Colton D., Engl H.W., Louis A.K., McLaughlin J.R., Rundell W. (eds.)Surveys on Solution Methods for Inverse Problems

Wien: Springer, 2000. - 275p.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.Convergence Rates Results for Iterative Methods for Solving Nonlinear Ill-Posed Problems.
Iterative Regularization Techniques in Image Reconstruction.
A Survey of Regularization Methods for First-Kind Volterra Equations.
Layer Stripping.
The Linear Sampling Method in Inverse Scattering Theory.
Carleman Estimates and Inverse Problems in the Last Two Decades.
Local Tomographic Methods in Sonar.
Efficient Methods in Hyperthermia Treatment Planning.
Solving Inverse Problems with Spectral Data.
Low Frequency Electromagnetic Fields in High Contrast Media.
Inverse Scattering in Anisotropic Media.
Inverse Problems as Statistics.