NEW! (2009)

A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way, by S. Mallat is the improved, revised version of his classic book. It should be noted that much of the work on this third edition was done by Gabriel Peyre. Some of the new developments of the past few years are now discussed in the book, including in Chapter 12, "Sparsity in redundant dictionaries", and Chapter 13, "Inverse problems". I don't know what Caltech does to its graduate students who used the 2nd edition of the book in a certain class, but there is a certain negative review of this book on Amazon that you should take with a grain of salt. Allow me to retort. First, it is said that this is an information dump. Nobody said that you should read the book in linear order --- the author himself lists possible course paths in the preface --- so this argument is very cheap in my view. Second, there is the complaint that the author does not give all the information necessary to do the numerical implementation: I'll rephrase that by saying that most of the information is in the book, but not in the form of pseudo-code. There is a reason why "Numerical recipes in C" is not on my night stand! "A wavelet tour" is a book meant to be read, and in addition, all the code is provided online. Third, it is said that the book has many typos. I agree that this is true for the 2nd edition, but did the reviewer bother to even open the 3rd edition before writing his review? I stand by my view that "A wavelet tour" is still, in 2009, the best book on wavelets for mathematically-inclined people. (Note to Academic Press: restore glossy pages, please.)

NEW! (2009)

Conceptual Wavelets by L. Fugal. From the author: "This book uses very little math, yet provides an in-depth understanding of the concepts and real-world applications of these powerful tools."

NEW! (2007)

The Numbers Behind NUMB3RS: Solving Crime with Mathematics by K. Devlin and G. Lorden is a beautifully written, high-school level account of most of the math that has been used in the popular CBS TV show Numb3rs. I mention it here because it showcases total variation image enhancement --- and how it has been successfully used as evidence in court! --- as well as wavelets for compressing the FBI's fingerprint database. Other topics include: statistical hypothesis testing and inference, data mining, cryptography, networks, game theory, DNA profiling, etc. Great fun, and a cheap paperback. Appeared in August 2007.

NEW!

Appeared in September 2006: M. Weeks's Digital Signal Processing Using MATLAB and Wavelets.

Somewhat NEW! yet intemporal

Appeared in July 2006: Fundamental Papers in Wavelet Theory, edited by C. Heil and D. Walnut. The table of contents can be found here. Your get your money's worth of pages with this thick volume: the 37 classic articles cover wavelet analysis exhaustively, in all its breadth and depth. And today (24 Aug 2007) it sells for $37 on amazon! You do the math, it's cheaper than going to the photocopy machine. Most papers appeared before the Internet era so you won't find them on the web.

Stephane Mallat's book A Wavelet Tour of Signal Processing is a must for anybody interested in learning about wavelets. It provides a clear and solid theoretical foundation directed towards applications. Its unusual breadth makes it interesting to engineers, physicists and mathematicians alike. The subject of wavelets crystallized in the early 90's so this book (published in 1999) will stay a reference for quite a while. Mallat is one of the main contributors to the theory of wavelets and multiresolution analysis. This book is used as the main reference for the class "Wavelets and modern signal processing" at Caltech. My favorite chapters contain material on: Fourier transforms and series, sampling and aliasing, Time-frequency transforms, Frames, Orthonormal bases of wavelets, multiresolution analysis, Wavelet packets, Approximation theory of wavelet thresholding, Statistical estimation with wavelets, and Coding theory.

Ingrid Daubechies' Ten Lectures on Wavelets is one of the best-selling math books of the 90's. It is truly a marvel of scientific exposition. Wavelets are introduced from a more mathematical prospective than in Mallat's book, so it might not be a good pick for the non-mathematically-inclined beginner. The book beautifully covers in details: Wavelets with continuous parameters (CWT), wavelets with discrete parameters (DWT), multiresolution analysis, Gabor and wavelet frames, and compactly-supported wavelets (which bear Daubechies' name).

The World According to Wavelets: The Story of a Mathematical Technique in the Making, by science writer Barbara Burke Hubbard. This is a very pleasant account of the history of wavelets, mostly from the eighties and nineties, and is full of anecdotes and quotations from the leading researchers. It also contains interesting bits of popular intuition on the why and how of wavelets, far from the usual technical books (although the author tries her hands at explaining and even proving some facts about Fourier transform in the appendix, like the uncertainty principle). This book reads very much like a novel. Perfect to motivate students :)

All the rest:

• Introductory Wavelet Books
• Wavelets in Signal Processing
• Wavelets in Image Processing
• Wavelets in Statistics
• Wavelets in Numerical Analysis
• Wavelets in Mathematics
• Wavelets in Physics