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Inverse Problems, Image Analysis, and Medical Imaging
Edited by: M. Zuhair Nashed, University of Central Florida, Orlando, FL, and Otmar Scherzer, University of Innsbruck, Austria
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Contemporary Mathematics
2002; 305 pp; softcover
Volume: 313
ISBN-10: 0-8218-2979-3
ISBN-13: 978-0-8218-2979-0
List Price: US$91
Member Price: US$72.80
Order Code: CONM/313
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This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA.

The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics.

This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging.

The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.

Readership

Graduate students and research mathematicians; electrical engineers interested in signal processing and image processing; researchers in medical imaging.

Table of Contents

  • R. B. Alexeev and A. B. Smirnova -- Regularization of nonlinear unstable operator equations by secant methods with application to gravitational sounding problem
  • J. J. Benedetto and S. Sumetkijakan -- A fractal set constructed from a class of wavelet sets
  • M. Boutin -- Joint invariant signatures for curve recognition
  • T. F. Chan and J. Shen -- Inpainting based on nonlinear transport and diffusion
  • U. Clarenz, M. Droske, and M. Rumpf -- Towards fast non-rigid registration
  • C. De Mol and M. Defrise -- A note on wavelet-based inversion algorithms
  • M. El-Gamel and A. I. Zayed -- A comparison between the wavelet-Galerkin and the Sinc-Galerkin methods in solving nonhomogeneous heat equations
  • B. Fischer and J. Modersitzki -- Fast diffusion registration
  • C. W. Groetsch and O. Scherzer -- Iterative stabilization and edge detection
  • F. A. Grünbaum -- Backprojections in tomography, spherical functions and addition formulas: A few challenges
  • B. A. Mair and J. A. Zahnen -- Mathematical models for 2d positron emission tomography
  • O. Scherzer -- Explicit versus implicit relative error regularization on the space of functions of bounded variation
  • F. Stenger, A. R. Naghsh-Nilchi, J. Niebsch, and R. Ramlau -- Sampling methods for approximate solution of pde
  • J. Weickert and T. Brox -- Diffusion and regularization of vector- and matrix-valued images
  • I. Yamada, N. Ogura, and N. Shirakawa -- A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems
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