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Sampling, Wavelets, and Tomography

  • John J. Benedetto
  • Ahmed I. Zayed

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Hans G. Feichtinger, Tobias Werther
    Pages 83-113
  3. P. P. Vaidyanathan
    Pages 115-136
  4. Stéphane Jaffard
    Pages 157-177
  5. Adel Faridani
    Pages 225-254
  6. Alexander Katsevich, Guenter Lauritsch
    Pages 255-287
  7. David C. Wilson, Bernard A. Mair
    Pages 311-340
  8. Back Matter
    Pages 341-345

About this book

Introduction

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field.

This state-of-the-art book not only presents new results in these research areas, but it also demonstrates the role of sampling in both wavelet theory and tomography. Specific topics covered include:

* Robustness of Regular Sampling in Sobolev Algebras * Irregular and Semi-Irregular Weyl-Heisenberg Frames * Adaptive Irregular Sampling in Meshfree Flow Simulation * Sampling Theorems for Non-Bandlimited Signals * Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets * Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces * Sampling Theory and Parallel-Beam Tomography * Thin-Plate Spline Interpolation in Medical Imaging * Filtered Back-Projection Algorithms for Spiral Cone Computed Tomography

Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work.

Contributors: J.J. Benedetto, N.K. Bose, P.G. Casazza, Y.C. Eldar, H.G. Feichtinger, A. Faridani, A. Iske, S. Jaffard, A. Katsevich, S. Lertrattanapanich, G. Lauritsch, B. Mair, M. Papadakis, P.P. Vaidyanathan, T. Werther, D.C. Wilson, A.I. Zayed

 

Keywords

Algebra Fourier analysis Interpolation Jitter Signal Wavelet algorithm algorithms calculus computed tomography (CT) filters image processing linear optimization simulation wavelets

Editors and affiliations

  • John J. Benedetto
    • 1
  • Ahmed I. Zayed
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of Mathematical SciencesDePaul UniversityChicagoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8212-5
  • Copyright Information Springer Science+Business Media New York 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6495-8
  • Online ISBN 978-0-8176-8212-5
  • Buy this book on publisher's site