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Cohen, Jonathan (Herausgeber); Zayed, Ahmed I. (Herausgeber)

Wavelets and Multiscale Analysis: Theory and Applications (Gebundene Ausgabe)

Reihe: Applied and Numerical Harmonic

SPRINGER VERLAG GMBH, Birkhäuser Boston, März 2011

2011 - 338 S. - Sprache: Englisch - 244x164x32 mm

ISBN: 0817680942 EAN: 9780817680947

Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems. Overall, the book is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.

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Comprises?work?from top researchers in the fieldProvides a comprehensive overview of fundamental conceptsDemonstrates?state-of the-art applications to signal and image processing, denoising, tomography, and medical imagingExplores new ideas in data processingValuable for a wide audience, including?graduate students, researchers, and practitioners in mathematics, engineering, and physics


Preface.- Contributors.- 1 An Introduction to Wavelets and Multi-scale Analysis: Theory and Applications.- Part I The Mathematical Theory of Wavelets.- 2 The Construction of Wavelet Sets.- 3 The Measure of the Closure of a Wavelet Set May Be >2pi.- Quincunx Wavelets on T^2.- Crystallographic Haar-type Composite Dilation Wavelets.- 6 From Full Rank Subdivision Schemes to Multichannel Wavelets: A Constructive Approach.- 7 Unitary Systems and Bessel Generator Multipliers.- 8 The Zak Transform(s).- Part II The Geometry of Large Data Sets.- 9 Harmonic Analysis of Digital Databases.- 10 Some Recent Advances in Multiscale Geometric Analysis of Point Clouds.- 11 Signal Ensemble Classification Using Low-Dimensional Embeddings and Earth Mover's Distance.- Part III Applications of Wavelets.- 12 Wavelets on Manifolds and Statistical Applications to Cosmology.- 13 Wavelets, a Numerical Tool for Atmospheric Data Analysis.- 14 Denoising Speech Signals for Digital Hearing Aids: A Wavelet Based Approach.- Index.

ISBN 0-817680-94-2, ISBN 0-81-768094-2, ISBN 0-81768-094-2, ISBN 0-817-68094-2, ISBN 0-8176-8094-2

ISBN 978-0-817680-94-7, ISBN 978-0-81-768094-7, ISBN 978-0-81768-094-7, ISBN 978-0-817-68094-7, ISBN 978-0-8176-8094-7

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