Wavelets and Multiscale Signal Processing

Since their appearance in the mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in mathematical analysis and in applications to numerical analysis and signal processing. This book is based on Ondelettes et Traitement Numerique du Signal by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing. Throughout, the book concentrates on the fundamentals. It begins with a chapter on the concept of multi-resolution analysis, which contains complete proofs of the basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case (Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of the filters, and the importance of regularity for the algorithms are the subjects of Chapter 3. Chapter 5 looks at multiscale decomposition as it applies to stochastic processing, in particular to signal and image processing. This book should be of interest to graduate applied mathematicians/researchers in engineering; time series analysts; those studying hydrodynamics, aeronautics, meteorology and geophysics.