by Stephane Mallat
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Product Description
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École
Polytechnique in Paris.
Key Features
* Provides a broad perspective on the principles and applications of transient signal processing with wavelets
* Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms
* Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection,
multifractal analysis, and time-varying frequency measurements
* Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet
* Content is accessible on several level of complexity, depending on the individual reader's needs
New to the Second Edition
* Optical flow calculation and video compression algorithms
* Image models with bounded variation functions
* Bayes and Minimax theories for signal estimation
* 200 pages rewritten and most illustrations redrawn
* More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
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Average Customer Review:
0 of 0 people found the following review helpful:
 Great Book, 2007-03-20
A great tool for Harmonic Analysis. The book is really well written, a most read for any one who is interested in the area of wavelets, S.P. or harmonic analysis.
5 of 5 people found the following review helpful:
The most universal treatment of the subject, 2005-06-08
I say universal because this book would appeal to engineers, computer scientists, and mathematicians alike. Mallat was particularly successful to present the topic in a sufficiently rigorous way but without losing sight of the practical and more intuitive side. The presentation comprises the mathematical and the signal processing viewpoints simultaneously. The wavelet field is very vast by now with several subfields. In this respect, Mallat made a great selection of topics in this book. There is a chapter on estimation which offers great review material and pretty much the state-of-the art on signal estimation over a wavelet basis. The chapter on approximation is particularly useful for those who are not well versed in approximation theory and thus are unable to understand other treatments. If you're interested in learning wavelet theory to solve practical problems such as image compression, signal estimation, etc, this is the book to have.
7 of 11 people found the following review helpful:
 The worst textbook I have ever seen, 2004-02-12
I just finished Chapter 3 of this book, but I have had enough of it. Conceptions about Fourier Transform are not clear at all. And the most unbearable thing is that, there are many printing errors which may lead to misunderstanding.
3 of 7 people found the following review helpful:
Algorithms and much more!, 2002-07-10
The subject of wavelets has many facets, --infinite in all directions;-- some of the more exciting sides of the subject
are algorithmic, and the underlying mathematical principles are both simple and powerful. Stephane Mallat's great, and readable, book, in both of its editions, brings
this out wonderfully!
23 of 25 people found the following review helpful:
A bold approach to wavelet transforms that simplifies, 2002-04-24
This is an outstanding tour through the field of wavelet decompositions of both continuous and discrete signals. It employs the formalism of Hilbert space, instead of linear algebra. This is important because the power of this formalism yields insights into the subject matter that are practically impossible in linear algebra. The formalized approach allows a wide variety of subjects to be placed on a common basis (no pun intended). For example, the transition of the treatment of the Fourier transform into Hilbert space, brings to bear the powerful guns of that space (such guns as inner product and completeness), and allows for a truly elegant proof of the Parseval and Plancherel formulas.
Parseval's theorem, simply stated, is that the inner products in Hilbert space are conserved by the Fourier transform. How simple. Linear algebra approaches cannot hope to make things this simple.
Proof of the General Sampling Theorem is equally elegant; it is shown that the projection of the function to be decomposed onto a basis function gives the discrete spectral coefficient.
Readers will also enjoy the treatment of windowed Fourier transforms and frames.
I should add a note about the style of the treatise. This treatise is not ordinary. It consistently uses very precise and carefully defined symbology. Contrary to popular belief, this makes the text easier to read, not more difficult. Once the reader understands the symbol set being used (they are all defined in the front of the text), even the proofs are tractable. Yes, I said proofs. That is another aspect of the text. There are proofs embedded in the text, without loss of continuity or clarity. Proofs are necessary to a good understanding of the subject matter. The formalism of theorems, lemmas and propositions makes the conclusions understandable, because the theorems, lemmas and propositions supporting the conclusions are identifiable.
I applaud the author for his approach and recommend that other text book writers use the same approach.
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