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ISBN 10: 0123743702
ISBN 13: 978-0123743701
Author: Stephane Mallat
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 University
The 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.
A Wavelet Tour of Signal Processing 3rd Table of contents:
Chapter 1: Sparse Representations
1.1: COMPUTATIONAL HARMONIC ANALYSIS
1.2: APPROXIMATION AND PROCESSING IN BASES
1.3: TIME-FREQUENCY DICTIONARIES
1.4: SPARSITY IN REDUNDANT DICTIONARIES
1.5: INVERSE PROBLEMS
1.6: TRAVEL GUIDE
Chapter 2: The Fourier Kingdom
2.1: LINEAR TIME-INVARIANT FILTERING
2.2: FOURIER INTEGRALS
2.3: PROPERTIES
2.4: TWO-DIMENSIONAL FOURIER TRANSFORM
2.5: EXERCISES
Chapter 3: Discrete Revolution
3.1: SAMPLING ANALOG SIGNALS
3.2: DISCRETE TIME-INVARIANT FILTERS
3.3: FINITE SIGNALS
3.4: DISCRETE IMAGE PROCESSING
3.5: EXERCISES
Chapter 4: Time Meets Frequency
4.1: TIME-FREQENCY ATOMS
4.2: WINDOWED FOURIER TRANSFORM
4.3: WAVELET TRANSFORMS
4.4: TIME-FREQUENCY GEOMETRY OF INSTANTANEOUS FREQUENCIES
4.5: QUADRATIC TIME-FREQUENCY ENERGY
4.6: EXERCISES
Chapter 5: Frames
5.1: FRAMES AND RIESZ BASES
5.2: TRANSLATION-INVARIANT DYADIC WAVELET TRANSFORM
5.3: SUBSAMPLED WAVELET FRAMES
5.4: WINDOWED FOURIER FRAMES
5.5: MULTISCALE DIRECTIONAL FRAMES FOR IMAGES
5.6: EXERCISES
Chapter 6: Wavelet Zoom
6.1: LIPSCHITZ REGULARITY
6.2: WAVELET TRANSFORM MODULUS MAXIMA
6.3: MULTISCALE EDGE DETECTION
6.4: MULTIFRACTALS
6.5: EXERCISES
Chapter 7: Wavelet Bases
7.1: ORTHOGONAL WAVELET BASES
7.2: CLASSES OF WAVELET BASES
7.3: WAVELETS AND FILTER BANKS
7.4: BIORTHOGONAL WAVELET BASES
7.5: WAVELET BASES ON AN INTERVAL
7.6: MULTISCALE INTERPOLATIONS
7.7: SEPARABLE WAVELET BASES
7.8: LIFTING WAVELETS
7.9: EXERCISES
Chapter 8: Wavelet Packet and Local Cosine Bases
8.1: WAVELET PACKETS
8.2: IMAGE WAVELET PACKETS
8.3: BLOCK TRANSFORMS
8.4: LAPPED ORTHOGONAL TRANSFORMS
8.5: LOCAL COSINE TREES
8.6: EXERCISES
Chapter 9: Approximations in Bases
9.1: LINEAR APPROXIMATIONS
9.2: NONLINEAR APPROXIMATIONS
9.3: SPARSE IMAGE REPRESENTATIONS
9.4: EXERCISES
Chapter 10: Compression
10.1: TRANSFORM CODING
10.2: DISTORTION RATE OF QUANTIZATION
10.3: HIGH BIT RATE COMPRESSION
10.4: SPARSE SIGNAL COMPRESSION
10.5: IMAGE-COMPRESSION STANDARDS
10.6: EXERCISES
Chapter 11: Denoising
11.1: ESTIMATION WITH ADDITIVE NOISE
11.2: DIAGONAL ESTIMATION IN A BASIS
11.3: THRESHOLDING SPARSE REPRESENTATIONS
11.4: NONDIAGONAL BLOCK THRESHOLDING
11.5: DENOISING MINIMAX OPTIMALITY
11.6: EXERCISES
Chapter 12: Sparsity in Redundant Dictionaries
12.1: IDEAL SPARSE PROCESSING IN DICTIONARIES
12.2: DICTIONARIES OF ORTHONORMAL BASES
12.3: GREEDY MATCHING PURSUITS
12.4: I1 PURSUITS
12.5: PURSUIT RECOVERY
12.6: MULTICHANNEL SIGNALS
12.7: LEARNING DICTIONARIES
12.8: EXERCISES
Chapter 13: Inverse Problems
13.1: LINEAR INVERSE ESTIMATION
13.2: THRESHOLDING ESTIMATORS FOR INVERSE PROBLEMS
13.3: SUPER-RESOLUTION
13.4: COMPRESSIVE SENSING
13.5: BLIND SOURCE SEPARATION
13.6: EXERCISES
APPENDIX: Mathematical Complements
A.1: FUNCTIONS AND INTEGRATION
1.2: BANACH AND HILBERT SPACES
A.3: BASES OF HILBERT SPACES
A.4: LINEAR OPERATORS
A.5: SEPARABLE SPACES AND BASES
A.6: RANDOM VECTORS AND COVARIANCE OPERATORS
A.7: DIRACS
Bibliography
Index
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