibility to work with well-localized bases in functional spaces and with the general type of operators (including pseudodifferential) in such bases.
Some Results on the Wavelet Packet Decomposition of Nonstationary Processes
Directory of Open Access Journals (Sweden)
Touati Sami
2002-01-01
Full Text Available Wavelet/wavelet packet decomposition has become a very useful tool in describing nonstationary processes. Important examples of nonstationary processes encountered in practice are cyclostationary processes or almost-cyclostationary processes. In this paper, we study the statistical properties of the wavelet packet decomposition of a large class of nonstationary processes, including in particular cyclostationary and almost-cyclostationary processes. We first investigate in a general framework, the existence and some properties of the cumulants of wavelet packet coefficients. We then study more precisely the almost-cyclostationary case, and determine the asymptotic distributions of wavelet packet coefficients. Finally, we particularize some of our results in the cyclostationary case before providing some illustrative simulations.
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y; Vandergheynst, P; Blanc, O
2007-01-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of intere...
Texture classification using wavelet preprocessing and vector quantization
Lam, Eric P.
2007-04-01
In this paper, we will discuss a technique of texture image classification using a wavelet decomposition with selective wavelet packet node decomposition. This new approach uses a two-channel wavelet decomposition which is extended to two dimensions. Using the strength as a metric, selective wavelet decomposition is controlled. The metric is used to allow further decomposition or to terminate recursive decompositions. Decision of continuing further decompositions is based on each subband's strength with respect to the strengths of other subbands of the same wavelet decomposition level. Once the decompositions stop, the structure of the packet is stored in a data structure. Using the information from the data structure, dominating channels are extracted. These are defined as paths from the root of the packet to the leaf with the highest strengths. The list of dominating channels are used to train a learning vector quantization neural network.
Orthogonal M-band compactly supported interpolating wavelet theory
Institute of Scientific and Technical Information of China (English)
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
Denoising in Wavelet Packet Domain via Approximation Coefficients
Directory of Open Access Journals (Sweden)
Zahra Vahabi
2012-01-01
Full Text Available In this paper we propose a new approach in the wavelet domain for image denoising. In recent researches wavelet transform has introduced a time-Frequency transform for computing wavelet coefficient and eliminating noise. Some coefficients have effected smaller than the other's from noise, so they can be use reconstruct images with other subbands. We have developed Approximation image to estimate better denoised image. Naturally noiseless subimage introduced image with lower noise. Beside denoising we obtain a bigger compression rate. Increasing image contrast is another advantage of this method. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.100 images of LIVE Dataset were tested, comparing signal to noise ratios (SNR,soft thresholding was %1.12 better than hard thresholding, POAC was %1.94 better than soft thresholding and POAC with wavelet packet was %1.48 better than POAC.
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.
Image Compression Using Discrete Wavelet Transform
Directory of Open Access Journals (Sweden)
Mohammad Mozammel Hoque Chowdhury
2012-07-01
Full Text Available Image compression is a key technology in transmission and storage of digital images because of vast data associated with them. This research suggests a new image compression scheme with pruning proposal based on discrete wavelet transformation (DWT. The effectiveness of the algorithm has been justified over some real images, and the performance of the algorithm has been compared with other common compression standards. The algorithm has been implemented using Visual C++ and tested on a Pentium Core 2 Duo 2.1 GHz PC with 1 GB RAM. Experimental results demonstrate that the proposed technique provides sufficient high compression ratios compared to other compression techniques.
Simulation-based design using wavelets
Williams, John R.; Amaratunga, Kevin S.
1994-03-01
The design of large-scale systems requires methods of analysis which have the flexibility to provide a fast interactive simulation capability, while retaining the ability to provide high-order solution accuracy when required. This suggests that a hierarchical solution procedure is required that allows us to trade off accuracy for solution speed in a rational manner. In this paper, we examine the properties of the biorthogonal wavelets recently constructed by Dahlke and Weinreich and show how they can be used to implement a highly efficient multiscale solution procedure for solving a certain class of one-dimensional problems.
Wavelet-Based Quantum Field Theory
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Mikhail V. Altaisky
2007-11-01
Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Automatic Target Detection Using Wavelet Transform
Directory of Open Access Journals (Sweden)
Ganesan L
2004-01-01
Full Text Available Automatic target recognition (ATR involves processing images for detecting, classifying, and tracking targets embedded in a background scene. This paper presents an algorithm for detecting a specified set of target objects embedded in visual images for an ATR application. The developed algorithm employs a novel technique for automatically detecting man-made and non-man-made single, two, and multitargets from nontarget objects, located within a cluttered environment by evaluating nonoverlapping image blocks, where block-by-block comparison of wavelet cooccurrence feature is done. The results of the proposed algorithm are found to be satisfactory.
Cardiac Arrhythmia Classification by Wavelet Transform
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Hadji Salah
2015-05-01
Full Text Available Cardiovascular diseases are the major public health parameter; they are the leading causes of mortality in the world. In fact many studies have been implemented to reduce the risk, including promoting education, prevention, and monitoring of patients at risk. In this paper we propose to develop classification system heartbeats. This system is based mainly on Wavelet Transform to extract features and Kohonen self-organization map the arrhythmias are considered in this study: N,(Normal, V(PrematureVentricular, A(AtrialPremature, S(Extrasystolesupraventriculaire, F(FusionN+S, R(RightBundle Branch.
Abstract harmonic analysis of continuous wavelet transforms
Führ, Hartmut
2005-01-01
This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula.
Wavelet analysis of the nuclear phase space
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The description of transport phenomena in nuclear matter is addressed in a new approach based on the mathematical theory of wavelets and the projection methods of statistical physics. The advantage of this framework is to offer the opportunity to use information concepts common to both the formulation of physical properties and the mathematical description. This paper focuses on two features, the extraction of relevant informations using the geometrical properties of the underlying phase space and the optimization of the theoretical and numerical treatments based on convenient choices of the representation spaces. (author). 34 refs.
A New Text Location Approach Based Wavelet
Institute of Scientific and Technical Information of China (English)
Weihua Li; Zhen Fang; Shuozhong Wang
2002-01-01
With the advancement of content-based retrieval technology, the importance of semantics for text information contained in images attracts many researchers. An algorithm which will automatically locate the textual regions in the input image will facilitate the retrieving task, and the optical character recognizer can then be applied to only those regions of the image which contain text. In this paper a new text location method based wavelet is described, which can be used to locate textual regions from complex image and video frame. Experimental results show that the textual regions in image can be located effectively and quickly.
Feature Extraction by Wavelet Decomposition of Surface
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Prashant Singh
2010-07-01
Full Text Available The paper presents a new approach to surface acoustic wave (SAW chemical sensor array design and data processing for recognition of volatile organic compounds (VOCs based on transient responses. The array is constructed of variable thickness single polymer-coated SAW oscillator sensors. The thickness of polymer coatings are selected such that during the sensing period, different sensors are loaded with varied levels of diffusive inflow of vapour species due to different stages of termination of equilibration process. Using a single polymer for coating the individual sensors with different thickness introduces vapour-specific kinetics variability in transient responses. The transient shapes are analysed by wavelet decomposition based on Daubechies mother wavelets. The set of discrete wavelet transform (DWT approximation coefficients across the array transients is taken to represent the vapour sample in two alternate ways. In one, the sets generated by all the transients are combined into a single set to give a single representation to the vapour. In the other, the set of approximation coefficients at each data point generated by all transients is taken to represent the vapour. The latter results in as many alternate representations as there are approximation coefficients. The alternate representations of a vapour sample are treated as different instances or realisations for further processing. The wavelet analysis is then followed by the principal component analysis (PCA to create new feature space. A comparative analysis of the feature spaces created by both the methods leads to the conclusion that both methods yield complimentary information: the one reveals intrinsic data variables, and the other enhances class separability. The present approach is validated by generating synthetic transient response data based on a prototype polyisobutylene (PIB coated 3-element SAW sensor array exposed to 7 VOC vapours: chloroform, chlorobenzene o
Image Mosaic Techniques OptimizationUsing Wavelet
Institute of Scientific and Technical Information of China (English)
ZHOUAn-qi; CUILi
2014-01-01
This essay concentrates on two key procedures of image mosaic——image registration and imagefusion.Becauseof the character of geometric transformation invariance of edge points, wecalculate the angle difference of the direction vector ofedge points in different images anddraw an angle difference histogramto adjust the rotationproblem. Through this way, algorithm based on gray information is expandedandcan be used in images withdisplacementand rotation. Inthe term of image fusion, wavelet multi-scale analysis is used to fuse spliced images. In order to choose the best method of imagefusion,weevaluate the results of different methods of image fusion by cross entropy.
Lung tissue classification using wavelet frames.
Depeursinge, Adrien; Sage, Daniel; Hidki, Asmâa; Platon, Alexandra; Poletti, Pierre-Alexandre; Unser, Michael; Müller, Henning
2007-01-01
We describe a texture classification system that identifies lung tissue patterns from high-resolution computed tomography (HRCT) images of patients affected with interstitial lung diseases (ILD). This pattern recognition task is part of an image-based diagnostic aid system for ILDs. Five lung tissue patterns (healthy, emphysema, ground glass, fibrosis and microdules) selected from a multimedia database are classified using the overcomplete discrete wavelet frame decompostion combined with grey-level histogram features. The overall multiclass accuracy reaches 92.5% of correct matches while combining the two types of features, which are found to be complementary.
