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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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ISSN
1569-3945
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Volume 15, Issue 4 (Jul 2007)

Issues

Surrogate functionals and thresholding for inverse interface problems

S. Kindermann
  • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email:
/ R. Ramlau
  • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email:
Published Online: 2007-06-27 | DOI: https://doi.org/10.1515/jiip.2007.021

We propose a new algorithm for computing regularized solutions to inverse problems where the unknown functions is a characteristic function and where the forward operator is linear. Our approach can be seen as an alternative to the level-set method and is based on an efficient computation of minimizers for a Tikhonov functional. One main ingredient is to use surrogate functionals to define an iteration which has a subsequence converging to a limit that can be interpreted as a critical point. For the minimization of the surrogate functionals we propose the method of exact relaxation, which allows us to compute exact minimizer for the corresponding binary optimization problem.

Key Words: Inverse problem,; interface problem,; regularization,; thresholding,; bounded variation,; exact relaxation,; surrogate functional,; level set method,; topological derivative.

About the article

Published Online: 2007-06-27

Published in Print: 2007-07-20


Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2007.021.

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