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**Wavelets and multiscale signal processing. Transl. from the French.**
*(English)*
Zbl 0848.42021

Applied Mathematics and Mathematical Computation. 11. London: Chapman & Hall. 232 p. (1995).

Foreword to the English edition: “This book is based on Albert Cohen’s doctoral thesis, which was written at the University of Paris-Dauphine under the guidance of Professor Yves Meyer. It was published in 1992 by Masson, Paris (cf. Zbl 0826.42024). Since this first publication, research on wavelets and multiscale methods has progressed significantly, and interest in these fields has extended to a large scientific community. In spite of this progress, it was clear to us that the relations between filter branks and wavelet bases constitute a consistent and indispensable core for the theory and applications of wavelets and that it was useful to present these relations in detail. Our main concern in this edition has been to keep this focus on the core material, while at the same time providing ‘pointers’ to the latest results and related developments.

The major results presented here are from Cohen’s thesis and from subsequent work done by Cohen and his collaborators. This English edition was translated by Robert D. Ryan. Extensive revisions were made jointly by Cohen and Ryan. These include revisions in Chapter 3, a new Section 4.3, and a rewritten Chapter 5. Most of the figures and plates have been redone to reflect changes in the text. In addition, an effort has been made to elaborate a number of the proofs to make the arguments more readily available to students and to others who are not experts in the field”.

The major results presented here are from Cohen’s thesis and from subsequent work done by Cohen and his collaborators. This English edition was translated by Robert D. Ryan. Extensive revisions were made jointly by Cohen and Ryan. These include revisions in Chapter 3, a new Section 4.3, and a rewritten Chapter 5. Most of the figures and plates have been redone to reflect changes in the text. In addition, an effort has been made to elaborate a number of the proofs to make the arguments more readily available to students and to others who are not experts in the field”.

### MSC:

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

42-02 | Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

65T50 | Numerical methods for discrete and fast Fourier transforms |

68U10 | Computing methodologies for image processing |