A wavelet tour of signal processing : the sparse way
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representatio...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Amsterdam
Elsevier/Academic Press
2009
Elsevier Science & Technology Academic Press |
| Edition | 3 |
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| Online Access | Get full text |
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| Abstract | Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.Features:* Balances presentation of the mathematics with applications to signal processing* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox* Companion website for instructors and selected solutions and code available for studentsNew in this edition* Sparse signal representations in dictionaries* Compressive sensing, super-resolution and source separation* Geometric image processing with curvelets and bandlets* Wavelets for computer graphics with lifting on surfaces* Time-frequency audio processing and denoising* Image compression with JPEG-2000* New and updated exercisesA Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.Companion website: A Numerical Tour of Signal Processing
Includes all the latest developments since the book was published in 1999, including itsapplication to JPEG 2000 and MPEG-4Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolboxBalances presentation of the mathematics with applications to signal processing |
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| AbstractList | Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.Features:* Balances presentation of the mathematics with applications to signal processing* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox* Companion website for instructors and selected solutions and code available for studentsNew in this edition* Sparse signal representations in dictionaries* Compressive sensing, super-resolution and source separation* Geometric image processing with curvelets and bandlets* Wavelets for computer graphics with lifting on surfaces* Time-frequency audio processing and denoising* Image compression with JPEG-2000* New and updated exercisesA Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.Companion website: A Numerical Tour of Signal Processing
Includes all the latest developments since the book was published in 1999, including itsapplication to JPEG 2000 and MPEG-4Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolboxBalances presentation of the mathematics with applications to signal processing |
| Author | Mallat, S. G. (Stephane G.) Peyré, Gabriel |
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| Notes | Bibliography: p. 765-793 Includes index |
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| PublicationPlace | Amsterdam |
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| Publisher | Elsevier/Academic Press Elsevier Science & Technology Academic Press |
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| Snippet | Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet,... |
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| SubjectTerms | Mathematics Signal processing Signal processing -- Mathematics Wavelets (Mathematics) |
| TableOfContents | Front Cover -- A Wavelet Tour of Signal Processing -- Copyright Page -- Dedication Page -- Table of Contents -- Preface to the Sparse Edition -- Notations -- Chapter 1. Sparse Representations -- 1.1 Computational Harmonic Analysis -- 1.1.1 The Fourier Kingdom -- 1.1.2 Wavelet Bases -- 1.2 Approximation and Processing in Bases -- 1.2.1 Sampling with Linear Approximations -- 1.2.2 Sparse Nonlinear Approximations -- 1.2.3 Compression -- 1.2.4 Denoising -- 1.3 Time-Frequency Dictionaries -- 1.3.1 Heisenberg Uncertainty -- 1.3.2 Windowed Fourier Transform -- 1.3.3 Continuous Wavelet Transform -- 1.3.4 Time-Frequency Orthonormal Bases -- 1.4 Sparsity in Redundant Dictionaries -- 1.4.1 Frame Analysis and Synthesis -- 1.4.2 Ideal Dictionary Approximations -- 1.4.3 Pursuit in Dictionaries -- 1.5 Inverse Problems -- 1.5.1 Diagonal Inverse Estimation -- 1.5.2 Super-resolution and Compressive Sensing -- 1.6 Travel Guide -- 1.6.1 Reproducible Computational Science -- 1.6.2 Book Road Map -- Chapter 2. The Fourier Kingdom -- 2.1 Linear Time-Invariant Filtering -- 2.1.1 Impulse Response -- 2.1.2 Transfer Functions -- 2.2 Fourier Integrals -- 2.2.1 Fourier Transform in L1(R) -- 2.2.2 Fourier Transform in L2(R) -- 2.2.3 Examples -- 2.3 Properties -- 2.3.1 Regularity and Decay -- 2.3.2 Uncertainty Principle -- 2.3.3 Total Variation -- 2.4 Two-Dimensional Fourier Transform -- 2.5 Exercises -- Chapter 3. Discrete Revolution -- 3.1 Sampling Analog Signals -- 3.1.1 Shannon-Whittaker Sampling Theorem -- 3.1.2 Aliasing -- 3.1.3 General Sampling and Linear Analog Conversions -- 3.2 Discrete Time-Invariant Filters -- 3.2.1 Impulse Response and Transfer Function -- 3.2.2 Fourier Series -- 3.3 Finite Signals -- 3.3.1 Circular Convolutions -- 3.3.2 Discrete Fourier Transform -- 3.3.3 Fast Fourier Transform -- 3.3.4 Fast Convolutions -- 3.4 Discrete Image Processing 6.4.1 Fractal Sets and Self-Similar Functions -- 6.4.2 Singularity Spectrum -- 6.4.3 Fractal Noises -- 6.5 Exercises -- Chapter 7. Wavelet Bases -- 7.1 Orthogonal Wavelet Bases -- 7.1.1 Multiresolution Approximations -- 7.1.2 Scaling Function -- 7.1.3 Conjugate Mirror Filters -- 7.1.4 In Which Orthogonal Wavelets Finally Arrive -- 7.2 Classes of Wavelet Bases -- 7.2.1 Choosing a Wavelet -- 7.2.2 Shannon, Meyer, Haar, and Battle-Lemarié Wavelets -- 7.2.3 Daubechies Compactly Supported Wavelets -- 7.3 Wavelets and Filter Banks -- 7.3.1 Fast Orthogonal Wavelet Transform -- 7.3.2 Perfect Reconstruction Filter Banks -- 7.3.3 Biorthogonal Bases of l2(Z) -- 7.4 Biorthogonal Wavelet Bases -- 7.4.1 Construction of Biorthogonal Wavelet Bases -- 7.4.2 Biorthogonal Wavelet Design -- 7.4.3 Compactly Supported Biorthogonal Wavelets -- 7.5 Wavelet Bases on an Interval -- 7.5.1 Periodic Wavelets -- 7.5.2 Folded Wavelets -- 7.5.3 Boundary Wavelets -- 7.6 Multiscale Interpolations -- 7.6.1 Interpolation and Sampling Theorems -- 7.6.2 Interpolation Wavelet Basis -- 7.7 Separable Wavelet Bases -- 7.7.1 Separable Multiresolutions -- 7.7.2 Two-Dimensional Wavelet Bases -- 7.7.3 Fast Two-Dimensional Wavelet Transform -- 7.7.4 Wavelet Bases in Higher Dimensions -- 7.8 Lifting Wavelets -- 7.8.1 Biorthogonal Bases over Nonstationary Grids -- 7.8.2 Lifting Scheme -- 7.8.3 Quincunx Wavelet Bases -- 7.8.4 Wavelets on Bounded Domains and Surfaces -- 7.8.5 Faster Wavelet Transform with Lifting -- 7.9 Exercises -- Chapter 8. Wavelet Packet and Local Cosine Bases -- 8.1 Wavelet Packets -- 8.1.1 Wavelet Packet Tree -- 8.1.2 Time-Frequency Localization -- 8.1.3 Particular Wavelet Packet Bases -- 8.1.4 Wavelet Packet Filter Banks -- 8.2 Image Wavelet Packets -- 8.2.1 Wavelet Packet Quad-Tree -- 8.2.2 Separable Filter Banks -- 8.3 Block Transforms -- 8.3.1 Block Bases 8.3.2 Cosine Bases -- 8.3.3 Discrete Cosine Bases -- 8.3.4 Fast Discrete Cosine Transforms -- 8.4 Lapped Orthogonal Transforms -- 8.4.1 Lapped Projectors -- 8.4.2 Lapped Orthogonal Bases -- 8.4.3 Local Cosine Bases -- 8.4.4 Discrete Lapped Transforms -- 8.5 Local Cosine Trees -- 8.5.1 Binary Tree of Cosine Bases -- 8.5.2 Tree of Discrete Bases -- 8.5.3 Image Cosine Quad-Tree -- 8.6 Exercises -- Chapter 9. Approximations in Bases -- 9.1 Linear Approximations -- 9.1.1 Sampling and Approximation Error -- 9.1.2 Linear Fourier Approximations -- 9.1.3 Multiresolution Approximation Errors with Wavelets -- 9.1.4 Karhunen-Loève Approximations -- 9.2 Nonlinear Approximations -- 9.2.1 Nonlinear Approximation Error -- 9.2.2 Wavelet Adaptive Grids -- 9.2.3 Approximations in Besov and Bounded Variation Spaces -- 9.3 Sparse Image Representations -- 9.3.1 Wavelet Image Approximations -- 9.3.2 Geometric Image Models and Adaptive Triangulations -- 9.3.3 Curvelet Approximations -- 9.4 Exercises -- Chapter 10. Compression -- 10.1 Transform Coding -- 10.1.1 Compression State of the Art -- 10.1.2 Compression in Orthonormal Bases -- 10.2 Distortion Rate of Quantization -- 10.2.1 Entropy Coding -- 10.2.2 Scalar Quantization -- 10.3 High Bit Rate Compression -- 10.3.1 Bit Allocation -- 10.3.2 Optimal Basis and Karhunen-Loève -- 10.3.3 Transparent Audio Code -- 10.4 Sparse Signal Compression -- 10.4.1 Distortion Rate and Wavelet Image Coding -- 10.4.2 Embedded Transform Coding -- 10.5 Image-Compression Standards -- 10.5.1 JPEG