A Wavelet Tour of Signal Processing: The Sparse Way 3rd Edition by Stephane Mallat (PDF)

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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 UniversityThe 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 toolboxNew 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 exercisesA 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.

User’s Reviews

Editorial Reviews: Review “There is no question that this revision should be published. 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 Review The undisputed reference on wavelet signal processing by the key pioneer in the field – Stéphane Mallat. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has broad coverage of wavelet methods in signal processing, compression, image processing, and more, with clearly explained mathematics behind the applications. I am a pure mathematician by training, and this book is the Bible so far as I am concerned for a clear explanation of applications via rigorous mathematics. Sparse methods are the unifying theme of the book. Sparse methods allow for concise representations for applications. I could not recommend a better book for wavelets with signal processing applications, especially for readers who want or need a rigorous presentation of the mathematics of wavelets

⭐I own now all three editions of this work (!) Although initially you have to regard the cost of “upgrading” each addition as painful, the truth is each edition has provided significant contributions to this rapidly expanding field of study, and these advances are presented in the considered, rigorous, and systematic way that has come to characterize S. Mallat’s volumes. As is inevitable there are editorial corrections in formulae; however, I have come to view them as “exercises” to confirm that I am following the lines of reasoning in the development.The pending challenge for subsequent editions: how do you accommodate the fellow traveler on this adventure by providing the chapters on new material and revision of perspectives on current material without bearing the burden of repurchasing the (now voluminous) quantity of original material? Perhaps an electronic version would provide the potential for such flexibility. I think the question needs to be addressed, because this work is quickly becoming the “le Bourbaki” for signal processing.

⭐This is an advanced highly mathematical treatement of wavelets. Unlike Fourier transforms, wavelet decompositions of signals preserve both scale (the inverse of frequency) and position. The book presents an unusually thorough treatment of diverse practical wavelet applications. For readers familiar with MATLAB, all the examples in the book can be reproduced with MATLAB “workouts.” The actively supported WAVELAB850 library containing the workouts and supporting utilities can be downloaded on the internet free. The author of the book Stephan Mallat was a key contributor to the development of wavelet theory. His style of presentation is demanding but worth the effort. The book is a nice complement to the more reader friendly text book “Wavelets and Filter Banks” by Gilbert Strang and truong Nguyen.

⭐The information is presented very briefly and very abstractly. It is difficult to understand what the book is saying unless you are already familiar with the material. I had a very difficult time learning from this text; I am very familiar with DSP but new to frames, wavelets, etc.That being said, if you are looking for a good reference book, the concise nature of this book may be a good thing.

⭐I bought this book based on the author Mallat being a big name in the field of wavelets. I was trying to use it as self-study as an introduction to wavelets. The style of writing is like a stream of conscienceness. I’m guessing the book is meant as a reference for experts in the field. If you are looking for an introduction, this is not the book.

⭐I read this and still really don’t know a darn thing about using wavelets. Not the place for a PhD in physics to learn how to process real data with wavelets..

⭐* Updated December 2011 *

⭐is a comprehensive treatment. Mallat’s storied text is designed to cover the gamut of various signal processing shorthand methods, with brief discussion of their applications and inter-relationships.Mallat’s approach is not a “one-size-fits-all” solution. He does not attempt to formulate a universal method. Instead, he gives us a tour of the key methods and delves into each one based upon its relevance for a given application.THE TOURIncluded is a hodgepodge of subjects related to signal processing:- Computational Harmonic Analysis – Fourier and wavelet transforms (continuous, discrete, etc.)- Approximations – linear, sparse non-linear, with nice treatments of sampling and approximation error- Time frequency dictionaries, with use of the Heisenberg Uncertainty theorem and Heisenberg boxes- Wavelet bases (orthogonal, discrete, bi-orthogonal, etc.) and filter banks- Frames and Riesz bases- Diagonal inverse estimation- Compression- Denoising- Sparse decomposition in redundant dictionaries- Signal recovery (inverse methods)- An appendix of mathematical functions provided without proofTHE PROPER USE & THE PROPER AUDIENCEBecause of the dearth of comprehensive texts on this topic, some may look to this book to be all things to all people. That it is not. While I do agree that this book may have some weaknesses as a text book, the breadth and depth of the material is too great to be overshadowed.As a reference text, this work covers all the bases and is a good entry point into more specialized texts. But more than a reference book, this text is a practical cookbook that is ideal for those actually working on signal processing.Those looking for a “teach yourself signal-processing” text or even a pre-packaged course book should use this book in concert with other more specialized texts, or start with a more basic introduction altogether.The “Mathematical Complements” appendix provides a short introduction to theorems that the reader should research further if they don’t already have a good understanding of the topic.The chapter on Fourier transforms, chapter 2, is a very good treatment of the subject. And the follow-up chapter covers discrete sampling in a way that is both accessible and interesting. These two chapters provide a good foundation for academic study, and seem to my untrained eye to be usable as a part of a graduate course curriculum.Finally, the bibliography contains tons of references to articles and texts that can be leveraged for a course of study. So while this book may not be ideal as a ready-to-consume course text, it certainly provides the foundation and direction needed for a student to delve deeper into the topic.EXERCISES, ALGORITHMS & TOOLSThe exercises at the end of each chapter are provided without solution. However, there is a companion website for instructors as some solutions are provided for students on-line.Of note is that WaveLab is used to implement the examples in the book, and it can be used to recreate them. MatLab is thus a necessary complement to this text for those wishing to work through the examples at the end of each chapter in a rigorous academic method.CONCLUSIONMallat is very good at covering the multiple steps in a process in a way that is logical and concise. But the vast amount of information he imparts, as well as his penchant for not belaboring the intricacies of each transform, may leave some wanting for more.While I was initially seduced into a critical view of this material, after re-reading it I am instead inclined to be more impressed and appreciative. This book is not exhaustive and it is not a tool for all situations and all people. But if you focus on it for what it is instead of what it isn’t, it is a valuable and impressive work.The relevance of this material is broad, covering audio and image processing as well as scientific analysis. I am happy that I had an opportunity to be introduced to this work. I look forward to studying this topic more deeply.

⭐A very good book

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