Amended (Wavelet Multiband OFDM Cognitive Radio System
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J. Avila
2015-05-01
Full Text Available This study focuses on improving the functioning of multiband Orthogonal Frequency Division Multiplexing (OFDM system by utilizing wavelet transform as a substitute to Fast Fourier Transform (FFT. The performance is further refined by apt inclusion of modulation technique. Error control codes are utilized which aims at the removal of error from the transmitted bits. In addition to attain diversity Alamouti code is concatenated with error control codes. OFDM is the best fit for cognitive radio and sensing the free holes is the key task of any cognitive system. This study additionally also analyses the performance of energy detection based spectrum sensing in the presence of various noise models.
Texture Image Classification Based on Gabor Wavelet
Institute of Scientific and Technical Information of China (English)
DENG Wei-bing; LI Hai-fei; SHI Ya-li; YANG Xiao-hui
2014-01-01
For a texture image, by recognizining the class of every pixel of the image, it can be partitioned into disjoint regions of uniform texture. This paper proposed a texture image classification algorithm based on Gabor wavelet. In this algorithm, characteristic of every image is obtained through every pixel and its neighborhood of this image. And this algorithm can achieve the information transform between different sizes of neighborhood. Experiments on standard Brodatz texture image dataset show that our proposed algorithm can achieve good classification rates.
Discrete wavelet analysis for multiparticle production experiments
Georgopoulos, G; Vassiliou, Maria
2000-01-01
In high energy nucleus-nucleus collisions (SPS, RHIC, LHC) and in cosmic ray interactions, many particles are produced in the available phase space. We make an attempt to apply the wavelets technique in order to classify such events according to the event pattern and also to locate the so-called "clustering" in a distribution. After describing the method, we demonstrate its power (a) to a single event, produced by a pion condensation theoretical model, (b) to a sample of Pb-Pb simulated data at 158 GeV/c per nucleon taking into account all the experimental uncertainties. (15 refs).
Wavelet-based technique for target segmentation
Sadjadi, Firooz A.
1995-07-01
Segmentation of targets embedded in clutter obtained by IR imaging sensors is one of the challenging problems in automatic target recognition (ATR). In this paper a new texture-based segmentation technique is presented that uses the statistics of 2D wavelet decomposition components of the lcoal sections of the image. A measure of statistical similarity is then used to segment the image and separate the target from the background. This technique is applied on a set of real sequential IR imagery and has shown to produce a high degree of segmentation accuracy across varying ranges.
Directory of Open Access Journals (Sweden)
Qin Ma
2008-05-01
Full Text Available Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.
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
On the optimal choice of wavelet function for multiscale honed surface characterization
Energy Technology Data Exchange (ETDEWEB)
Mezghani, S; Mansori, M El [Arts and Metiers ParisTech, LMPF, rue St Dominique - BP 508, 51006 Chalons-en-Champagne (France); Sabri, L [RENAULT S.A.S., Direction de la Mecanique/Direction de l' Ingenierie Process, Rueil Malmaison, Paris (France); Zahouani, H, E-mail: sabeur.mezghani@ensam.eu [Ecole Centrale de Lyon, LTDS UMR CNRS 5513, 36 avenue Guy de Collongue, 69131 Ecully Cedex (France)
2011-08-19
Multiscale surface topography characterization is mostly suited than standard approaches because it is more adapted to the multi-stage process generation. Wavelet transform represents a power tool to perform the multiscale decomposition of the surface topography in a wide range of wavelength. However, characterization results depend closely on the topography data acquisition instrument (resolution, height accuracy, sensitivity...) and also on the wavelet analysis method (discrete or continuous transform). In particular, the choice of wavelet function can have significant effect on the analysis results. In this paper, we present experimental work on a number of popular wavelets functions with the aim of finding wavelets that exhibit optimal description of honed surface features when continuous wavelet transform is used. We demonstrate that the regularity property of wavelet function has a significant influence on the characterization performances. This comparative study shows also that the Morlet wavelet is the more adapted wavelet basis function for multiscale characterization of honed surfaces using continuous wavelet transform.
Implementation of Texture Based Image Retrieval Using M-band Wavelet Transform
Institute of Scientific and Technical Information of China (English)
LiaoYa-li; Yangyan; CaoYang
2003-01-01
Wavelet transform has attracted attention because it is a very useful tool for signal analyzing. As a fundamental characteristic of an image, texture traits play an important role in the human vision system for recognition and interpretation of images. The paper presents an approach to implement texture-based image retrieval using M-band wavelet transform. Firstly the traditional 2-band wavelet is extended to M-band wavelet transform. Then the wavelet moments are computed by M-band wavelet coefficients in the wavelet domain. The set of wavelet moments forms the feature vector related to the texture distribution of each wavelet images. The distances between the feature vectors describe the similarities of different images. The experimental result shows that the M-band wavelet moment features of the images are effective for image indexing.The retrieval method has lower computational complexity, yet it is capable of giving better retrieval performance for a given medical image database.
Implementation of Texture Based Image Retrieval Using M-band Wavelet Transform
Institute of Scientific and Technical Information of China (English)
Liao Ya-li; Yang Yan; Cao Yang
2003-01-01
Wavelet transform has attracted attention because it is a very useful tool for signal analyzing. As a fundamental characteristic of an image, texture traits play an important role in the human vision system for recognition and interpretation of images. The paper presents an approach to implement texture-based image retrieval using M-band wavelet transform. Firstly the traditional 2-band wavelet is extended to M-band wavelet transform. Then the wavelet moments are computed by M-band wavelet coefficients in the wavelet domain. The set of wavelet moments forms the feature vector related to the texture distribution of each wavelet images. The distances between the feature vectors describe the similarities of different images. The experimental result shows that the M-band wavelet moment features of the images are effective for image indexing. The retrieval method has lower computational complexity, yet it is capable of giving better retrieval performance for a given medical image database.
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...
Wavelet analysis of solar decimeter spikes
Fernandes, F. C. R.; Bolzan, M. J. A.; Rosa, R. R.; Prestes, A.; Cecatto, J. R.; Sawant, H. S.
2012-04-01
The Brazilian Solar Spectroscope (BSS), in operation at INPE, Brazil, have recorded a group of radio spikes observed on June 24, 1999 (16:53 - 16: 56 UT), in the decimeter frequency range of 1000-2500 MHz, with high temporal resolution of 100 ms and spectral resolution of 10 MHz. This event presents distinct clusters of spikes with intermittent behavior. The spectral and temporal behaviors of the observed groups of spikes of radio were investigated, applying wavelet techniques, which permits to determine the cadence of the clusters. From the dynamic spectra, the following observational parameters were determined: the total duration of the event and of each cluster, the total frequency band and cluster bands, in the case of the harmonic structures. The wavelet analysis shows an average periodicity of about 17 seconds (and harmonics) for the cadence of intermittent clusters of spikes. The analysis also suggested a semi-harmonic frequency ratio of 1:1.2. The same methodology of analysis is being applied to other selected groups of spikes recorded by BSS. These results will be presented and discussed.
Inertial Sensor Signals Denoising with Wavelet Transform
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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 Cleaning of Solar Dynamic Radio Spectrograms
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
By applying the state-of-the-art mathematical apparatus, the wavelet transformation, we explore the possibility of a dynamic cleaning of raw data obtained with the Chinese solar radio spectrographs over a wide wavelength range (from 0.7 to 7.6 GHz). We consider the problem of eliminating the interference caused by combination rates of data sampling (10-20ms), and the low-frequency interference (4-30 s) caused by the receiving equipment changing its characteristics with time. It is shown that the best choice to reconstruct a signal suffering from amplitude, frequency and phase instabilities, is by means of wavelet transformation at both high and low frequencies. We analysed observational data which contained interferences of nonsolar origin such as instrumental effects and other man-made signals. A subsequent comparison of the reference data obtained with the acoustooptical receiver of the Siberian Solar Radio Telescope (SSRT) with the "cleaned"spectra confirms the correctness of this approach.
Research of Signal De-noising Technique Based on Wavelet
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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
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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.
Joint Time-Frequency And Wavelet Analysis - An Introduction
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Majkowski Andrzej
2014-12-01
Full Text Available A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency. The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.
Digital Watermarking Algorithm Based on Wavelet Transform and Neural Network
Institute of Scientific and Technical Information of China (English)
WANG Zhenfei; ZHAI Guangqun; WANG Nengchao
2006-01-01
An effective blind digital watermarking algorithm based on neural networks in the wavelet domain is presented. Firstly, the host image is decomposed through wavelet transform. The significant coefficients of wavelet are selected according to the human visual system (HVS) characteristics. Watermark bits are added to them. And then effectively cooperates neural networks to learn the characteristics of the embedded watermark related to them. Because of the learning and adaptive capabilities of neural networks, the trained neural networks almost exactly recover the watermark from the watermarked image. Experimental results and comparisons with other techniques prove the effectiveness of the new algorithm.
Reusability of Patterns Using Discrete Wavelet Transformation in Watermarking
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Gurpreet Kaur
2014-03-01
Full Text Available Digital image watermarking is hiding information in any form in original image without degrading its perceptual quality. Watermarking is done for copyright protection of the original data. In this paper, a hybrid and robust watermarking technique for copyright protection based on Discrete Cosine Transform and Discrete Wavelet Transform is proposed. Wavelet transform has been applied widely in watermarking research as its excellent multi-resolution analysis property. The watermark is embedded based on the frequency coefficients of the discrete wavelet transform. The robustness of the technique is tested by applying noise attacks on the host signal and here the host signal is the database set containing satellite images.
Image compression with a hybrid wavelet-fractal coder.
Li, J; Kuo, C J
1999-01-01
A hybrid wavelet-fractal coder (WFC) for image compression is proposed. The WFC uses the fractal contractive mapping to predict the wavelet coefficients of the higher resolution from those of the lower resolution and then encode the prediction residue with a bitplane wavelet coder. The fractal prediction is adaptively applied only to regions where the rate saving offered by fractal prediction justifies its overhead. A rate-distortion criterion is derived to evaluate the fractal rate saving and used to select the optimal fractal parameter set for WFC. The superior performance of the WFC is demonstrated with extensive experimental results.
THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION
Institute of Scientific and Technical Information of China (English)
刘海峰; 周炜星; 王辅臣; 龚欣; 于遵宏
2002-01-01
Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.
Image denoising using least squares wavelet support vector machines
Institute of Scientific and Technical Information of China (English)
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.
Image compression with embedded wavelet coding via vector quantization
Katsavounidis, Ioannis; Kuo, C.-C. Jay
1995-09-01
In this research, we improve Shapiro's EZW algorithm by performing the vector quantization (VQ) of the wavelet transform coefficients. The proposed VQ scheme uses different vector dimensions for different wavelet subbands and also different codebook sizes so that more bits are assigned to those subbands that have more energy. Another feature is that the vector codebooks used are tree-structured to maintain the embedding property. Finally, the energy of these vectors is used as a prediction parameter between different scales to improve the performance. We investigate the performance of the proposed method together with the 7 - 9 tap bi-orthogonal wavelet basis, and look into ways to incorporate loseless compression techniques.
Comparative performance of wavelets and JPEG coders at high quality
Algazi, V. Ralph; Estes, Robert R., Jr.
1997-04-01
In recent work, we have examined the performance of wavelet coders using a perceptually relevant image quality metric, the picture quality scale (PQS). In that study, we considered some of the design options available with respect to choice of wavelet basis, quantizer, and method for error- free encoding of the quantized coefficients, including the EZW methodology. A specific combination of these design options provides the best trade off between performance and PQS quality. Here, we extend this comparison by evaluating the performance of JPEG and the previously chosen optimal wavelet scheme, focusing principally on the high quality range.
Secured Data Transmission Using Wavelet Based Steganography and cryptography
Directory of Open Access Journals (Sweden)
K.Ravindra Reddy
2014-02-01
Full Text Available Steganography and cryptographic methods are used together with wavelets to increase the security of the data while transmitting through networks. Another technology, the digital watermarking is the process of embedding information into a digital (image signal. Before embedding the plain text into the image, the plain text is encrypted by using Data Encryption Standard (DES algorithm. The encrypted text is embedded into the LL sub band of the wavelet decomposed image using Least Significant Bit (LSB method. Then the inverse wavelet transform is applied and the resultant image is transmitted to the receiver. The receiver will perform the same operations in reverse order
Contrast Enhancement of Radiographs Using Shift Invariant Wavelet Transform
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel approach using shift invariant wavelet transform is presented for the contrast enhancement of radiographs. By exploiting cross-scale correlation among wavelet coefficients, edge information of radiographic images is extracted and protected, while noise is smoothed out in the wavelet domain. Radiographs are then reconstructed from the transform coefficients modified at multi-scales by nonlinear enhancement operator. The method can achieve effectively contrast enhancement and edge-preserved denoising simultaneously, yet it is capable of giving visually distinct images and offering considerable benefits in medical diagnosis.
Novel Fractional Wavelet Transform with Closed-Form Expression
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K. O. O. Anoh
2014-01-01
Full Text Available A new wavelet transform (WT is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT. The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown.
Variable mass pendulum behaviour processed by wavelet analysis
Caccamo, M. T.; Magazù, S.
2017-01-01
The present work highlights how, in order to characterize the motion of a variable mass pendulum, wavelet analysis can be an effective tool in furnishing information on the time evolution of the oscillation spectral content. In particular, the wavelet transform is applied to process the motion of a hung funnel that loses fine sand at an exponential rate; it is shown how, in contrast to the Fourier transform which furnishes only an average frequency value for the motion, the wavelet approach makes it possible to perform a joint time-frequency analysis. The work is addressed at undergraduate and graduate students.
A dual Fourier-wavelet domain authentication-identification watermark.
Ahmed, Farid
2007-04-16
A dual Fourier-Wavelet domain watermarking technique for authentication and identity verification is proposed. Discrete wavelet transform (DWT) domain spread spectrum is used for embedding identity (such as registration number, transaction ID etc.) information. While a blind detector detects an ID, it is important to validate with other ancillary data. To satisfy that requirement, we embed a robust signature and hide it in a mid-band wavelet subband using Fourier domain bit-embedding algorithm. Results are furnished to show the compression tolerance of the method.
MIXED SCHEME FOR IMAGE EDGE DETECTION BASED ON WAVELET TRANSFORM
Institute of Scientific and Technical Information of China (English)
Xie Hongmei; Yu Bianzhang; Zhao Jian
2004-01-01
A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.
Growth—phase Classification Using Wavelets in Fermentation Processes
Institute of Scientific and Technical Information of China (English)
SUIQingmei; WANGZheng′ou
2002-01-01
The wavelet transform is developed to identify the different phases in a fermentation process.In this method,the wavelet transform modulus maxima are used to estimate the local maximum points of the second derivative of the growth curve in order to classify the different phases of fermentation process.Moreover,the method can effectively get rid of noise from the signal,making use of the different chacters showed by signal and nose in the wavelet transform modulus maxima.Compared with neural network modeling,the presented method needs less quantity of information and calculation.The results of experiments show that this method is effective.
EEG Artifact Removal Using a Wavelet Neural Network
Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom
2011-01-01
!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.
Hardware Architectures for the Orthogonal and Biorthogonal Wavelet Transform
Directory of Open Access Journals (Sweden)
G. Knowles
2002-01-01
Full Text Available In this note, optimal hardware architectures for the orthogonal and biorthogonal wavelet transforms are presented. The approach used here is not the standard lifting method, but takes advantage of the symmetries inherent in the coefficients of the transforms and the decimation/interpolation operators. The design is based on a highly optimized datapath, which seamlessly integrates both orthogonal and biorthogonal transforms, data extension at the edges and the forward and inverse transforms. The datapath design could be further optimized for speed or low power. The datapath is controlled by a small fast control unit which is hard programmed according to the wavelet or wavelets required by the application.
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.
Wavelet analysis of acoustic emission signals from thermal barrier coatings
Institute of Scientific and Technical Information of China (English)
YANG Li; ZHOU Yi-chun
2006-01-01
The wavelet transform is applied to the analysis of acoustic emission signals collected during tensile test of the ZrO2-8% Y2O3 (YSZ) thermal barrier coatings (TBCs). The acoustic emission signals are de-noised using the Daubechies discrete wavelets,and then decomposed into different wavelet levels using the programs developed by the authors. Each level is examined for its specific frequency range. The ratio of energy in different levels to the total energy gives information on the failure modes (coating micro-failures and substrate micro-failures) associated with TBCs system.
Edge Adapted Wavelets, Solar Magnetic Activity, and Climate Change
Johnson, Robert W
2009-01-01
The continuous wavelet transform is adapted to account for signal truncation through renormalization and by modifying the shape of the analyzing window. Comparison is made of the instant and integrated wavelet power with previous algorithms. The edge adapted and renormalized admissible wavelet transforms are used to estimate the level of solar magnetic activity from the sunspot record. The solar activity is compared to Oerlemans' temperature reconstruction and to the Central England Temperature record. A correlation is seen for years between 1610 and 1990, followed by a strong deviation as the recently observed temperature increases.
Minimum-energy wavelet frame on the interval
Institute of Scientific and Technical Information of China (English)
GAO XiePing; CAO ChunHong
2008-01-01
The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper.They are as follows:1) give the definition of interval minimum-energy wavelet frame;2) give the necessary and sufficient conditions for the minimum-energy frames for L2[0,1];3) present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support γ;4) give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1].
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.
Wavelets an elementary treatment of theory and applications
Koornwinder, T H
1993-01-01
Nowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet
A wavelet approach to binary blackholes with asynchronous multitasking
Lim, Hyun; Hirschmann, Eric; Neilsen, David; Anderson, Matthew; Debuhr, Jackson; Zhang, Bo
2016-03-01
Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking.
Li, Jingsong; Yu, Benli; Fischer, Horst
2015-04-01
This paper presents a novel methodology-based discrete wavelet transform (DWT) and the choice of the optimal wavelet pairs to adaptively process tunable diode laser absorption spectroscopy (TDLAS) spectra for quantitative analysis, such as molecular spectroscopy and trace gas detection. The proposed methodology aims to construct an optimal calibration model for a TDLAS spectrum, regardless of its background structural characteristics, thus facilitating the application of TDLAS as a powerful tool for analytical chemistry. The performance of the proposed method is verified using analysis of both synthetic and observed signals, characterized with different noise levels and baseline drift. In terms of fitting precision and signal-to-noise ratio, both have been improved significantly using the proposed method.
Directory of Open Access Journals (Sweden)
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.
Hill, Paul; Achim, Alin; Al-Mualla, Mohammed Ebrahim; Bull, David
2016-04-11
Accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression, fusion and denoising. Conventional Contrast Sensitivity Functions (CSFs) have been obtained using fixed sized Gabor functions. However, the basis functions of multiresolution decompositions such as wavelets often resemble Gabor functions but are of variable size and shape. Therefore to use conventional contrast sensitivity functions in such cases is not appropriate. We have therefore conducted a set of psychophysical tests in order to obtain the contrast sensitivity function for a range of multiresolution transforms: the Discrete Wavelet Transform (DWT), the Steerable Pyramid, the Dual-Tree Complex Wavelet Transform (DT-CWT) and the Curvelet Transform. These measures were obtained using contrast variation of each transforms' basis functions in a 2AFC experiment combined with an adapted version of the QUEST psychometric function method. The results enable future image processing applications that exploit these transforms such as signal fusion, super-resolution processing, denoising and motion estimation, to be perceptually optimised in a principled fashion. The results are compared to an existing vision model (HDR-VDP2) and are used to show quantitative improvements within a denoising application compared to using conventional CSF values.
