Customer Reviews

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

5 star:		(12)
4 star:		(9)
3 star:		(2)
2 star:		(3)
1 star:		(1)

 

 

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.

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 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....

Mallat's book is by now a classic, which I have always used in classes
as the main reference text for the field. It combines complete mastery
of the subject (Mallat himself has been one of the subject's main contributors)
with an exceptionally clear style and tutorial talent. The book is easily suitable both
for introductory and advanced graduate courses, and its entertaining style makes it
particularly attractive for self-study as well.

The third edition is a welcome and timely update. It gives a general
perspective on sparse representations for signal and image processing,
which have become an important approach to develop new
signal processing algorithms. It includes the most recent l1
minimization algorithms and applications to compressive sensing,
super-resolution estimation for inverse problems, and source
separation. A web site [...] also provides on-line
software to reproduce the figures, and updates on typos (very few
actually). Most highly recommended for anyone with interest in modern
signal processing.

I picked this book up after talking with some of the DSP guys at my office on what was the best book to get started in field with. Almost all of them had some version of this text on their desk or knew where to get their hands on one. All of them spoke very highly of it and I was excited to find a new edition copy.

Having looked through the book and read the sections relating to stuff I do or have done I have a few observations:

This is an awesome reference book if you remember something from class a few years ago and need a refresher.

Each chapter has a list of questions at the end, sadly I can't find a list of answers in the book or available online.

This is not a book for a beginner. If you don't have a background in the subject or a good source to ask questions of I don't think you'll be able to get much out of it.

I would have benefited from some real time examples either on a CD/website for some of the concepts to bridge the gap between text and application. The book has numerous figures showing various levels of processing that would make a great java applet example. If I was taking a college class I'm sure this would be more accessible, trying to study on my own at home and work it's hard to come by examples that illustrate the cases from the text.

All in all it's an amazing text and reference, just not for the newbie.

Since its introduction, "a Wavelet tour of signal processing" is considered as the best book in this crowded field of research. I have used it every year since the introduction of the first edition. in my wavelet course. The students love it and they look at it as the "bible". It is also used as the main reference book for my M.Sc and Ph.D students who are doing theses on wavelet and its many derivatives. The book covers in depth all aspects of wavelet (theory and applications). It provides in crystal clear presentation all the aspects that undergraduate, graduate and researchers in every level need to have.
S. Mallat is doing what others do not do: he continues to update the book to reflect this dynamic field of research. Since this is an exciting evolving field of research, its dynamic evolution takes it every couple of years into a different fascinating direction. Using wavelets to achieve sparse representation is the new state-of-the-art technology. This new edition titled "A wavelet Tour of Signal Processing: The sparse way" upgrades innovatively the second edition of "A wavelet Tour of Signal Processing". It enhances substantially the second edition from 1998 by adding more applications and new avenues of research into the book.
The second edition of 1999 is considered by many as the best book and its presence in each library is a must. The newer edition titled "a Wavelet tour of signal processing: The sparse way" is better in every parameter than the second edition from 1998. Most of the main chapters from the second edition (such as Chapters II,III,IV, V, VI, VII, VIII and IX) appear and upgraded in the newer edition. S. Mallat did here the correct choice. These chapters are needed for deep understanding of wavelet signal processing. The newer edition adds to several different chapters sparse representations with bases, sparse time-frequency representations, sparse signal estimation, spare compression, dictionary representation and geometric sparse representation .
The book is intended as a graduate-level textbook. Its clarity and great exposition makes it suitable for advanced undergraduate students and for courses on signal processing and wavelets that are currently being taught in advanced undergraduate courses. I adopt it for undergraduate and graduate courses with huge success.
The exercises are very challenging and solving them is a good sign of deep understanding of the material.
In summary, the 2009 newer edition contains a wealth of information for students and researchers. It is highly recommended to be adopted as the graduate text for wavelet courses and wavelet research.

And Mallat did it again. In no time he came up with a revised version of his top-ranked book 'A Wavelet Tour of Signal Processing' including the new subject of sparsity. I already own a copy for my own personal reference, and ordered one for our library at the math department.

