'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. This book 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 are available for students. The features new in this edition include: 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; and, 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 Ecole 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. The 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.

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
Chapter10 Compression
Chapter11 Denoising
Chapter12 Sparsity in Redundant Dictionaries
Chapter13 Inverse Problems