RFI Mitigation in Microwave Radiometry Using Wavelets
Directory of Open Access Journals (Sweden)
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
Addison, Paul S
2015-01-01
A novel method of identifying stable phase coupling behavior of two signals within the wavelet transform time-frequency plane is presented. The technique employs the cross-wavelet transform to provide a map of phase coupling followed by synchrosqueezing to collect the stable phase regime information. The resulting synchrosqueezed cross-wavelet transform method (Synchro-CrWT) is illustrated using a synthetic signal and then applied to the analysis of the relationship between biosignals used in the analysis of cerebral autoregulation function.
Fast Wavelet-Based Visual Classification
Yu, Guoshen
2008-01-01
We investigate a biologically motivated approach to fast visual classification, directly inspired by the recent work of Serre et al. Specifically, trading-off biological accuracy for computational efficiency, we explore using wavelet and grouplet-like transforms to parallel the tuning of visual cortex V1 and V2 cells, alternated with max operations to achieve scale and translation invariance. A feature selection procedure is applied during learning to accelerate recognition. We introduce a simple attention-like feedback mechanism, significantly improving recognition and robustness in multiple-object scenes. In experiments, the proposed algorithm achieves or exceeds state-of-the-art success rate on object recognition, texture and satellite image classification, language identification and sound classification.
Wavelet-based Multiresolution Particle Methods
Bergdorf, Michael; Koumoutsakos, Petros
2006-03-01
Particle methods offer a robust numerical tool for solving transport problems across disciplines, such as fluid dynamics, quantitative biology or computer graphics. Their strength lies in their stability, as they do not discretize the convection operator, and appealing numerical properties, such as small dissipation and dispersion errors. Many problems of interest are inherently multiscale, and their efficient solution requires either multiscale modeling approaches or spatially adaptive numerical schemes. We present a hybrid particle method that employs a multiresolution analysis to identify and adapt to small scales in the solution. The method combines the versatility and efficiency of grid-based Wavelet collocation methods while retaining the numerical properties and stability of particle methods. The accuracy and efficiency of this method is then assessed for transport and interface capturing problems in two and three dimensions, illustrating the capabilities and limitations of our approach.
A simple denoising algorithm using wavelet transform
Roy, M F; Kulkarni, B D; Sanderson, J; Rhodes, M; Stappen, M; Roy, Manojit; Sanderson, John; Rhodes, Martin; Stappen, Michel vander
1999-01-01
We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The algorithm has been applied to three model flow systems - Lorenz, Autocatalator, and Rossler systems - all evolving chaotically. The method is seen to work quite well for a wide range of noise strengths, even as large as 10% of the signal level. We have also applied the method successfully to noisy time series data obtained from the measurement of pressure fluctuations in a fluidized bed, and also to that obtained by conductivity measurement in a liquid surfactant experiment. In all the illustrations we have been able to observe that there is a clean separation in the frequencies covered by the differentiated signal and white noise.
Wavelet analysis of sunspot relative numbers
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The time series of the monthly smoothed sunspot numbers in 1749-2000 is analyzed with the wavelet.The result shows that besides the known time-variation of the period about 11 years, other main periods of the sunspot numbers, such as the periods of about 100 years and so on,vary with time. We suggest that the time-variation of the main periods is the manifestation of the complex variation of sunspot numbers. It is significant to make a thorough study of the character and mechanism of the time-variation of the periods for proving prediction of sunspot numbers, especially for understanding the variation process of sunspot numbers.
Wavelet Based Fractal Analysis of Airborne Pollen
Degaudenzi, M E
1999-01-01
The most abundant biological particles in the atmosphere are pollen grains and spores. Self protection of pollen allergy is possible through the information of future pollen contents in the air. In spite of the importance of airborne pol len concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of the daily pollen forecasts have resulted in failures. Previous analysis of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply the wavelet transform to study the multifractal characteristics of an a irborne pollen time series. We find the persistence behaviour associated to low pollen concentration values and to the most rare events of highest pollen co ncentration values. The information and the correlation dimensions correspond to a chaotic system showing loss of information with time evolution.
Network Anomaly Detection Based on Wavelet Analysis
Directory of Open Access Journals (Sweden)
Ali A. Ghorbani
2008-11-01
Full Text Available Signal processing techniques have been applied recently for analyzing and detecting network anomalies due to their potential to find novel or unknown intrusions. In this paper, we propose a new network signal modelling technique for detecting network anomalies, combining the wavelet approximation and system identification theory. In order to characterize network traffic behaviors, we present fifteen features and use them as the input signals in our system. We then evaluate our approach with the 1999 DARPA intrusion detection dataset and conduct a comprehensive analysis of the intrusions in the dataset. Evaluation results show that the approach achieves high-detection rates in terms of both attack instances and attack types. Furthermore, we conduct a full day's evaluation in a real large-scale WiFi ISP network where five attack types are successfully detected from over 30 millions flows.
Discrete directional wavelet bases for image compression
Dragotti, Pier L.; Velisavljevic, Vladan; Vetterli, Martin; Beferull-Lozano, Baltasar
2003-06-01
The application of the wavelet transform in image processing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show very interesting gains compared to the standard two-dimensional analysis.
Multiple access communications using wavelet technology
Orr, Richard S.; Pike, Cameron; Bates, Margaret L.
1995-04-01
A class of waveforms developed for covert, or low probability of intercept/detection (LPI/D) communications has been tested for its applicability to code-division multiple access (CDMA) communications. This paper reports some results of the investigation. The waveforms, constructed by techniques based on wavelet transforms, show the characteristics of bandpass Gaussian noise under a number of statistical tests. We refer to these as single-scale waveforms because of an aspect of their construction. By a combination of analysis and simulation, the single-scale waveforms have been compared to conventional CDMA techniques, and it is concluded that on the additive, white Gaussian noise channel, they outperform the conventional by 75 - 200% in capacity (number of supportable users per unit bandwidth at fixed SNR and bit error rate).
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Modelling spatial density using continuous wavelet transforms
Indian Academy of Sciences (India)
D Sudheer Reddy; N Gopal Reddy; A K Anilkumar
2013-02-01
Due to increase in the satelite launch activities from many countries around the world the orbital debris issue has become a major concern for the space agencies to plan a collision-free orbit design. The risk of collisions is calculated using the in situ measurements and available models. Spatial density models are useful in understanding the long-term likelihood of a collision in a particular region of space and also helpful in pre-launch orbit planning. In this paper, we present a method of estimating model parameters such as number of peaks and peak locations of spatial density model using continuous wavelets. The proposed methodology was experimented with two line element data and the results are presented.
Making electromagnetic wavelets: II. Spheroidal shell antennas
Energy Technology Data Exchange (ETDEWEB)
Kaiser, Gerald [Center for Signals and Waves, 3803 Tonkawa Trail 2, Austin, TX (United States)
2005-01-14
In the companion paper, a charge-current distribution was obtained for radiating electromagnetic wavelets. However, it cannot be realized because of two drawbacks: (a) it requires the existence of magnetic charges, and (b) the charge-current distribution, which is concentrated on a spheroidal surface S{sub {alpha}}, is too singular for practical implementation. Both of these difficulties are resolved here. The first is resolved by using Hertz vectors to generate a charge-current distribution on S{sub {alpha}} due solely to bound electric charges. The second is resolved by replacing S{sub {alpha}} with a spheroidal shell of finite thickness. This generalizes the usual boundary conditions on an interface between electromagnetic media by allowing the transition to be gradual.
New Blocking Artifacts Reduction Method Based on Wavelet Transform
Institute of Scientific and Technical Information of China (English)
SHI Min; YI Qing-ming
2007-01-01
It is well known that a block discrete cosine transform compressed image exhibits visually annoying blocking artifacts at low-bit-rate. A new post-processing deblocking algorithm in wavelet domain is proposed. The algorithm exploits blocking-artifact features shown in wavelet domain. The energy of blocking artifacts is concentrated into some lines to form annoying visual effects after wavelet transform. The aim of reducing blocking artifacts is to capture excessive energy on the block boundary effectively and reduce it below the visual scope. Adaptive operators for different subbands are computed based on the wavelet coefficients. The operators are made adaptive to different images and characteristics of blocking artifacts. Experimental results show that the proposed method can significantly improve the visual quality and also increase the peak signal-noise-ratio(PSNR) in the output image.
Coherent vorticity extraction in turbulent boundary layers using orthogonal wavelets
Energy Technology Data Exchange (ETDEWEB)
Khujadze, George; Oberlack, Martin [Chair of Fluid Dynamics, Technische Universitaet Darmstadt (Germany); Yen, Romain Nguyen van [Institut fuer Mathematik, Freie Universitaet Berlin (Germany); Schneider, Kai [M2P2-CNRS and CMI, Universite de Provence, Marseille (France); Farge, Marie, E-mail: khujadze@fdy.tu-darmstadt.de [LMD-IPSL-CNRS, Ecole Normale Superieure, Paris (France)
2011-12-22
Turbulent boundary layer data computed by direct numerical simulation are analyzed using orthogonal anisotropic wavelets. The flow fields, originally given on a Chebychev grid, are first interpolated on a locally refined dyadic grid. Then, they are decomposed using a wavelet basis, which accounts for the anisotropy of the flow by using different scales in the wall-normal direction and in the planes parallel to the wall. Thus the vorticity field is decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. It is shown that less than 1% of the coefficients retain the coherent structures of the flow, while the majority of the coefficients corresponds to a structureless, i.e., noise-like background flow. Scale-and direction-dependent statistics in wavelet space quantify the flow properties at different wall distances.
Robust Depth-Weighted Wavelet for Nonparametric Regression Models
Institute of Scientific and Technical Information of China (English)
Lu LIN
2005-01-01
In the nonpaxametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method.
