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Discovering Wavelets

Edward Aboufadel, Steven Schlicker

ISBN: 978-1-118-03115-5 February 2011 144 Pages


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
Wavelets, Fingerprints, and Image Processing.

Wavelets and Orthogonal Decompositions.

Multiresolutions, Cascades, and Filters.

Sample Projects.



...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)