Four short courses on harmonic analysis: wavelets, frames, time-frequency methods, and applications to signal and image analysis / Brigitte Forster, Peter Massopust

Auteur secondaire : Christensen, Ole (1966-) - Collaborateur ; Labate, Demetrio - Collaborateur ; Forster, Brigitte (1947-) - Editeur scientifique ; Gröchenig, Karlheinz (1959-) - Collaborateur ; Massopust, Peter Robert (1958-) - Editeur scientifiqueType de document: Monographie Collection: Applied and numerical harmonic analysis Langue: anglaisPays: Etats UnisÉditeur: Boston : Birkhauser, 2009Description: 1 vol. (XVIII-247 p.) : fig. ; 24 cm ISBN: 9780817648909 ; rel. Note: Les chapitres 2, 3, 4, et 5 de ce livre sont basés sur des conférences données par leurs auteurs à l'école d'été : New trends and directions in harmonic analysis, approximation theory, and image analysis (Inzell, Allemagne, 17-21 septembre 2007).Résumé: This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: Frames and bases in mathematics and engineering ; Wavelets with composite dilations and their applications ; Wavelets on the sphere and their applications ; Wiener's Lemma: theme and variations. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory. (Source : 4ème de couverture).Bibliographie: Bibliogr. p. 235-244. Index. Sujets MSC: 42-02 Harmonic analysis on Euclidean spaces -- Research exposition (monographs, survey articles)
42B35 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Function spaces arising in harmonic analysis
42Cxx Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis
41A15 Approximations and expansions -- Approximations and expansions -- Spline approximation
43A90 Abstract harmonic analysis -- Abstract harmonic analysis -- Spherical functions
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Les chapitres 2, 3, 4, et 5 de ce livre sont basés sur des conférences données par leurs auteurs à l'école d'été : New trends and directions in harmonic analysis, approximation theory, and image analysis (Inzell, Allemagne, 17-21 septembre 2007).

Bibliogr. p. 235-244. Index

This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn.

Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: Frames and bases in mathematics and engineering ; Wavelets with composite dilations and their applications ; Wavelets on the sphere and their applications ; Wiener's Lemma: theme and variations. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory. (Source : 4ème de couverture)

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