Optimization and Assessment of Wavelet Packet Decompositions with Evolutionary Computation
Directory of Open Access Journals (Sweden)
Schell Thomas
2003-01-01
Full Text Available In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basis algorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basis algorithm is only suboptimal. We apply methods from the field of evolutionary computation (EC to test the quality of the near-best-basis results. We observe a phenomenon: the results of the near-best-basis algorithm are inferior in terms of cost-function optimization but are superior in terms of rate/distortion performance compared to EC methods.
ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
MEI Shu-li; LU Qi-shao; ZHANG Sen-wen; JIN Li
2005-01-01
The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
Improved zerotree coding algorithm for wavelet image compression
Chen, Jun; Li, Yunsong; Wu, Chengke
2000-12-01
A listless minimum zerotree coding algorithm based on the fast lifting wavelet transform with lower memory requirement and higher compression performance is presented in this paper. Most state-of-the-art image compression techniques based on wavelet coefficients, such as EZW and SPIHT, exploit the dependency between the subbands in a wavelet transformed image. We propose a minimum zerotree of wavelet coefficients which exploits the dependency not only between the coarser and the finer subbands but also within the lowest frequency subband. And a ne listless significance map coding algorithm based on the minimum zerotree, using new flag maps and new scanning order different form Wen-Kuo Lin et al. LZC, is also proposed. A comparison reveals that the PSNR results of LMZC are higher than those of LZC, and the compression performance of LMZC outperforms that of SPIHT in terms of hard implementation.
A Secret Image Sharing Method Using Integer Wavelet Transform
Directory of Open Access Journals (Sweden)
Li Ching-Chung
2007-01-01
Full Text Available A new image sharing method, based on the reversible integer-to-integer (ITI wavelet transform and Shamir's threshold scheme is presented, that provides highly compact shadows for real-time progressive transmission. This method, working in the wavelet domain, processes the transform coefficients in each subband, divides each of the resulting combination coefficients into shadows, and allows recovery of the complete secret image by using any or more shadows . We take advantages of properties of the wavelet transform multiresolution representation, such as coefficient magnitude decay and excellent energy compaction, to design combination procedures for the transform coefficients and processing sequences in wavelet subbands such that small shadows for real-time progressive transmission are obtained. Experimental results demonstrate that the proposed method yields small shadow images and has the capabilities of real-time progressive transmission and perfect reconstruction of secret images.
Fusion of Daubechies Wavelet Coefficients for Human Face Recognition
Bhowmik, Mrinal Kanti; Nasipuri, Mita; Basu, Dipak Kumar; Kundu, Mahantapas
2010-01-01
In this paper fusion of visual and thermal images in wavelet transformed domain has been presented. Here, Daubechies wavelet transform, called as D2, coefficients from visual and corresponding coefficients computed in the same manner from thermal images are combined to get fused coefficients. After decomposition up to fifth level (Level 5) fusion of coefficients is done. Inverse Daubechies wavelet transform of those coefficients gives us fused face images. The main advantage of using wavelet transform is that it is well-suited to manage different image resolution and allows the image decomposition in different kinds of coefficients, while preserving the image information. Fused images thus found are passed through Principal Component Analysis (PCA) for reduction of dimensions and then those reduced fused images are classified using a multi-layer perceptron. For experiments IRIS Thermal/Visual Face Database was used. Experimental results show that the performance of the approach presented here achieves maximum...
Automated Classification of Glaucoma Images by Wavelet Energy Features
Directory of Open Access Journals (Sweden)
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.
Multiscale edge detection of noisy images using wavelets
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The classical edge detectors work fine with the high quality pictures, but often are not good enough for noisy images because they cannot distinguish edges of different significance. The paper presented a novel approach to multiscale edge detection for noisy images using wavelet transforms based on Lipschitz regularity coefficients and a cascade algorithm. The relationship between wavelet transform and Lipschitz regularity was establishod. The proposed wavelet based edge detection algorithm combined the coefficients of wavelet transforms along with a cascade algorithm which significantly improves the result. The comparison between the proposed method and the classical edge detectors was carried out. The algorithm was applied to various images and its performance was discussed. The results of edge detection of contaminated images using the proposed algorithm show that it works better than the classical edge detectors.
Early Detection of Rogue Waves by the Wavelet Transforms
Bayindir, Cihan
2015-01-01
We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the development of rogue waves in a chaotic wave field. Compared to the Fourier spectra, the wavelet spectra is capable of detecting not only the emergence of a rogue wave but also its possible spatial (or temporal) location. Due to this fact, wavelet transform is also capable of predicting the characteristic distances between successive rogue waves. Therefore multiple simultaneous breaking of the successive rogue waves on ships or on the offshore structures can be predicted and avoided by smart designs and operations.
THE WAVELET ANALYSIS METHOD ON THE TRANSIENT SIGNAL
Institute of Scientific and Technical Information of China (English)
吴淼
1996-01-01
Many dynamic signals of mining machines are transient, such as load signals when roadheader's cutting head being cut-in or cut-out and response signals produced by these loads. For these transient signals, the traditional Fourier analysis method is quite inadequate,The limitations of analysis, resolution by using Short-Time Fourier Transform (STFT) on them were discussed in this paper. Because of wavelet transform having the characteristics of flexible window and multiresolution analysis, we try to apply it to analyse these transientsignal. In order to give a pratical example,using D 18 wavelet and Mallat's tree algorithm with MATLAB, the discrete wavelet transform was calculated for the simulating response signals of a three-degree-of freedom vibration system when it was under impulse and random excitations. The results of the wavelet transform made clear its effectiveness and superiority in analysing transient signals of mining machines.
Doppler radar fall activity detection using the wavelet transform.
Su, Bo Yu; Ho, K C; Rantz, Marilyn J; Skubic, Marjorie
2015-03-01
We propose in this paper the use of Wavelet transform (WT) to detect human falls using a ceiling mounted Doppler range control radar. The radar senses any motions from falls as well as nonfalls due to the Doppler effect. The WT is very effective in distinguishing the falls from other activities, making it a promising technique for radar fall detection in nonobtrusive inhome elder care applications. The proposed radar fall detector consists of two stages. The prescreen stage uses the coefficients of wavelet decomposition at a given scale to identify the time locations in which fall activities may have occurred. The classification stage extracts the time-frequency content from the wavelet coefficients at many scales to form a feature vector for fall versus nonfall classification. The selection of different wavelet functions is examined to achieve better performance. Experimental results using the data from the laboratory and real inhome environments validate the promising and robust performance of the proposed detector.
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.
monthly energy consumption forecasting using wavelet analysis and ...
African Journals Online (AJOL)
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paper, a wavelet transform and radial basis function neural network based energy forecast model is developed to .... These prop- erties lead to quicker learning in comparison to ..... Machine Learning and Cybernetics,. IEEE Transactions, 8: ...
Hand posture recognizer based on separator wavelet networks
Bouchrika, Tahani; Jemai, Olfa; Zaied, Mourad; Ben Amar, Chokri
2015-12-01
This paper presents a novel hand posture recognizer based on separator wavelet networks (SWNs). Aiming at creating a robust and rapid hand posture recognizer, we have contributed by proposing a new training algorithm for the wavelet network classifier based on fast wavelet transform (FWN). So, the contribution resides in reducing the number of WNs modeling training data. To make that, inspiring from the adaboost feature selection method, we thought to create SWNs (n-1 WNs for n classes) instead of modeling each training sample by its wavelet network (WN). By proposing the new training algorithm, the recognition phase will be positively influenced. It will be more rapid thanks to the reduction of the number of comparisons between test images WNs and training WNs. Comparisons with other works, employing universal hand posture datasets are presented and discussed. Obtained results have shown that the new hand posture recognizer is comparable to previously established ones.
Tree-structured wavelet transform signature for classification of melanoma
Patwardhan, Sachin V.; Dhawan, Atam P.; Relue, Patricia A.
2002-05-01
The purpose of this work is to evaluate the use of a wavelet transform based tree structure in classifying skin lesion images in to melanoma and dysplastic nevus based on the spatial/frequency information. The classification is done using the wavelet transform tree structure analysis. Development of the tree structure in the proposed method uses energy ratio thresholds obtained from a statistical analysis of the coefficients in the wavelet domain. The method is used to obtain a tree structure signature of melanoma and dysplastic nevus, which is then used to classify the data set in to the two classes. Images are classified by using a semantic comparison of the wavelet transform tree structure signatures. Results show that the proposed method is effective and simple for classification based on spatial/frequency information, which also includes the textural information.
Multi-resolution analysis for ear recognition using wavelet features
Shoaib, M.; Basit, A.; Faye, I.
2016-11-01
Security is very important and in order to avoid any physical contact, identification of human when they are moving is necessary. Ear biometric is one of the methods by which a person can be identified using surveillance cameras. Various techniques have been proposed to increase the ear based recognition systems. In this work, a feature extraction method for human ear recognition based on wavelet transforms is proposed. The proposed features are approximation coefficients and specific details of level two after applying various types of wavelet transforms. Different wavelet transforms are applied to find the suitable wavelet. Minimum Euclidean distance is used as a matching criterion. Results achieved by the proposed method are promising and can be used in real time ear recognition system.
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.
Random seismic noise attenuation using the Wavelet Transform
Aliouane, L.; Ouadfeul, S.; Boudella, A.; Eladj, S.
2012-04-01
In this paper we propose a technique of random noises attenuation from seismic data using the discrete and continuous wavelet transforms. Firstly the discrete wavelet transform (DWT) is applied to denoise seismic data. This last is based on the threshold method applied at the modulus of the DWT. After we calculate the continuous wavelet transform of the denoised seismic seismogram, the final denoised seismic seismogram is the continuous wavelet transform coefficients at the low scale. Application at a synthetic seismic seismogram shows the robustness of the proposed tool for random noises attenuation. We have applied this idea at a real seismic data of a vertical seismic profile realized in Algeria. Keywords: Seismic data, denoising, DWT, CWT, random noise.
