Ten Lectures on Wavelets

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.

Spis treści:
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.