A Wavelet Tour of Signal Processing: The Sparse Way
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"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
Product Description
'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.
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27 reviews
24 of 27 people found the following review helpful
looks deceive
19 Mar 2009
Format: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.
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.
7 of 8 people found the following review helpful
Totally unorganized, and imossible to comprehend
8 May 2010
Format: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....
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....
4 of 4 people found the following review helpful
Pretty encyclopedic these days
3 Sep 2009
Format:Hardcover|Amazon Vine™ Review
(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.
-- 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.
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