Image denoising based on wavelet cone of influence analysis
Pang, Wei; Li, Yufeng
2009-11-01
Donoho et al have proposed a method for denoising by thresholding based on wavelet transform, and indeed, the application of their method to image denoising has been extremely successful. But this method is based on the assumption that the type of noise is only additive Gaussian white noise, which is not efficient to impulse noise. In this paper, a new image denoising algorithm based on wavelet cone of influence (COI) analyzing is proposed, and which can effectively remove the impulse noise and preserve the image edges via undecimated discrete wavelet transform (UDWT). Furthermore, combining with the traditional wavelet thresholding denoising method, it can be also used to restrain more widely type of noise such as Gaussian noise, impulse noise, poisson noise and other mixed noise. Experiment results illustrate the advantages of this method.
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.
Wavelets Applied to CMB Maps a Multiresolution Analysis for Denoising
Sanz, J L; Cayon, L; Martínez-González, E; Barriero, R B; Toffolatti, L
1999-01-01
Analysis and denoising of Cosmic Microwave Background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on $12^{\\circ}.8\\times 12^{\\circ}.8$ maps with resolution resembling the experimental one expected for future high resolution space observations. Semianalytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumental noise. CMB maps with a signal-to-noise, $S/N \\sim 1$, are denoised with an error improvement factor between 3 and 5. Moreover we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the $C_{\\ell}$'s up to $l\\sim 1500$ with errors always below $20% $ in cases with $S/N \\ge 1$.
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.
Optimization of Wavelet-Based De-noising in MRI
Directory of Open Access Journals (Sweden)
K. Bartusek
2011-04-01
Full Text Available In the paper, a method for MR image enhancement using the wavelet analysis is described. The wavelet analysis is concentrated on the influence of threshold level and mother wavelet choices on the resultant MR image. The influence is expressed by the measurement and mutual comparison of three MT image parameters: signal to noise ratio, image contrast, and linear slope edge approximation. Unlike most standard methods working exclusively with the MR image magnitude, in our case both the MR image magnitude and the MR image phase were used in the enhancement process. Some recommendations are mentioned in conclusion, such as how to use a combination of mother wavelets with threshold levels for various types of MR images.
Implementing a global DEM database on the sphere based on spherical wavelets
Zhao, Di; Zhao, Xuesheng; Shan, Shigang; Yao, Liangjun
2010-11-01
Wavelets have been proven to be an exceedingly powerful and highly efficient tool for fast computational algorithms in the fields of image data analysis and compression. Traditionally, the classical constructed wavelets are often employed to Euclidean infinite domains (such as the real line R and plane R2). In this paper, a spherical wavelet constructed for discrete DEM data based on the sphere is approached. Firstly, the discrete biorthogonal spherical wavelet with custom properties is constructed with the lifting scheme based on wavelet toolbox in Matlab. Then, the decomposition and reconstruction algorithms are proposed for efficient computation and the related wavelet coefficients are obtained. Finally, different precise images are displayed and analyzed at the different percentage of wavelet coefficients. The efficiency of this spherical wavelet algorithm is tested by using the GTOPO30 DEM data and the results show that at the same precision, the spherical wavelet algorithm consumes smaller storage volume. The results are good and acceptable.
Extraction of MHD Signal Based on Wavelet Transform
Institute of Scientific and Technical Information of China (English)
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.
A Fractional Random Wavelet Transform Based Image Steganography
G.K. Rajini; RAMACHANDRA REDDY G.
2015-01-01
This study presents a novel technique for image steganography based on Fractional Random Wavelet Transform. This transform has all the features of wavelet transform with randomness and fractional order built into it. The randomness and fractional order in the algorithm brings in robustness and additional layers of security to steganography. The stegano image generated by this algorithm contains both cover image and hidden image and image degradation is not observed in it. The steganography st...
Schrödinger like equation for wavelets
Directory of Open Access Journals (Sweden)
A. Zúñiga-Segundo
2016-01-01
Full Text Available An explicit phase space representation of the wave function is build based on a wavelet transformation. The wavelet transformation allows us to understand the relationship between s − ordered Wigner function, (or Wigner function when s = 0, and the Torres-Vega-Frederick’s wave functions. This relationship is necessary to find a general solution of the Schrödinger equation in phase-space.
Wavelet operational matrix method for solving the Riccati differential equation
Li, Yuanlu; Sun, Ning; Zheng, Bochao; Wang, Qi; Zhang, Yingchao
2014-03-01
A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.
Greedy Wavelet Projections are Bounded on BV (Preprint)
2003-10-30
functions of bounded variation on IRd with d ??? 2. Let ????, ?? ??? ??, be a wavelet basis of compactly supported functions normalized in BV, i.e...Wojtaszczyk October 30, 2003 Abstract Let BV = BV(IRd) be the space of functions of bounded variation on IRd with d ≥ 2. Let ψλ, λ ∈ ∆, be a wavelet basis...greedy approximation, functions of bounded variation , thresholding, bounded projections. 1 Introduction The space BV := BV(Ω) of functions of
Music Tune Restoration Based on a Mother Wavelet Construction
Fadeev, A. S.; Konovalov, V. I.; Butakova, T. I.; Sobetsky, A. V.
2017-01-01
It is offered to use the mother wavelet function obtained from the local part of an analyzed music signal. Requirements for the constructed function are proposed and the implementation technique and its properties are described. The suggested approach allows construction of mother wavelet families with specified identifying properties. Consequently, this makes possible to identify the basic signal variations of complex music signals including local time-frequency characteristics of the basic one.
Identification of Electrooculography Signals Frequency Energy Distribution Using Wavelet Algorithm
Directory of Open Access Journals (Sweden)
W. M. Bukhari
2011-01-01
Full Text Available Problem statement: The time frequency analysis of non-stationary signals has been the considerable research effort in recent years. Wavelet transform is one of the favored tool for the analyzing the biomedical signals. Approach: We describe the identification of Electro-Oculograph (EOG signals of eye movement potentials by using wavelet algorithm which gives a lot of information than FFT. The capability of wavelet transform was to distribute the signal energy with the change of time in different frequency bands. This will showed the characteristic of the signals since energy was an important physical variable in signal analysis. The EOG signals were captured using electrodes placed on the forehead around the eyes to record the eye movements. The wavelet features used to determine the characteristic of eye movement waveform. This technique adopted because it was a non-invasive, inexpensive and accurate. The new technology enhancement has allowed the EOG signals captured using the Neuronal EEG-9200. The recorded data was composed of an eye movement toward four directions, i.e., downward, upward, leftward and rightward. The proposed analysis for each eyes signal is analyzed by using Wavelet Transform (WT with energy algorithm and by comparing the energy distribution with the change of time and frequency of each signal. Results: A wavelet Scalogram was plotted to display the different percentages of energy for each wavelet coefficient towards different movement. Conclusion: From the result, it is proved that the different EOG signals exhibit differences in signals energy with their corresponding scale such as leftward with scale 6 (8- 16Hz, rightward with scale 8 (2-4Hz, downward with scale 9 (1-2Hz and upward with level 7 (4-8Hz. Statistically, the results in this study indicate that there are 93% (averages significance differences in the extracted features of wavelet Scalogram analysis.
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.
DIVERGENCE - FREE WAVELET SOLUTION TO THE STOKES PROBLEM
Institute of Scientific and Technical Information of China (English)
Yingchun Jiang
2007-01-01
In this paper, we use divergence-free wavelets to give an adaptive solution to the velocity field of the Stokes problem. We first use divergence-free wavelets to discretize the divergence-free weak formulation of the Stokes problem and obtain a discrete positive definite linear system of equations whose coefficient matrix is quasi-sparse; Secondly, an adaptive scheme is used to solve the discrete linear system of equations and the error estimation and complexity analysis are given.
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...
Multistep Wind Speed Forecasting Based on Wavelet and Gaussian Processes
Niya Chen; Zheng Qian; Xiaofeng Meng
2013-01-01
Accurate wind speed forecasts are necessary for the safety and economy of the renewable energy utilization. The wind speed forecasts can be obtained by statistical model based on historical data. In this paper, a novel W-GP model (wavelet decomposition based Gaussian process learning paradigm) is proposed for short-term wind speed forecasting. The nonstationary and nonlinear original wind speed series is first decomposed into a set of better-behaved constitutive subseries by wavelet decomposi...
Classification of Underwater Signals Using Wavelet-Based Decompositions
1998-06-01
proposed by Learned and Willsky [21], uses the SVD information obtained from the power mapping, the second one selects the most within-a-class...34 SPIE, Vol. 2242, pp. 792-802, Wavelet Applications, 1994 [14] R. Coifman and D. Donoho, "Translation-Invariant Denoising ," Internal Report...J. Barsanti, Jr., Denoising of Ocean Acoustic Signals Using Wavelet-Based Techniques, MSEE Thesis, Naval Postgraduate School, Monterey, California
Detection the Character Wave in Epileptic EEG by Wavelet
Institute of Scientific and Technical Information of China (English)
CHEN Huafu; NIU Hai
2004-01-01
Human epilepsy is an intrinsic brain pathology,which can be characterized by repetitive high-amplitude electroencephalograph (EEG) activity.The wavelet transform provides an important tool in signal analysis and feature extraction.In this paper,the modulus maximum pair of a wavelet transform is used to detect the singularity value of the sharps and the spikes embedded in the background activities of the epilepsy EEG.The efficacy of the proposed method has been tested with clinical EEG.
Significance-linked connected component analysis for wavelet image coding.
