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Ten Lectures on WaveletsTen Lectures on Wavelets

Ingrid Daubechies



CBMS-NSF Regional Conference Series in Applied Mathematics 61



". . . this is a clearly written introduction to the mathematics of wavelets that provides solid background material on most of the major aspects of the current theory. Especially appealing is the way in which the relationships between wavelets and other areas are pointed out. . . . I feel certain that this will be the major introductory text on wavelets for some time to come. It will definitely be a welcome addition to the library of anyone interested in learning the basics of wavelets." -- Christopher Heil, SIAM Review, Vol. 35, No. 4, December, 1993.

"This book is both a tutorial on wavelets and a review of the most advanced research in this domain...it also gives many practical examples and describes several applications (in particular, in signal processing, image coding and numerical analysis.)" -- Albert Cohen (Paris), Mathematical Reviews, Issue 93e

"Ten Lectures on Wavelets is arranged in ten chapters, one for each 'lecture.' If anyone is thinking of using this as a basis for a course, don't let the title concern you, plenty of material exists to fill lectures beyond the tenth class. The ten lectures are clearly geared to a very knowledgeable group of listeners. The text would make an excellent choice for a combined graduate-level course in mathematics and electrical engineering...The material covered is extremely recent; the author references papers published in 1992. There is also an extensive reference list with contributions from a variety of sources. Those interested in pursuing this topic will find this an excellent source of current research topics and applications...I heartily recommend this book to anyone who seriously wants to know the state of the art in wavelets. The modest cost of thirty dollars is a real bargain for the wealth of information it contains...I have changed from one who is skeptical because of wavelets being fashionable to one who has the opinion that wavelets are here to stay and will become a standard tool in many applications. This book is likely to become a classic text in mathematics and a reference to those seriously using wavelets. It is exciting to read a soon-to-be classic." --Lawrence A. Ray, Eastman Kodak Company, Journal of Electronic Imaging, July 1992, Vol. 1, No. 3

"The book by Daubechies, who is one of the main developers of the (wavelet) theory, is the result of an intensive short course. The presentation is completely engrossing; it is like reading a good, thick Russian novel. Daubechies has a real knack for making the material appealing and lively, and there is a definite 'slowing down for details' at the points that require further elucidation . . . This book can be used for many different purposes, from individual reading to graduate-level course-work, and it will likely become a classic." -- F. Alberto Grunbaum, Science, August 7, 1992.


Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details.

This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.

The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. Because of their interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds.

Contents

Introduction; Preliminaries and Notation; The What, Why, and How of Wavelets; The Continuous Wavelet Transform; Discrete Wavelet Transforms: Frames; Time-Frequency Density and Orthonormal Bases; Orthonormal Bases of Wavelets and Multiresolutional Analysis; Orthonormal Bases of Compactly Supported Wavelets; More About the Regularity of Compactly Supported Wavelets; Symmetry for Compactly Supported Wavelet Bases; Characterization of Functional Spaces by Means of Wavelets; Generalizations and Tricks for Orthonormal Wavelet Bases; References; Indexes.

1992 / xix + 357 pages / Softcover / ISBN-13: 978-0-898712-74-2 / ISBN-10: 0-89871-274-2 /
List Price $82.00 / SIAM/CBMS Member Price $57.40 / Order Code CB61
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