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

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.

application to JPEG 2000 and MPEG-4

- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface to the Sparse Edition
- ACKNOWLEDGMENTS
- Notations
- Chapter 1: Sparse Representations
- Chapter 2: The Fourier Kingdom
- Chapter 3: Discrete Revolution
- Chapter 4: Time Meets Frequency
- Chapter 5: Frames
- Chapter 6: Wavelet Zoom
- Chapter 7: Wavelet Bases
- Chapter 8: Wavelet Packet and Local Cosine Bases
- Chapter 9: Approximations in Bases
- Chapter 10: Compression
- Chapter 11: Denoising
- Chapter 12: Sparsity in Redundant Dictionaries
- Chapter 13: Inverse Problems
- APPENDIX: Mathematical Complements
- Bibliography
- Index