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A Wavelet Tour of Signal Processing, 3rd Edition

Book Description

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.

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 students

New 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 exercises

A 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 its
    application to JPEG 2000 and MPEG-4
  • Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox
  • Balances presentation of the mathematics with applications to signal processing
  • Table of Contents

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