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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

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Surrogate functionals and thresholding for inverse interface problems

S. Kindermann1 / R. Ramlau2

1Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email:

2Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. 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

Publication History

Published Online:
2007-06-27

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.

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[1]
Lughofer and Kindermann
IEEE Transactions on Fuzzy Systems, 2010

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