Customer Reviews

Wavelet Analysis: The Scalable Structure of Information

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In most books on wavelets, signal and image processing are the only topics of application considered, because they are written by people from that field. However, the applicability of wavelets is much wider. For instance, the solution of partial differential equations, which has allowed the entrance of wavelets to the finite element world. This and other links to classical math problems, such as fractal geometry, are carefully addressed in this book besides the conventional signal processing issues. I recommend it for people of various fields.

The Wells-Resnikoff book on wavelets is in my opinion
one of the best:-- both with regard to the math--the proofs and all that!--, and the applications. The ideas in the book are timeless, and, I expect, it will be a great book for decades to come. It is very strong on both scores. And it is beautifully written: It is all there,- the history, the
motivation, the philosophical points, the applications, the guided tours with friendly author-explainations of what it is all about. For me, this book was a page-turner. I read it on
a long plane flight,- on my way to a wavelet conference in Guangzhou, China. -- And I didn't have jet-lag when I arrived
more than a day later. It may be a bit demanding on some students, but it will be well worth their effort!

This is a wonderful book for the pure mathematicians out there. Unlike many other texts, this book spans the entire range of explanation from high-level outline through the algebraic foundations to real-world applications. If you're just interested in applying wavelets with a minimum of fuss, you may want another book. But if you want to really understand the theory behind them, this is the one for you.

I am a graduate student in Math and was attracted to the book because it treats topics -- wavelets of rank other than 2, tilings, and others -- that are missing from many of the standard texts. Wavelets are approached through the introduction of matrices with certain algebraic properties rather than through orthonormal bases in L2 or scaling functions.

Interesting, say I. This will give me a different perspective on many of the basic results and let me read some papers I've been struggling with.

The book, however, did not fully live up to my expectations. Many difficult concepts are introduced in a cursory way, and the proofs skip a lot of details. This is not uncommon in graduate level texts, as it is expected that the reader can fill in the gaps. When I filled in the gaps, however, I discovered more than a few errors. Often, these were just distractions such as missing or incorrect constants. But at least one proof contained more serious errors.

Graduate level math is hard enough without having to figure out what the authors *meant* to say. I would advise a student of my level of sophistication to look elsewhere.

If the authors were less enthusiastic about mathematics for its own sake, they probably would have written a better book. This one is said to be suitable for undergraduates, but I don't think so. I have a master's degree in electrical engineering, and several of the mathematical concepts they mention were just vaguely familiar names to me. That would be OK if I were persuaded that those concepts were essential to an understanding of wavelets, but I'm not. The book seems somewhat ill organized as well; new terminology should be defined before it's used, not fifty pages later.

This is The Read-First book on Wavelets!