Chai, B B; Vass, J; Zhuang, X
1999-01-01
Recent success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation. There have been several very competitive wavelet coders developed, namely, Shapiro's (1993) embedded zerotree wavelets (EZW), Servetto et al.'s (1995) morphological representation of wavelet data (MRWD), and Said and Pearlman's (see IEEE Trans. Circuits Syst. Video Technol., vol.6, p.245-50, 1996) set partitioning in hierarchical trees (SPIHT). We develop a novel wavelet image coder called significance-linked connected component analysis (SLCCA) of wavelet coefficients that extends MRWD by exploiting both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. Extensive computer experiments on both natural and texture images show convincingly that the proposed SLCCA outperforms EZW, MRWD, and SPIHT. For example, for the Barbara image, at 0.25 b/pixel, SLCCA outperforms EZW, MRWD, and SPIHT by 1.41 dB, 0.32 dB, and 0.60 dB in PSNR, respectively. It is also observed that SLCCA works extremely well for images with a large portion of texture. For eight typical 256x256 grayscale texture images compressed at 0.40 b/pixel, SLCCA outperforms SPIHT by 0.16 dB-0.63 dB in PSNR. This performance is achieved without using any optimal bit allocation procedure. Thus both the encoding and decoding procedures are fast.
Motion-compensated wavelet video coding using adaptive mode selection
Zhai, Fan; Pappas, Thrasyvoulos N.
2004-01-01
A motion-compensated wavelet video coder is presented that uses adaptive mode selection (AMS) for each macroblock (MB). The block-based motion estimation is performed in the spatial domain, and an embedded zerotree wavelet coder (EZW) is employed to encode the residue frame. In contrast to other motion-compensated wavelet video coders, where all the MBs are forced to be in INTER mode, we construct the residue frame by combining the prediction residual of the INTER MBs with the coding residual of the INTRA and INTER_ENCODE MBs. Different from INTER MBs that are not coded, the INTRA and INTER_ENCODE MBs are encoded separately by a DCT coder. By adaptively selecting the quantizers of the INTRA and INTER_ENCODE coded MBs, our goal is to equalize the characteristics of the residue frame in order to improve the overall coding efficiency of the wavelet coder. The mode selection is based on the variance of the MB, the variance of the prediction error, and the variance of the neighboring MBs' residual. Simulations show that the proposed motion-compensated wavelet video coder achieves a gain of around 0.7-0.8dB PSNR over MPEG-2 TM5, and a comparable PSNR to other 2D motion-compensated wavelet-based video codecs. It also provides potential visual quality improvement.
Myoelectric signal compression using zero-trees of wavelet coefficients.
Norris, Jason A; Englehart, Kevin B; Lovely, Dennis F
2003-11-01
Recent progress in the diagnostic use of the myoelectric signal for neuromuscular diseases, coupled with increasing interests in telemedicine applications, mandate the need for an effective compression technique. The efficacy of the embedded zero-tree wavelet compression algorithm is examined with respect to some important analysis parameters (the length of the analysis segment and wavelet type) and measurement conditions (muscle type and contraction type). It is shown that compression performance improves with segment length, and that good choices of wavelet type include the Meyer wavelet and the fifth order biorthogonal wavelet. The effects of different muscle sites and contraction types on compression performance are less conclusive.A comparison of a number of lossy compression techniques has revealed that the EZW algorithm exhibits superior performance to a hard thresholding wavelet approach, but falls short of adaptive differential pulse code modulation. The bit prioritization capability of the EZW algorithm allows one to specify the compression factor online, making it an appealing technique for streaming data applications, as often encountered in telemedicine.
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.
Analysis and removing noise from speech using wavelet transform
Tomala, Karel; Voznak, Miroslav; Partila, Pavol; Rezac, Filip; Safarik, Jakub
2013-05-01
The paper discusses the use of Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT) wavelet in removing noise from voice samples and evaluation of its impact on speech quality. One significant part of Quality of Service (QoS) in communication technology is the speech quality assessment. However, this part is seriously overlooked as telecommunication providers often focus on increasing network capacity, expansion of services offered and their enforcement in the market. Among the fundamental factors affecting the transmission properties of the communication chain is noise, either at the transmitter or the receiver side. A wavelet transform (WT) is a modern tool for signal processing. One of the most significant areas in which wavelet transforms are used is applications designed to suppress noise in signals. To remove noise from the voice sample in our experiment, we used the reference segment of the voice which was distorted by Gaussian white noise. An evaluation of the impact on speech quality was carried out by an intrusive objective algorithm Perceptual Evaluation of Speech Quality (PESQ). DWT and SWT transformation was applied to voice samples that were devalued by Gaussian white noise. Afterwards, we determined the effectiveness of DWT and SWT by means of objective algorithm PESQ. The decisive criterion for determining the quality of a voice sample once the noise had been removed was Mean Opinion Score (MOS) which we obtained in PESQ. The contribution of this work lies in the evaluation of efficiency of wavelet transformation to suppress noise in voice samples.
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.
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.
2008-08-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.
Wavelet-based denoising using local Laplace prior
Rabbani, Hossein; Vafadust, Mansur; Selesnick, Ivan
2007-09-01
Although wavelet-based image denoising is a powerful tool for image processing applications, relatively few publications have addressed so far wavelet-based video denoising. The main reason is that the standard 3-D data transforms do not provide useful representations with good energy compaction property, for most video data. For example, the multi-dimensional standard separable discrete wavelet transform (M-D DWT) mixes orientations and motions in its subbands, and produces the checkerboard artifacts. So, instead of M-D DWT, usually oriented transforms suchas multi-dimensional complex wavelet transform (M-D DCWT) are proposed for video processing. In this paper we use a Laplace distribution with local variance to model the statistical properties of noise-free wavelet coefficients. This distribution is able to simultaneously model the heavy-tailed and intrascale dependency properties of wavelets. Using this model, simple shrinkage functions are obtained employing maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimators. These shrinkage functions are proposed for video denoising in DCWT domain. The simulation results shows that this simple denoising method has impressive performance visually and quantitatively.
Energy Technology Data Exchange (ETDEWEB)
Garcia R, A. [ININ, Carretera Mexico-Toluca S/N, 52750 La Marquesa, Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: ramador@nuclear.inin.mx
2007-07-01
At the moment the signals are used to diagnose the state of the systems, by means of the extraction of their more important characteristics such as the frequencies, tendencies, changes and temporary evolutions. This characteristics are detected by means of diverse analysis techniques, as Autoregressive methods, Fourier Transformation, Fourier transformation in short time, Wavelet transformation, among others. The present work uses the one Wavelet transformation because it allows to analyze stationary, quasi-stationary and transitory signals in the time-frequency plane. It also describes a methodology to select the scales and the Wavelet function to be applied the one Wavelet transformation with the objective of detecting to the dominant system frequencies. (Author)
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.
Optical phase distribution evaluation by using zero order Generalized Morse Wavelet
Kocahan, Özlem; Elmas, Merve Naz; Durmuş, ćaǧla; Coşkun, Emre; Tiryaki, Erhan; Özder, Serhat
2017-02-01
When determining the phase from the projected fringes by using continuous wavelet transform (CWT), selection of wavelet is an important step. A new wavelet for phase retrieval from the fringe pattern with the spatial carrier frequency in the x direction is presented. As a mother wavelet, zero order generalized Morse wavelet (GMW) is chosen because of the flexible spatial and frequency localization property, and it is exactly analytic. In this study, GMW method is explained and numerical simulations are carried out to show the validity of this technique for finding the phase distributions. Results for the Morlet and Paul wavelets are compared with the results of GMW analysis.
Uniform approximation of Gaussian wavelet for biomedical signal processing in analog domain.
Makkena, Goutham; Bvvsn, Prabhakara Rao; Srinivas, M B
2013-01-01
Signal processing in analog domain is favorable when power consumption is a critical design constraint. Continuous Wavelet Transform (CWT), which is increasingly being used in characterizing biomedical signals, when implemented in analog domain consumes less power provided the mother wavelet is properly approximated. This paper presents an approximation of Gaussian wavelet by making use of the Uniform approximation. Simulations of the approximated wavelet and the actual wavelet in MATLAB are performed and the results discussed. Simulations show that (i) approximation obtained closely matches the mother wavelet chosen and (ii) a stable approximation which helps in physical realization using any circuit design methodology.
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...
Institute of Scientific and Technical Information of China (English)
Xiang Jiawei; He Zhengjia; Chen Xuefeng
2006-01-01
Based on B-spline wavelet on the interval (BSWI), two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based lements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.
Fractional snow cover mapping from MODIS data using wavelet-artificial intelligence hybrid models
Moosavi, Vahid; Malekinezhad, Hossein; Shirmohammadi, Bagher
2014-04-01
This study was carried out to evaluate the wavelet-artificial intelligence hybrid models to produce fractional snow cover maps. At first, cloud cover was removed from MODIS data and cloud free images were produced. SVM-based binary classified ETM+ imagery were then used as reference maps in order to obtain train and test data for sub-pixel classification models. ANN and ANFIS-based modeling were performed using raw data (without wavelet-based preprocessing). In the next step, several mother wavelets and levels were used in order to decompose the original data to obtain wavelet coefficients. Then, the decomposed data were used for further modeling processes. ANN, ANFIS, wavelet-ANN and wavelet-ANFIS models were compared to evaluate the effect of wavelet transformation on the ability of artificial intelligence models. It was demonstrated that wavelet transformation as a preprocessing approach can significantly enhance the performance of ANN and ANFIS models. This study indicated an overall accuracy of 92.45% for wavelet-ANFIS model, 86.13% for wavelet-ANN, 72.23% for ANFIS model and 66.78% for ANN model. In fact, hybrid wavelet-artificial intelligence models can extract the characteristics of the original signals (i.e. model inputs) accurately through decomposing the non-stationary and complex signals into several stationary and simpler signals. The positive effect of fuzzification as well as wavelet transformation in the wavelet-ANFIS model was also confirmed.
