Inverse Problems, Image Analysis, and Medical Imaging
About this Title
M. Zuhair Nashed and Otmar Scherzer, Editors
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.
Graduate students and research mathematicians; electrical engineers interested in signal processing and image processing; researchers in medical imaging.
Table of Contents
- Roman B. Alexeev and Alexandra B. Smirnova – Regularization of nonlinear unstable operator equations by secant methods with application to gravitational sounding problem [MR 1940986]
- John J. Benedetto and Songkiat Sumetkijakan – A fractal set constructed from a class of wavelet sets [MR 1940987]
- Mireille Boutin – Joint invariant signatures for curve recognition [MR 1940988]
- Tony F. Chan and Jianhong Shen – Inpainting based on nonlinear transport and diffusion [MR 1940989]
- U. Clarenz, M. Droske and M. Rumpf – Towards fast non-rigid registration [MR 1940990]
- Christine De Mol and Michel Defrise – A note on wavelet-based inversion algorithms [MR 1940991]
- Mohamed El-Gamel and Ahmed I. Zayed – A comparison between the wavelet-Galerkin and the sinc-Galerkin methods in solving nonhomogeneous heat equations [MR 1940992]
- Bernd Fischer and Jan Modersitzki – Fast diffusion registration [MR 1940993]
- C. W. Groetsch and O. Scherzer – Iterative stabilization and edge detection [MR 1940994]
- F. Alberto Grünbaum – Backprojections in tomography, spherical functions and addition formulas: a few challenges [MR 1940995]
- B. A. Mair and J. A. Zahnen – Mathematical models for 2D positron emission tomography [MR 1940996]
- O. Scherzer – Explicit versus implicit relative error regularization on the space of functions of bounded variation [MR 1940997]
- Frank Stenger, Ahmad Reza Naghsh-Nilchi, Jenny Niebsch and Ronny Ramlau – Sampling methods for approximate solution of PDE [MR 1940998]
- Joachim Weickert and Thomas Brox – Diffusion and regularization of vector- and matrix-valued images [MR 1940999]
- Isao Yamada, Nobuhiko Ogura and Nobuyasu Shirakawa – A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems [MR 1941000]