Four Short Courses on Harmonic Analysis

Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis

  • Brigitte Forster
  • Peter Massopust

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Peter Massopust, Brigitte Forster
    Pages 1-49
  3. Ole Christensen
    Pages 51-86
  4. Pierre Vandergheynst, Yves Wiaux
    Pages 131-174
  5. Back Matter
    Pages 235-247

About this book

Introduction

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.

Keywords

B-spline generat B-spline generated frames Fourier analysis Wiener's lemma composite dilations composite wavelets frames and bases harmonic analysis image analysis image processing signal processing spectral invariance spherical functions time-frequency methods wavelets on the sphere

Editors and affiliations

  • Brigitte Forster
    • 1
  • Peter Massopust
    • 2
    • 1
  1. 1.Zentrum Mathematik, M6 Technische Universität MünchenGarching b. MünchenGermany
  2. 2.Institute of Biomathematics and BiometryHelmholtz Zentrum MünchenNeuherbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4891-6
  • Copyright Information Birkhäuser Boston 2010
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4890-9
  • Online ISBN 978-0-8176-4891-6
  • About this book