Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
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Surrogate functionals and thresholding for inverse interface problems
1Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email: (email)
2Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email: (email)
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 4, Pages 387–401, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2007.021, June 2007
- Published Online:
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.
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