(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.)Form a very mundane point of view, i do like "The World According to Wavelets: The Story of a Mathematical Technique in the Making", by Barbara Burke Hubbard. On a more technical side, there are some tutorials and reviews on wavelets gathered at WITS, where is the starlet (*let)? a collection of wavelet names in *letIf you are especially interested in an history of 2D wavelets, with geometric, directional features, you may have a look at A panorama on Multiscale Geometric Representations by Laurent Jacques, Laurent Duval, Caroline Chaux and Gabriel Peyré (Signal Processing, 2011.
Each of these sources may provide you with additional references, tutorials, etc.The de-facto reference book for learning wavelets is this : A Wavelet Tour of Signal Processing, by Stephen Mallat. You will find everything you need here.Among online resources, I would recommend this: A Numerical Tour of Signal Processing, by Gariel Peyre. They are quite beginner friendly, I feel. Rather than teaching the theory in detail, he teaches it's implementation through step-by-step instructions. He only briefly mentions the theory in his posts. These two should be more than sufficient for you learn everything about wavelets. I recommend Prof Vikram Gadre's lecture series at IIT Bombay titled:Advanced Digital Signal Processing - Multirate and Wavelets NPTEL :: Electronics & Communication Engineering. His style of teaching is heavily based on intuition. He has posted about 50 videos including problem sets,quizzes and handouts. It is very comprehensive. You might want to increase the playback speed by watching the videos on YouTube as his speed of talking is a bit slow.
It may depend on your background. For a mathematician, would suggest Daubechies, Ten Lectures on Wavelets, or Mallat, A Wavelet Tour of Signal Processing.An introductory textbook is Strang, Wavelets and Filter Banks. Strang's course, along with lecture notes and problem sets, is here: http://ocw.mit.edu/courses/mathe...For applications to data compression, I would highly recommend the chapters on subband coding and wavelets in Sayood, Introduction to Data Compression. There's also a brief treatment in Numerical Recipes, and Stollnitz, Wavelets for Computer Graphics is good too.//////Wavelets-F...Li et al., Survey of Wavelet Applications in Data Mining, http://citeseerx.ist.psu.edu/vie...What are some alternatives to wavelets? Sign up or log in to customize your list. Here's how it works: Anybody can ask a question The best answers are voted up and rise to the top Are there any suggestions for introductory books on wavelets? I want a book, not online material or tutorials.
The canonical answer used to be Ingrid Daubechies, Ten lectures on wavelets (1992), ISBN 0898712742. It may be somewhat outdated by now, but probably still good. In a course on Fourier Analysis, we used Fourier Analysis and Applications by Gasquet and Witomski (translated by Ryan). The subtitle is "Filtering, Numerical Computation, Wavelets". The wavelets section is one chapter at the end so it doesn't go into much detail specifically on wavelets. So if you already know a lot of Fourier analysis then I wouldn't use this book, but if you also need to know the Fourier analysis background then it's a reasonable place to start. It's quite readable as well. Publisher: Springer, Texts in Applied Mathematics 30 MathSciNet: MR1657104 (includes review) I think "Ripples in Mathematics: The Discrete Wavelet Transform" by Arne Jensen and Anders la Cour-Harbo (Springer 2001) is a masterpiece of elegant exposition. You can find it here. I learned more about wavelets from this book than from any other source.
A very gentle introduction is Boggess & Narcowich, A First Course in Wavelets with Fourier Analysis. I should warn you, though, they're pretty fast and loose with the hypotheses of their theorems. You'll be fine if you've studied advanced linear algebra, and especially fine if you already know some Fourier analysis. There's also Mallat's A Wavelet Tour of Signal Processing: The Sparse Way. I haven't read very much of it, so I don't have a strong opinion on it yet. It's definitely more difficult than Boggess & Narcowich, but then it probably has about ten times the content (no exaggeration). A Primer on Wavelets and Their Scientific Applications by James S. Walker Real Analysis with an Introduction to Wavelets and Applications by Hong, Wang and Gardner All The Mathematics You Missed recommends The World According to Wavelets by Barbara Burke Hubbard. I haven't read it myself, though. When I started out on wavelets, I really liked "Wavelets: A Primer" by Christian Blatter (ISBN: 1568810954) which is pretty self-contained in that it even contains a thorough review of the Fourier analysis used.