Wavelets: An Elementary Treatment of Theory and Applications

Front Cover
T. H. Koornwinder
World Scientific, 1993 - Mathematics - 225 pages
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Nowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet bases adapted to inhomogeneous cases.
 

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Contents

Preface
1
Mathematical Preliminaries
13
The Continuous Wavelet Transform
27
Discrete Wavelets and Multiresolution Analysis
49
Image Compression using Wavelets
81
Computing with Daubechies Wavelets
93
Wavelet bases adapted to inhomogeneous cases
107
Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis
129
Calculation of the Wavelet Decomposition using Quadrature Formulae
139
Fast Wavelet Transforms and CalderonZygmund Operators
161
The Finite Wavelet Transform with an Application to Seismic Processing
183
Wavelets Understand Fractals
209
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