Wavelets and Multiscale Analysis

Theory and Applications

  • Jonathan Cohen
  • Ahmed I. Zayed
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. The Mathematical Theory of Wavelets

    1. Front Matter
      Pages 15-15
    2. John J. Benedetto, Robert L. Benedetto
      Pages 17-56
    3. Kenneth R. Hoover, Brody Dylan Johnson
      Pages 65-82
    4. Jeffrey D. Blanchard, Kyle R. Steffen
      Pages 83-108
    5. Deguang Han, David R. Larson
      Pages 131-150
    6. Eugenio Hernández, Hrvoje Šikić, Guido L. Weiss, Edward N. Wilson
      Pages 151-157
  3. The Geometry of Large Data Sets

    1. Front Matter
      Pages 159-160
    2. Ronald R. Coifman, Matan Gavish
      Pages 161-197
    3. Guangliang Chen, Anna V. Little, Mauro Maggioni, Lorenzo Rosasco
      Pages 199-225
  4. Applications of Wavelets

    1. Front Matter
      Pages 257-257
    2. Daryl Geller, Azita Mayeli
      Pages 259-277
    3. Parick Fischer, Ka-Kit Tung
      Pages 279-298
    4. Nathaniel Whitmal, Janet Rutledge, Jonathan Cohen
      Pages 299-331
  5. Back Matter
    Pages 333-335

About this book

Introduction

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.

Keywords

denoising filter banks generalized shift-invariant subspaces geometric harmonic analysis harmonic analysis multiscale analysis nonlinear approximations operator algebras periodic wavelet frames wavelets

Editors and affiliations

  • Jonathan Cohen
    • 1
  • Ahmed I. Zayed
    • 2
  1. 1., Department of Mathematical SciencesDePaul UniversityChicagoUSA
  2. 2., Department of Mathematical SciencesDePaul UniversityChicagoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8095-4
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8094-7
  • Online ISBN 978-0-8176-8095-4