A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way [Hardcover]

Stephane Mallat (Author)

Book Description

Publication Date: December 25, 2008 | ISBN-10: 0123743702 | ISBN-13: 978-0123743701 | Edition: 3

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
* Companion website for instructors and selected solutions and code available for students

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.

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

Balances presentation of the mathematics with applications to signal processing

Editorial Reviews

Review

"This graduate-level textbook presents an excellently written, comprehensive survey of all major concepts, techniques, and applications of sparse representations which play a key role in signal processing" -- Manfred Tasche (Rostock), Zentralblatt MATH

"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

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.

Product Details

• Hardcover: 832 pages
• Publisher: Academic Press; 3 edition (December 25, 2008)
• Language: English
• ISBN-10: 0123743702
• ISBN-13: 978-0123743701
• Product Dimensions: 9.4 x 7.4 x 1.8 inches
• Shipping Weight: 3.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (27 customer reviews)
• Amazon Best Sellers Rank: #335,159 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

23 of 26 people found the following review helpful:

2.0 out of 5 stars looks deceive, March 19, 2009

By 

Alex Gittens "the limiter" (Pasadena, CA USA) - See all my reviews
(REAL NAME)   

This review is from: A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way (Hardcover)

The main attraction of Mallat's book is the wide range of the material it covers, but I feel that this feature is more than outweighed by its multitude of failings. Having used it as a textbook in an applied math course, I'm intimately acquainted with those failings.

At first glance, this is an impressive work: it covers everything from Fourier analysis (in L1,L2,distributions,discrete) and the sampling theorem, to frames and Riesz bases, to the continuous wavelet transform, to the discrete wavelet transform, to wavelets on intervals, to wavelets via lifting, and talks about using wavelets to characterize regularity and fractal signals-- and that's just what I've looked at so far--... so it's quite encyclopedic. Perhaps that is why the book is unpalatable; it has more the character of an information dump than the leisurely tour suggested by the title.

The order of the presentation is horribly confusing: the results on frames, wavelets, and Riesz bases are presented in a mishmash that makes it hard to keep in mind the logical order of their development. Lots of important details aren't mentioned, or are given short shrift, e.g. the properties of the discrete Fourier transform are not enumerated the way those of the continuous Fourier transform are, so you must verify that analogues hold. In particular, little to no attention is given to numerical implementation of the algorithms-- e.g. he shows spectrograms and periodograms without saying how they are generated-- and when some lip service is paid to these issues, he is sparse on the details, and confusing. This is particularly annoying because the gaps in your knowledge don't show until you start trying to program these algorithms.

All of these failings pale in comparison to the poor editing: this book *abounds* in typos, both subtle and obvious. You simply can't take anything it states at face value.

My suggestion: pick an area you're interested in (frames, dyadic wavelets, second generation wavelets, numerical implementations of wavelets, etc.) and find a more appropriate specialized book.

4 of 4 people found the following review helpful:

4.0 out of 5 stars Pretty encyclopedic these days, September 3, 2009

By 

Joel Kolstad "Zimbo" (Portland, OR USA) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way (Hardcover)

(What's this?)

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.

5 of 6 people found the following review helpful:

1.0 out of 5 stars Totally unorganized, and imossible to comprehend, May 8, 2010

By 

OM "theRealPharoah" (Boston, MA) - See all my reviews

This review is from: A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way (Hardcover)

This book may be okay as a reference book for someone who already has a PhD in Mathematics and is very familiar with function spaces and decompositions.

The author has truly advance the state of the art with his groundbreaking papers in wavelets/filter banks, but he has no business writing a book.

I have been trying to use this as a text book for my image processing with wavelets class and it has given my an enormous amounts of pain an agony. I can not find a single topic that I can read and understand from his book, so I had to look at other references.

In chapter 5 he keeps referring to the fact that you have to read chapter 7 first --- why not reverse the order then?

In chapter 1, he would suddenly start referring to advanced concepts which he has not yet talked about.

Not to mention the large number of typos.

what a mess....