The writing of the book is superb! Mallat again improved his already masterpiece of writing - Let me quote Prof. Benedetto (Founding Editor of the Journal of Fourier Analysis and Applications and Director of the Norbert Wiener Center for Harmonic Analysis and Applications), who wrote a review about 10 books on wavelets. This is what he had to say about (the first edition of) Mallat's book:

"A Wavelet Tour of Signal Processing by Mallat will join the ranks of Meyers (Ondelettes et Op'erateurs) and Daubechies (Ten Lectures on Wavelets) as a central, inclusive, monumental, and seminal treatise on wavelet theory. (Waxing rhapsodic, the qualifier "millenial" also occurred to me.) At the risk of making arbitrary distinctions about categories whose very existence is questioned in certain company, Meyer's treatise is pure mathematics, Daubechies' treatise is applied mathematics, and Mallat's treatise is mathematical signal processing. They are all fundamental books in mathematics. Mallat has been involved with many of the most innovative wavelet ideas, both theoretical and applicable, from the late 1980s with the now classical Mallat-Meyer MRA theory and algorithm... His book reflects his fundamental ideas at the origin of the subject as well as his scientific point of view in terms of digital image processing. It also reflects a catholic point of view by making a serious multidisciplinary exposition.
Mallat has not only written a treatise, but also an excellent graduate text for students in computer science, electrical engineering, and mathematics."

I cannot agree more with these words and definitely believe that this new edition is even more suited than the earlier ones to be used as a textbook. Moreover, with the inclusion of the new point of view of sparsity, it gives the topic a new twist.

It is also a fantastic reference - and will probably soon join the `worn' first edition on the shelves of most of us working in any of the areas covered by the book!

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 already had the second edition of this work by Stephane Mallot -- which I appreciated as the best introduction to some main applied areas of wavelets [and cousins]. My main interest in wavelet-type mathematics is in what relates to wave-dynamics for applied and theoretical physics. I also have a general curiosity about wavelets [and cousins] via their variform usage in other physical sciences and signal-processing. I view this work as the best detailed presentation of wavelets [and cousins] in general. "A Wavelet Tour of Signal Processing" is very well-organized into an entirely coherent "Wavelet Tour" that can be followed with moderate effort.

Stephane Mallot is clear and rational, and does not have much of a specialist-bias [despite the modest claim of this book's title], building-up wavelet-type mathematics [and applications] step-by-step in classic academic format. For example, both analog and discrete transform theory is developed after a general introduction to such transforms, including Fourier-related ones of course. This involves orthogonal and orthonormal bases, dyadics and representations, naturally. Those remain important for physics -- such as with related Hilbert-space mathematics. Quantum wave-dynamic wave-packet theory has been one of the main inspirations of wavelet-type mathematics [and vice versa].

But, this newer edition, "A Wavelet Tour of Signal Processing -- The Sparse Way", has a refocusing via sparse representations and processing. The topics so well-covered in the earlier edition are still well-done. But, "The Sparse Way" enhances the previous topics -- and seems to unify the whole presentation of wavelet-related topics -- equally useful for theory and applications. Likely usage may include grid, media, shock and scale matching-and-smoothing across such boundary-layer topological zones -- via sparse-processing "dictionaries" of redundant, thereby adaptable, wave-forms -- rather than rigid [exact a priori] orthonormal base-sets which can be tricky [if not impossible] in such cases. I have always liked a "Least Action" approach [when possible] -- minimizing energy-and-time to reach an optimum. "The Sparse Way" seems very in tune with that -- and is likely just a better viewpoint for understanding as well as calculation. Bravo Stephane Mallot +++

Signal processing is a rapid evolving field.
When wavelets erupted in the eighties, they created a big revolution in
most of the applications in the digital world. The theory developed so fast that
it was sometimes difficult to take advantage of all the benefits of this new tool.
The first edition of Mallat's book, written by one of the leaders in the field
made the perfect match between the theory and the applications.
A complete generation learned from those pages why wavelets were useful
and how they should be applied. Very soon a second edition appeared,
to catch up with new developments and applications.
Today, more than ten years after the second edition, wavelets have become
a known tool that is in the bag of every scientist.
The search for sparse representations in redundant dictionaries is in the scene
today.
Sparsity has become the central topic and a lot of development in this emergent
area is again spreading fast and disseminating in hundreds of articles.
And again this third edition of Mallat's book, one more time, comes at the right
time, to provide a clear picture of the impact of this new field in signal processing.

This is not an old edition plus some addendum's. Most of the book
has been rewritten to reflect the new point of view. And this is done with
the same peaceful and nice style that characterized the other editions.
Fortunately, nothing important of the old material has been sacrificed.