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Ten Lectures on Wavelets


By: Ingrid Daubechies

357 pages, Figs, tabs

Society for Industrial and Applied Mathermatics

Paperback | Dec 1992 | #44619 | ISBN: 0898712742
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NHBS Price: £51.00 $69/€58 approx

About this book

This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. 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. 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.

'This is a marvellous book written by one of the principal contributors to the field. ! a great part of the volume under review is dedicated to the engineering and physical origins of wavelets. ! The book style is alert and the interest of the potential reader is continuously kept alive. I think that this book is very useful to mathematicians as well as to people interested in the wavelets applications (engineers, physicists, etc.).' Nicolae Popa, Romanian Journal of Pure and Applied Mathematics 'Ingrid Daubechies is a leading wavelet theorist; this book gives a clear and systematic treatment of the mathematics. Applications are kept in mind all the time, but the main focus of attention is a rigorous development of the theory. ! The book is carefully written; proofs are given in detail for the benefit of non-expert readers yet there is plenty of broad-brush explanation to balance the rigorous mathematical detail.' D. H. Griffel, The Mathematical Gazette ' ! 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 '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).' Mathematical Reviews ' ! I heartily recommend this book to anyone who seriously wants to know the state of the art in wavelets. The modest ! 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.' Journal of Electronic Imaging "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.


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.

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