Surveys on Solution Methods for Inverse Problems

✍ Scribed by D. Colton, H. W. Engl, A. K. Louis (auth.), Dr. David Colton, Dr. Heinz W. Engl, Dr. Alfred K. Louis, Dr. Joyce R. McLaughlin, Dr. William Rundell (eds.)

• Publisher: Springer-Verlag Wien
• Year: 2000
• Tongue: English
• Leaves: 278
• Edition: 1
• Category: Library

✦ Synopsis

Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

✦ Table of Contents

Front Matter....Pages i-v
Introduction....Pages 1-5
Convergence Rates Results for Iterative Methods for Solving Nonlinear Ill-Posed Problems....Pages 7-34
Iterative Regularization Techniques in Image Reconstruction....Pages 35-52
A Survey of Regularization Methods for First-Kind Volterra Equations....Pages 53-82
Layer Stripping....Pages 83-106
The Linear Sampling Method in Inverse Scattering Theory....Pages 107-118
Carleman Estimates and Inverse Problems in the Last Two Decades....Pages 119-146
Local Tomographic Methods in Sonar....Pages 147-154
Efficient Methods in Hyperthermia Treatment Planning....Pages 155-167
Solving Inverse Problems with Spectral Data....Pages 169-194
Low Frequency Electromagnetic Fields in High Contrast Media....Pages 195-233
Inverse Scattering in Anisotropic Media....Pages 235-251
Inverse Problems as Statistics....Pages 253-275
Back Matter....Pages 277-281

✦ Subjects

Numerical Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Potential Theory