Series in Approximations and Decompositions - Vol. 1
WAVELETS: AN ELEMENTARY TREATMENT OF THEORY AND APPLICATIONS
edited by Tom H Koornwinder (University of Amsterdam)
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.
Contents:
- Wavelets: First Steps (N M Temme)
- Wavelets: Mathematical
Preliminaries (P W Hemker et al.)
- The Continuous Wavelet Transform (T H Koornwinder)
- Discrete Wavelets and Multiresolution Analysis (H J A M Heijmans)
- Image Compression Using Wavelets (P Nacken)
- Computing with Daubechies' Wavelets (A B Olde Daalhuis)
- Wavelet Bases Adapted to Inhomogeneous Cases (P W Hemker & F Plantevin)
- Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis (E H Dooijes)
- Calculation of the Wavelet Decomposition Using Quadrature Formulae (W Sweldens & R Piessens)
- Fast Wavelet Transforms and Calderón-Zygmund Operators (T H Koornwinder)
- The Finite Wavelet Transform with an Application to Seismic Processing (J A H Alkemade)
- Wavelets Understand Fractals (M Hazewinkel)
Readership: Applied mathematicians, numerical analysts, physicists,
electrical engineers and signal analysts (sounds, images).
"... highly recommended to everyone who needs a quick account of wavelet theory as well as some ideas of wavelet applications. Results and basic theorems are stated in a rigorous and very satisfactory way, without overloading the treatment by including too many concisely worked-out proofs. Those interested in a more complete treatment will find enough hints on where to look up the details. While not being a textbook for students at an intermediate level, it can be useful as an aid in more advanced courses or seminars. For specialists in the field, the book can serve as a nice reference work; engineers and other people interested in algorithms for the fast wavelet transform will find it a useful guide to go directly to their specific interests. I am convinced that this 'elementary treatment of theory and applications' will become a standard reference for a broad audience."
| Journal of Approximation Theory |
"As well as many exercises and remarks one finds lists of references after each chapter. These make the book valuable not only for graduate students but also for researchers.
| European Maths. Soc. Newsletter, 1995 |
| 240pp |
Pub. date: Jun 1993 |
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