Wavelets and Multiscale Analysis Theory and Applications ; [this book is a collection of papers written or co-authored by participants in the "Twenty Years of Wavelets" conference held at DePaul in May, 2009

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, features expository and research articles covering current and emerging areas in the theory and applications of wavelets. The book 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. Specific topics covered include: * wavelets on locally compact groups and Riemannian manifolds; * crystallographic composite dilation wavelets, quincunx and vector-valued wavelets; * multiscale analysis of large data sets; * geometric wavelets; * wavelets applications in cosmology, atmospheric data analysis and denoising speech signals. __Wavelets and Multiscale Analysis: Theory and Applications__ is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering. 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. Front Matter....Pages i-xiv An Introduction to Wavelets and Multiscale Analysis: Theory and Applications....Pages 1-14 Front Matter....Pages 15-15 The Construction of Wavelet Sets....Pages 17-56 The Measure of the Closure of a Wavelet Set May Be > 2π....Pages 57-64 Quincunx Wavelets on $${\mathbb{T}}^{2}$$ ....Pages 65-82 Crystallographic Haar-Type Composite Dilation Wavelets....Pages 83-108 From Full Rank Subdivision Schemes to Multichannel Wavelets: A Constructive Approach....Pages 109-130 Unitary Systems and Bessel Generator Multipliers....Pages 131-150 The Zak Transform(s)....Pages 151-157 Front Matter....Pages 159-160 Harmonic Analysis of Digital Data Bases....Pages 161-197 Some Recent Advances in Multiscale Geometric Analysis of Point Clouds....Pages 199-225 Signal Ensemble Classification Using Low-Dimensional Embeddings and Earth Mover’s Distance....Pages 227-256 Front Matter....Pages 257-257 Wavelets on Manifolds and Statistical Applications to Cosmology....Pages 259-277 Wavelets, a Numerical Tool for Atmospheric Data Analysis....Pages 279-298 Denoising Speech Signals for Digital Hearing Aids: A Wavelet Based Approach....Pages 299-331 Back Matter....Pages 333-335