A Primer on Wavelets and Their Scientific Applications
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In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments, this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications.
Ingeniously relying on elementary algebra and just a smidgen of calculus, Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing, as well in biology and medicine.
Nearly twice as long as the original, this new edition provides
· 104 worked examples and 222 exercises, constituting a veritable book of review material
· Two sections on biorthogonal wavelets
· A mini-course on image compression, including a tutorial on arithmetic compression
· Extensive material on image denoising, featuring a rarely covered technique for removing isolated, randomly positioned clutter
· Concise yet complete coverage of the fundamentals of time-frequency analysis, showcasing its application to audio denoising, and musical theory and synthesis
· An introduction to the multiresolution principle, a new mathematical concept in musical theory
· Expanded suggestions for research projects
· An enhanced list of references
· FAWAV: software designed by the author, which allows readers to duplicate described applications and experiment with other ideas.
To keep the book current, Professor Walker has created a supplementary website. This online repository includes ready-to-download software, and sound and image files, as well as access to many of the most important papers in the field.
Table of Contents
Haar Wavelets. Daubechies Wavelets. Two-Dimensional Wavelets. Frequency Analysis. Beyond Wavelets. Software for Wavelet Analysis.
"The book’s relative lack of formalism results in a low symbol-to-word ratio; here is a math text that can be read quickly yet with comprehension. This is in keeping with the goal of engaging the applications as quickly and painlessly as possible. With such accessibility and a first-rate supporting apparatus, this flexible book can teach various audiences the basics of wavelets, involve them in applications, and inspire them to learn more."
– David A. Huckaby, Angelo State University, in MAA Online, July 2008