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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR increased in 2014: 0.880
Rank 74 out of 310 in category Mathematics and 113 out of 255 in Applied Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 0.516
Source Normalized Impact per Paper (SNIP) 2014: 1.430
Impact per Publication (IPP) 2014: 0.613

Mathematical Citation Quotient (MCQ) 2014: 0.51

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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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