Customer Reviews

Discovering Wavelets

5 star:		(2)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

This book is an excellent practical introduction to wavelets. The mathematical level is appropriate for a non-mathematician learning about wavelets. Emphasis was placed on the Haar wavelet (although the Daubechies wavelet was introduced in section 3.6), making the concepts easier to understand. The problems were placed strategically throughout the chapters instead of at the end. This, I think, is the preferred method. Solving most of the problems (which was usually not difficult) was essential to understanding the material. The book is short, only four chapters, four appendices, and 125 pages. The chapter titles are: 1) Wavelets, Fingerprints, and Image Processing, 2) Wavelets and Orthogonal Decomposition, 3) Multiresolution, Cascades, and Filters, and 4) Sample Projects. On a scale of one (useless) to ten (very useful), I would rate the chapters: Ch1-8, Ch2-10, Ch3-9, and Ch4-3.

The shortcomings of the book are in what it lacks. It does not cover the relationship between Fourier analysis and wavelets, or how to apply the many different types of wavelets (other than Haar or Daubechies) to particular problems. The programming language used was Maple. I would have preferred pseudo code or C. The application of wavelets to images was somewhat limited.

In conclusion I would say this book is excellent as a stepping stone to other more advanced books on wavelets. It will not answer all of your wavelet questions, but it will significantly lessen the learning curve for the books that will.

Prior to this book I tried about 5 books and was not able to understand wavelets. This book gets directly to the point. It presents wavelets first as a tool (my interest) not as a "theory". However, the theory is introduced later. I am currently using wavelets in my research (analyzing geophysical signals).

As part of a graduate course I was taking, I needed to put a presentation together on multiresolution analysis. To be honest, I knew nothing about wavelets and most of the books (including the classics such as Mallat's "A Wavelet Tour of Signal Processing" and Daubechies' "10 Lectures on Wavelets") jumped right into the theory without laying, in my opinion, the necessary foundation. I was frustrated.

Then I came upon this book. It was fantastic. The presentation of the subject in linear algebra terms was novel and was just what I was looking for. The presentation was crisp, concise and easy to understand. The problems presented in the text were placed after main ideas were presented rather than at the end of the chapter. And, many of the problems were designed to be a continuation of the text itself. A great approach.

After studying the subject as it was presented, I was able to read through the classics with a better understanding and appreciation of the subject.

In short, this is a wonderful book and I highly recommend it.

This is a book about a very math heavy subject, but does try and put a more practical spin on it. If you have been away from math (Calculus and group theory) it MAY NOT be for you. If you pick up new things quickly, that is the intent.

If the book provided
a clear introduction to wavelets and their implementation,
this would be fine. In fact, this book is more like a set
of lecture notes than a complete text book. I had already implemented Haar
wavelets and had started working on Daubechies wavelets.
Even with this background, I found the coverage in this
book obscure and difficult to understand. The authors
approach wavelets, including Haar wavelets, through
linear algebra. While this can be justified by the fact
that complex wavelets like Daubechies are best described
this way, the coverage in this book is obscure. I compare
this to Gilbert Strang's short paper "Wavelets", published
in American Scientist, April 1994.
It is difficult for me to see how anyone could understand
Daubechies wavelets with this book alone.

My advice is buy another book.