This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics "Mallat has not only written a treatise, but also an excellent graduate text for students in computer science, electrical engineering, and mathematics" -- John J. Benedetto, SIAM review This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets. - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms. - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements. - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet. - Content is accessible on several level of complexity, depending on the individual reader's needs. - Reviews Fourier analysis and elementary signal processing. - Introduces windowed Fourier transforms, continuous wavelet transforms, and Wigner-Ville transforms. - Explains the construction of frames, wavelet orthogonal and biorthogonal bases, wavelet packet and local cosine bases. - Covers basic approximation theory with applications to signal estimation and transform coding. 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.