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Book review

Author(s) Meyer, Y.
Title Wavelets: algorithms and applications
Publisher SIAM
Year of publication 1993
Reviewed by Anatoly Zhigljavsky

The book is a translation from a recently published French original, it is based on a course of lectures given by the author at the Spanish Institute. The author, one of the world's leading experts in the wavelet theory, combines here clarity and terseness of exposition, rigorous mathematical style and diversity of questions considered.

Roughly, the book can be divided into three parts. The first one consists of four chapters and describes historical origins of the wavelet theory and many wavelet analysis algorithms. The second part is perhaps the most valuable in the book and contains another four chapters, it is devoted to applications of the wavelet analysis technique to signal and image processing and to computer vision problems. The final three chapters deal with applications involving the fractal structure of images. The questions considered in these chapters include applications of the wavelet theory to analysing turbulence and formation of distant galaxies and to proving the nowhere differentiability of the Weierstrass function <formula> and the differentiability of the Riemann function <formula> at the rational points t = p/q with odd p and q.

The book is concise and contains a lot of information in its 133 pages. It has an index and a good list of references and also it is well translated and well produced.

The book can be useful for both experts and beginners. It is especially recommended to skillful engineers with a good mathematical background that are faced with signal and image processing problems. In spite of that there have been recently published several good books on the wavelet theory, the present English edition of the already known Yeves Meyer work will certainly be very welcomed by the specialists.

The price is relatively low and everybody interested in either wavelet theory or its applications is advised to purchase the volume. The recommendation is extended to those looking after the mathematical sections of scientific libraries.