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.
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978-0-8218-2979-0 (9780821829790)
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Schweitzer Klassifikation
Regularization of nonlinear unstable operator equations by secant methods with application to gravitational sounding problem by R. B. Alexeev and A. B. Smirnova A fractal set constructed from a class of wavelet sets by J. J. Benedetto and S. Sumetkijakan Joint invariant signatures for curve recognition by M. Boutin Inpainting based on nonlinear transport and diffusion by T. F. Chan and J. Shen Towards fast non-rigid registration by U. Clarenz, M. Droske, and M. Rumpf A note on wavelet-based inversion algorithms by C. De Mol and M. Defdrise A comparison between the wavelet-Galerkin and the Sinc-Galerkin methods in solving nonhomogeneous heat equations by M. El-Gamel and A. I. Zayed Fast diffusion registration by B. Fischer and J. Modersitzki Iterative stabilization and edge detection by C. W. Groetsch and O. Scherzer Backprojections in tomography, spherical functions and addition formulas: A few challenges by F. A. Grunbaum Mathematical models for 2d positron emission tomography by B. A. Mair and J. A. Zahnen Explicit versus implicit relative error regularization on the space of functions of bounded variation by O. Scherzer Sampling methods for approximate solution of pde by F. Stenger, A. R. Naghsh-Nilchi, J. Niebsch, and R. Ramlau Diffusion and regularization of vector- and matrix-valued images by J. Weickert and T. Brox A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems by I. Yamada, N. Ogura, and N. Shirakawa.
