A Wavelet Tour of Signal Processing

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 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

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.

Mallat's 800 page tome here is a very encyclopedic coverage of contemporary wavelet techniques and tricks. It takes the form of a "traditional" textbook: While there are some very brief refreshers on linear algebra, calculus, and statistics in an appendix, make no mistake -- there's a lot of advanced mathematics in the book, beyond what many (probably even the majority) of engineers learn during their undergraduate years. Additionally, while there are plenty of good "homework" problems at the end of each chapter, no solutions are provided. This all has several implications: -- This isn't really the book you want for self-study if you aren't already familiar with wavelets. I'd suggest something like "A Primer on Wavelets and Their Scientific Applications" by Walker for that. -- It can be a fine book for a college class on wavelets. I suspect the best approach would be for an instructor to use his own notes, assign reading for reinforcement, and problems from the end of each chapter. The deal here is that, in many cases, making good use of the results doesn't always require a full understanding of the mathematical underpinnings of the subject, and an instructor can guide students around what matters if they just want to apply the results (most students) vs. obtaining a deeper understanding that could be used to conduct new research or whatever (the very occasional student). -- It is, of course, a fine reference for anyone already working in the field and familiar with the subject. Mallat is a pretty brilliant guy.Note that Google Books has a copy of the earlier 2nd edition on-line; this might be handy for some people.

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.

A very good book