Block Cosine Coding -- 10.5.2 JPEG-2000 Wavelet Coding -- 10.6 Exercises -- Chapter 11. Denoising -- 11.1 Estimation with Additive Noise -- 11.1.1 Bayes Estimation -- 11.1.2 Minimax Estimation -- 11.2 Diagonal Estimation in a Basis -- 11.2.1 Diagonal Estimation with Oracles -- 11.2.2 Thresholding Estimation -- 11.2.3 Thresholding Improvements 3.4.1 Two-Dimensional Sampling Theorems -- 3.4.2 Discrete Image Filtering -- 3.4.3 Circular Convolutions and Fourier Basis -- 3.5 Exercises -- Chapter 4. Time Meets Frequency -- 4.1 Time-Frequency Atoms -- 4.2 Windowed Fourier Transform -- 4.2.1 Completeness and Stability -- 4.2.2 Choice of Window -- 4.2.3 Discrete Windowed Fourier Transform -- 4.3 Wavelet Transforms -- 4.3.1 Real Wavelets -- 4.3.2 Analytic Wavelets -- 4.3.3 Discrete Wavelets -- 4.4 Time-Frequency Geometry of Instantaneous Frequencies -- 4.4.1 Analytic Instantaneous Frequency -- 4.4.2 Windowed Fourier Ridges -- 4.4.3 Wavelet Ridges -- 4.5 Quadratic Time-Frequency Energy -- 4.5.1 Wigner-Ville Distribution -- 4.5.2 Interferences and Positivity -- 4.5.3 Cohen's Class -- 4.5.4 Discrete Wigner-Ville Computations -- 4.6 Exercises -- Chapter 5. Frames -- 5.1 Frames and Riesz Bases -- 5.1.1 Stable Analysis and Synthesis Operators -- 5.1.2 Dual Frame and Pseudo Inverse -- 5.1.3 Dual-Frame Analysis and Synthesis Computations -- 5.1.4 Frame Projector and Reproducing Kernel -- 5.1.5 Translation-Invariant Frames -- 5.2 Translation-Invariant Dyadic Wavelet Transform -- 5.2.1 Dyadic Wavelet Design -- 5.2.2 Algorithme à Trous -- 5.3 Subsampled Wavelet Frames -- 5.4 Windowed Fourier Frames -- 5.4.1 Tight Frames -- 5.4.2 General Frames -- 5.5 Multiscale Directional Frames For Images -- 5.5.1 Directional Wavelet Frames -- 5.5.2 Curvelet Frames -- 5.6 Exercises -- Chapter 6. Wavelet Zoom -- 6.1 Lipschitz Regularity -- 6.1.1 Lipschitz Definition and Fourier Analysis -- 6.1.2 Wavelet Vanishing Moments -- 6.1.3 Regularity Measurements with Wavelets -- 6.2 Wavelet Transform Modulus Maxima -- 6.2.1 Detection of Singularities -- 6.2.2 Dyadic Maxima Representation -- 6.3 Multiscale Edge Detection -- 6.3.1 Wavelet Maxima for Images -- 6.3.2 Fast Multiscale Edge Computations -- 6.4 Multifractals 11.3 Thresholding Sparse Representations -- 11.3.1 Wavelet Thresholding -- 11.3.2 Wavelet and Curvelet Image Denoising -- 11.3.3 Audio Denoising by Time-Frequency Thresholding -- 11.4 Nondiagonal Block Thresholding -- 11.4.1 Block Thresholding in Bases and Frames -- 11.4.2 Wavelet Block Thresholding -- 11.4.3 Time-Frequency Audio Block Thresholding -- 11.5 Denoising Minimax Optimality -- 11.5.1 Linear Diagonal Minimax Estimation -- 11.5.2 Thresholding Optimality over Orthosymmetric Sets -- 11.5.3 Nearly Minimax with Wavelet Estimation -- 11.6 Exercises -- Chapter 12. Sparsity in Redundant Dictionaries -- 12.1 Ideal Sparse Processing in Dictionaries -- 12.1.1 Best M-Term Approximations -- 12.1.2 Compression by Support Coding -- 12.1.3 Denoising by Support Selection in a Dictionary -- 12.2 Dictionaries of Orthonormal Bases -- 12.2.1 Approximation, Compression, and Denoising in a Best Basis -- 12.2.2 Fast Best-Basis Search in Tree Dictionaries -- 12.2.3 Wavelet Packet and Local Cosine Best Bases -- 12.2.4 Bandlets for Geometric Image Regularity -- 12.3 Greedy Matching Pursuits -- 12.3.1 Matching Pursuit -- 12.3.2 Orthogonal Matching Pursuit -- 12.3.3 Gabor Dictionaries -- 12.3.4 Coherent Matching Pursuit Denoising -- 12.4 l1 Pursuits -- 12.4.1 Basis Pursuit -- 12.4.2 l1 Lagrangian Pursuit -- 12.4.3 Computations of l1 Minimizations -- 12.4.4 Sparse Synthesis versus Analysis and Total Variation Regularization -- 12.5 Pursuit Recovery -- 12.5.1 Stability and Incoherence -- 12.5.2 Support Recovery with Matching Pursuit -- 12.5.3 Support Recovery with l1 Pursuits -- 12.6 Multichannel Signals -- 12.6.1 Approximation and Denoising by Thresholding in Bases -- 12.6.2 Multichannel Pursuits -- 12.7 Learning Dictionaries -- 12.8 Exercises -- Chapter 13. Inverse Problems -- 13.1 Linear Inverse Estimation -- 13.1.1 Quadratic and Tikhonov Regularizations 13.1.2 Singular Value Decompositions |
| Title | A wavelet tour of signal processing : the sparse way |
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