A Wavelet Tour of Signal Processing: The Sparse Way, 3rd Edition
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
By Stephane Mallat
* Publisher: Academic Press
* Number Of Pages: 700
* Publication Date: 2008-12-26
* ISBN-10 / ASIN: 0123743702
* ISBN-13 / EAN: 9780123743701
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.
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 itsapplication to JPEG 2000 and MPEG-4Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolboxBalances presentation of the mathematics with applications to signal processingSummary: looks deceiveRating: 2The 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.
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