Sampling, Wavelets, and Tomography

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

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

"The book places emphasis on all three themes it considers. It presents applications with a broad perspective.... The book, containing contributions of some of the renowned scientists in the field, is interesting and informative, and presents an insightful approach towards wavelets, sampling theory, and tomography. To conclude, the book is of immense value to the mathematically inclined researcher whose work centers arround the application of sampling theory."   —Journal of the Indian Institute of Science

"This volume has been compiled by the editors with a readership of mathematicians, scientists, and engineers working in signal and image processing. It is a collection of invited articles on sampling, wavelets, and tomography, three active areas in contemporary mathematics having Fourier analysis as a common root. This state-of-the-art book not only presents new results in these research areas, but also demonstrates the role of sampling in both wavelet theory and tomography. One key feature of the book is an introductory chapter stressing the interdependence of the three main areas covered." —Int. Mathem. Nachrichten

"The aim of the book is to highlight the interconnections between sampling, wavelets and tomography, and to present new results. The first chapter of the book...provides the reader with an exceptional overview, and also with an illuminating review of the other chapters, pointing out the interconnections between them, and giving concise introduction into the three fundamental topics in the title, including fundamental definitions and results.... The book makes useful reading and gives clear nontedious presentation of the mathematical ideas involved." —Revue Roumaine de Mathématiques Pures et Appliquées

"This state-of-the-art book not only presents new results… but it also demonstrates the role of sampling in both wavelet theory and tomography.… The topicscovered (from frame theory, time-frequency analysis, to tomography or new results on wavelets) show the wide range in the high level of activity in this area." —Monatshefte für Mathematik

• Department of Mathematics, University of Maryland, College Park, USA

  John J. Benedetto

• Department of Mathematical Sciences, DePaul University, Chicago, USA

  Ahmed I. Zayed

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