**Contemporary Mathematics**

Volume: 313;
2002;
305 pp;
Softcover

MSC: Primary 00; 45; 65; 34; 35; 41; 42;

Print ISBN: 978-0-8218-2979-0

Product Code: CONM/313

List Price: $96.00

Individual Member Price: $76.80

**Electronic ISBN: 978-0-8218-7903-0
Product Code: CONM/313.E**

List Price: $96.00

Individual Member Price: $76.80

# Inverse Problems, Image Analysis, and Medical Imaging

Share this page *Edited by *
*M. Zuhair Nashed; Otmar Scherzer*

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.

#### Table of Contents

# Table of Contents

## Inverse Problems, Image Analysis, and Medical Imaging

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- Regularization of nonlinear unstable operator equations by secant methods with application to gravitational sounding problem 112 free
- A fractal set constructed from a class of wavelet sets 1930
- Joint invariant signatures for curve recognition 3748
- Inpainting based on nonlinear transport and diffusion 5364
- Towards fast non-rigid registration 6778
- A note on wavelet-based inversion algorithms 8596
- A comparison between the Wavelet-Galerkin and the Sinc-Galerkin methods in solving nonhomogeneous heat equations 97108
- Fast diffusion registration 117128
- Iterative stabilization and edge detection 129140
- Backprojections in tomography, spherical functions and addition formulas: a few challenges 143154
- Mathematical models for 2D positron emission tomography 153164
- Explicit versus implicit relative error regularization on the space of functions of bounded variation 171182
- Sampling methods for approximate solution of pde 199210
- Diffusion and regularization of vector- and matrix-valued images 251262
- A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems 269280

#### Readership

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