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

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.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

Autorentext

Stéphane Mallat is a Professor in the Computer Science Department of the Courant Institute of Mathematical Sciences at New York University,and a Professor in the Applied Mathematics Department at ccole Polytechnique, Paris, France. He has been a visiting professor in the ElectricalEngineering Department at Massachusetts Institute of Technology and in the Applied Mathematics Department at the University of Tel Aviv. Dr. Mallat received the 1990 IEEE Signal Processing Society's paper award, the 1993 Alfred Sloan fellowship in Mathematics, the 1997Outstanding Achievement Award from the SPIE Optical Engineering Society, and the 1997 Blaise Pascal Prize in applied mathematics, from theFrench Academy of Sciences.

Inhalt

Preface; Notations; Sparse Representations; Fourier Kingdom; Discrete Revolution; Time Meets Frequency; Frames; Wavelet Zoom; Wavelet Bases; Wavelet Packet and Local Cosine Bases; Approximations in Bases; Compression; Denoising; Sparse in Redundant Dictionaries; Mathematical Complements