Lossless wavelet compression on medical image
Zhao, Xiuying; Wei, Jingyuan; Zhai, Linpei; Liu, Hong
2006-09-01
An increasing number of medical imagery is created directly in digital form. Such as Clinical image Archiving and Communication Systems (PACS), as well as telemedicine networks require the storage and transmission of this huge amount of medical image data. Efficient compression of these data is crucial. Several lossless and lossy techniques for the compression of the data have been proposed. Lossless techniques allow exact reconstruction of the original imagery, while lossy techniques aim to achieve high compression ratios by allowing some acceptable degradation in the image. Lossless compression does not degrade the image, thus facilitating accurate diagnosis, of course at the expense of higher bit rates, i.e. lower compression ratios. Various methods both for lossy (irreversible) and lossless (reversible) image compression are proposed in the literature. The recent advances in the lossy compression techniques include different methods such as vector quantization. Wavelet coding, neural networks, and fractal coding. Although these methods can achieve high compression ratios (of the order 50:1, or even more), they do not allow reconstructing exactly the original version of the input data. Lossless compression techniques permit the perfect reconstruction of the original image, but the achievable compression ratios are only of the order 2:1, up to 4:1. In our paper, we use a kind of lifting scheme to generate truly loss-less non-linear integer-to-integer wavelet transforms. At the same time, we exploit the coding algorithm producing an embedded code has the property that the bits in the bit stream are generated in order of importance, so that all the low rate codes are included at the beginning of the bit stream. Typically, the encoding process stops when the target bit rate is met. Similarly, the decoder can interrupt the decoding process at any point in the bit stream, and still reconstruct the image. Therefore, a compression scheme generating an embedded code can
WAVELET ANALYSIS OF INTERANNUAL VARIATION OF TROPICAL CYCLONES IN GUANGDONG
Institute of Scientific and Technical Information of China (English)
刘春霞
2002-01-01
Climatological laws are studied for the annual frequency of tropical cyclone occurrence and the date of the yearly first landfall,which take place in the Guangdong province or pose serious threats on it from 1951 to 1999,using the data in the Yearly Book on Typhoons.A new method that has developed over recent years for the study of temporal sequences,the wavelet analysis,is used,in addition to more common statistical approaches.By analyzing two wavelet functions,MHAT and MORLET,we have compared the results of transformation of the wavelets provided that other conditions remain unchanged.It is discovered that the variance of MORLET wavelet has better indication of primary periods;period-time sequence charts can reflect major affecting periods for individual sections of time;when compared with the original sequence,the chart shows a little shift.On the other hand,such shift is absent in the MHAT wavelet,but its higher frequency part of variance covers up the primary periods to make its variance less predominant as compared to the MORLET wavelet.Besides,the work compares two different assumptions of an amplifying factor a.It is found that primary periods can be shown more clearly in the variance when a takes the exponential of 2 than it takes values continuously.Studying the annual frequency of tropical cyclones and the date of first appearance for periodic patterns,we have found that the primary periods extracted by this approach are similar to those obtained by wavelet transformation.
Characteristics and realization of the second generation surface acoustic wave's wavelet device
Institute of Scientific and Technical Information of China (English)
Wen Changbao; Zhu Changchun; Lu Wenke; Liu Qinghong; Liu Junhua
2006-01-01
To overcome the bulk acoustic wave (BAW), the triple transit signals and the discontinuous frequency band in the first generation surface acoustic wave's (FGSAW's) wavelet device, the full transfer multistrip coupler (MSC) is applied to implement wavelet device, and a novel structure of the second generation surface acoustic wave's (SGSAW's) wavelet device is proposed. In the SGSAW's wavelet device, the BAW is separated and eliminated in different acoustic propagating tracks, and the triple transit signal is suppressed. For arbitrary wavelet scale device, the center frequency is three times the radius of frequency band, which ensures that the frequency band of the SGSAW's wavelet device is continuous, and avoids losing signals caused by the discontinuation of frequency band. Experimental result confirms that the BAW suppression, ripples in band, receiving loss and insertion loss of the SGSAW's wavelet device are remarkably improved compared with those of the FGSAW's wavelet device.
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
Smoke detection using GLCM, wavelet, and motion
Srisuwan, Teerasak; Ruchanurucks, Miti
2014-01-01
This paper presents a supervised smoke detection method that uses local and global features. This framework integrates and extends notions of many previous works to generate a new comprehensive method. First chrominance detection is used to screen areas that are suspected to be smoke. For these areas, local features are then extracted. The features are among homogeneity of GLCM and energy of wavelet. Then, global feature of motion of the smoke-color areas are extracted using a space-time analysis scheme. Finally these features are used to train an artificial intelligent. Here we use neural network, experiment compares importance of each feature. Hence, we can really know which features among those used by many previous works are really useful. The proposed method outperforms many of the current methods in the sense of correctness, and it does so in a reasonable computation time. It even has less limitation than conventional smoke sensors when used in open space. Best method for the experimental results is to use all the mentioned features as expected, to insure which is the best experiment result can be achieved. The achieved with high accuracy of result expected output is high value of true positive and low value of false positive. And show that our algorithm has good robustness for smoke detection.
Optimizing cardiac resuscitation outcomes using wavelet analysis.
Umapathy, K; Krishnan, S; Masse, S; Hu, X; Dorian, P; Nanthakumar, K
2009-01-01
Ventricular fibrillation (VF) is the most lethal of cardiac arrhythmias that leads to sudden cardiac death if untreated within minutes of its occurrence. Defibrillation using electric shock resets the heart to return to spontaneous circulation (ROSC) state, however the success of which depends on various factors such as the viability of myocardium and the time lag between the onset of VF to defibrillation. Recent studies have reported that performing cardio pulmonary resuscitation (CPR) procedure prior to applying shock increases the survival rate especially when VF is untreated for more than 5 minutes. Considering the limited time within which the VF has to be treated for better survival rates, the choice of the right therapy (shock parameters, shock first or CPR first, drug administration) is vital. In aiding this choice, it would be of immense help for emergency medical staff (EMS) if an objective feedback could be provided at near real-time rate on the VF characteristics and its relation to the shock outcomes. Existing works in the literature have demonstrated correlation between the characteristics of the VF waveform and the outcome (ROSC) of the defibrillation. The proposed work improves on this by attempting to arrive at a near real-time monitoring tool in aiding the EMS staff. Using data collected from 16 pigs during VF, the proposed wavelet methodology achieved an overall accuracy of 94% in successfully predicting the shock outcomes.
WAKES: Wavelet Adaptive Kinetic Evolution Solvers
Mardirian, Marine; Afeyan, Bedros; Larson, David
2016-10-01
We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.
Wavelets and Geometric Structure for Function Spaces
Institute of Scientific and Technical Information of China (English)
Qi Xiang YANG
2004-01-01
With Littlewood-Paley analysis, Peetre and Triebel classified, systematically, almost all the usual function spaces into two classes of spaces: Besov spaces (B)s,q p(s ∈ R,0 ＜ p,q ≤∞) and Triebel-Lizorkin spaces (F)s,q p(s∈R,0＜p＜∞,0＜q≤∞); but the structure of dual spaces (D)s,q p of (F)s,q p(s∈R, 0＜p≤1≤q≤∞) is very different from that of Besov spaces or that of Triebel-Lizorkin spaces, and their structure cannot be analysed easily in the Littlewood-Paley analysis. Our main goal is to characterize (D)s,q p (s ∈ R, 0＜p= 1≤q≤∞) in tent spaces with wavelets. By the way, some applications are given: (i) Triebel-Lizorkin spaces for p = ∞ defined by Littlewood-Paley analysis cannot serve as the dual spaces of Triebel-Lizorkin spaces for p = 1; (ii) Some inclusion relations among these above spaces and some relations among(B)o,q1,(F)o,q1 and L1 are studied.
Wavelets for approximate Fourier transform and data compression
Guo, Haitao
This dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components
Institute of Scientific and Technical Information of China (English)
DUAN Chen-dong; JIANG Hong-kai; HE Zheng-jia
2004-01-01
In order to make trend analysis and prediction to acquisition data in a mechanical equipment condition monitoring system, a new method of trend feature extraction and prediction of acquisition data is proposed which constructs an adaptive wavelet on the acquisition data by means of second generation wavelet transform (SGWT). Firstly, taking the vanishing moment number of the predictor as a constraint, the linear predictor and updater are designed according to the acquisition data by using symmetrical interpolating scheme. Then the trend of the data is obtained through doing SGWT decomposition, threshold processing and SGWT reconstruction. Secondly, under the constraint of the vanishing moment number of the predictor, another predictor based on the acquisition data is devised to predict the future trend of the data using a non-symmetrical interpolating scheme. A one-step prediction algorithm is presented to predict the future evolution trend with historical data. The proposed method obtained a desirable effect in peak-to-peak value trend analysis for a machine set in an oil refinery.
Institute of Scientific and Technical Information of China (English)
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.
Signal Estimation Using Wavelet Analysis of Solution Monitoring Data for Nuclear Safeguards
Directory of Open Access Journals (Sweden)
Tom Burr
2013-03-01
Full Text Available Wavelets are explored as a data smoothing (or de-noising option for solution monitoring data in nuclear safeguards. In wavelet-smoothed data, the Gibbs phenomenon can obscure important data features that may be of interest. This paper compares wavelet smoothing to piecewise linear smoothing and local kernel smoothing, and illustrates that the Haar wavelet basis is effective for reducing the Gibbs phenomenon.