Discovering Wavelets [Hardcover]

Edward Aboufadel (Author), Steven Schlicker (Author)

Book Description

ISBN-10: 0471331937 | ISBN-13: 978-0471331933 | Publication Date: October 5, 1999 | Edition: 1

An accessible and practical introduction to wavelets

With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra.

The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-based search engine, processing with Daubechies' wavelets, and more.

Among the special features of Discovering Wavelets are:
* Real-life, hands-on examples that involve actual wavelet applications
* A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book
* Challenging problems that reinforce and expand on the ideas being developed
* An appendix containing the linear algebra needed to understand wavelets as presented in the book

Editorial Reviews

Review

...this text has the advantage of being self contained: the conceptual prerequisites are kept to a minimum and the student can quickly get to the applications with a reasonably complete understanding of how and why wavelets work in data processing. As such, this text should appeal to instructors and students who are interested in learning about how wavelets work without being required to learn the whole mathematical backdrop in which wavelet theory is developed. (Zentralblatt Math, Volume 940, No 15, 2000)

From the Back Cover

An accessible and practical introduction to wavelets

With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra.

The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-based search engine, processing with Daubechies' wavelets, and more.

Among the special features of Discovering Wavelets are:
* Real-life, hands-on examples that involve actual wavelet applications
* A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book
* Challenging problems that reinforce and expand on the ideas being developed
* An appendix containing the linear algebra needed to understand wavelets as presented in the book

See all Editorial Reviews

Product Details

• Hardcover: 144 pages
• Publisher: Wiley-Interscience; 1 edition (October 5, 1999)
• Language: English
• ISBN-10: 0471331937
• ISBN-13: 978-0471331933
• Product Dimensions: 9.6 x 6.4 x 0.6 inches
• Shipping Weight: 13 ounces (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,860,480 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 25 people found the following review helpful:

4.0 out of 5 stars Good Practical Introduction, February 25, 2000

By A Customer

This review is from: Discovering Wavelets (Hardcover)

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.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Discovering Wavelets, September 20, 2000

By A Customer

This review is from: Discovering Wavelets (Hardcover)

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).

3 of 3 people found the following review helpful:

5.0 out of 5 stars Great Book, June 13, 2003

By A Customer

This review is from: Discovering Wavelets (Hardcover)

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.