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Acta Applicandae

Book review

Author(s) Koornwinder, T.H. (ed.)
Title Wavelets: an elementary treatment of theory and applications
Publisher World Scientific
Year of publication 1993
Reviewed by Anatoly Zhigljavsky

The volume is based on an intensive course on the wavelet theory and applications hold at CWI, Amsterdam. Six authors among twelve, the total number, work at CWI, specifically, A. Daalhuis, M. Hazewinkel, H. Heijmans, P. Hemker, P. Nacken, and N. Temme. This and a high quality of the volume in general evidences that at present CWI is one of the leading scientific centers in the field of wavelets.

The book contains twelve contributions. Most of them describe material already known in literature and some contain new results. The first half of the book provides a good introduction into the classical wavelet theory. An emphasis is put on the continuous wavelet transform, on discrete wavelets generated by multiresolution analysis and on the Daubechies waveless of compact support. The second half of the volume deals with some particular aspects of the theory and various applied problems. Among the questions considered in this part are: image compression using wavelets, adaptation of wavelet bases to nonhomogeneous cases, fast wavelet transform, study of local structure of fractals with the help of wavelets, application to seismic processing. Mathematical prerequisites for the readers are not high. In spite of that there are 12 contributions in the volume, it can be considered as a unified work, and this is an editor's benefit.

Until recently there were no books on the wavelet theory, as the theory stands now. At recent years several good books appeared, particularly, I. Daubechies, Ten lectures on wavelets, SIAM, 1992; C.K. Chui, An introduction to wavelets, Academic Press, 1992; Y. Meyer, Wavelets: algorithms and applications, SIAM, 1993. The present volume can also be included into the list of good books on wavelets but it significantly differs from the others by the selection of topics. Also, the present book is well produced.

The price does not seem to be low but it is quite reasonable for a book of such volume and production quality. Taking into account a high scientific quality of the book, all specialists in the field of wavelet theory and its applications are advised to make a good investment by purchasing the volume. For the beginners willing to buy only one good book on waveless to start learning the subject, the mentioned book of Y. Meyer is perhaps more preferable since it is also good and costs only $19.50.