Since their appearance in 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 multiresolution 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.
Reihe
Auflage
Softcover reprint of the original 1st ed. 1995
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Illustrationen
30 s/w Abbildungen
22 Halftones, black and white
Maße
Höhe: 21.6 cm
Breite: 14 cm
Gewicht
ISBN-13
978-0-412-57590-7 (9780412575907)
DOI
10.1007/978-1-4899-4425-2
Schweitzer Klassifikation
Introduction. Multiresolution analysis. Introduction. The continuos point of view. The multivariate case. Conclusion. Wavelets and conjugate quadrature filters. Introduction. The general case. The finite case. Wavelets with compact support. Action of the FWT on oscillating signals. The Regularity of scaling functions and wavelets. Introduction. Regularity and oscillation. The subdivision algorithms. Spectral estimates of the regularity. Estimation of the Lp-Soboley exponent. Applications. Biorthogonal wavelet bases. Introduction. General principles of Subband coding. Unconditional biorthogonal wavelet bases. Dual filters and biorthogonal Riesz bases. Examples and applications. Stochastic processes. Introduction. Linear approximation. Linear approximation of images. Piecewise stationary processes. Nonlinear approximation. Quasi-analytic wavelet bases. Multivariate constructions. Multiscale unconditional bases. Notation. Reference.
