Surveys on Solution Methods for Inverse Problems

1. Front Matter

   Pages i-v

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2. Introduction

   • D. Colton, H. W. Engl, A. K. Louis, J. R. McLaughlin, W. Rundell

   Pages 1-5

3. Convergence Rates Results for Iterative Methods for Solving Nonlinear Ill-Posed Problems

   • H. W. Engl, O. Scherzer

   Pages 7-34

4. Iterative Regularization Techniques in Image Reconstruction

   • Martin Hanke

   Pages 35-52

5. A Survey of Regularization Methods for First-Kind Volterra Equations

   • Patricia K. Lamm

   Pages 53-82

6. Layer Stripping

   • John Sylvester

   Pages 83-106

7. The Linear Sampling Method in Inverse Scattering Theory

   • David Colton, Andreas Kirsch, Peter Monk

   Pages 107-118

8. Carleman Estimates and Inverse Problems in the Last Two Decades

   • Michael V. Klibanov

   Pages 119-146

9. Local Tomographic Methods in Sonar

   • Alfred K. Louis, Eric Todd Quinto

   Pages 147-154

10. Efficient Methods in Hyperthermia Treatment Planning

    • T. Köhler, P. Maass, P. Wust

    Pages 155-167

11. Solving Inverse Problems with Spectral Data

    • Joyce R. McLaughlin

    Pages 169-194

12. Low Frequency Electromagnetic Fields in High Contrast Media

    • Liliana Borcea, George C. Papanicolaou

    Pages 195-233

13. Inverse Scattering in Anisotropic Media

    • Gunther Uhlmann

    Pages 235-251

14. Inverse Problems as Statistics

    • P. B. Stark

    Pages 253-275

15. Back Matter

    Pages 277-281

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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.

• Ill-posed problems
• geophysics
• image processing
• inverse scattering theory
• regularization methods
• scattering theory
• tomography

• Department of Mathematical Sciences, University of Delaware, Newark, USA

  David Colton

• Institut für Mathematik, Johannes-Kepler-Universität, Linz, Austria

  Heinz W. Engl

• Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Federal Republic of Germany

  Alfred K. Louis

• Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, USA

  Joyce R. McLaughlin

• Department of Mathematics, Texas A & M University, College Station, USA

  William Rundell

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