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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
A Prelude to Sampling, Wavelets, and Tomography (Ahmed I. Zayed) Part I: Sampling and Frames Sampling Without Input Constraints: Consistent Reconstruction in Arbitrary Spaces (Yonina C. Eldar) An Introduction to Irregular Weyl-Heisenberg Frames (Peter G. Casazza) Robustness of Regular Sampling in Sobolev Algebras (Hans G. Feichtinger and Tobias Werther) Adaptive Irregular Sampling in Meshfree Flow Simulation (Armin Iske) Part II: Wavelets Polynomial Matrix Factorization, Multidimensional Filter Banks and Wavelets (N. K. Bose and S. Lertrattanapanich) Sampling Theorems for Non-Bandlimited Signals (P. P. Vaidyanathan) Function Spaces Based on Wavelet Expansions (Stéphane Jaffard) Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces (Manos Papadakis) Part III: Tomography Sampling Theory and Parallel-Beam Tomography (Adel Faridani) Filtered Backprojection Algorithms For Spiral Cone Beam CT (Alexander Katsevich and Guenter Lauritsch) Thin-Plate Spline Interpolation (David C. Wilson and Bernard Mair) Index