Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets

F. Lenzen, J. Lellmann, F. Becker, C. Schnörr

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


© 2014 Society for Industrial and Applied Mathematics. We consider a class of quasi-variational inequalities (QVIs) for adaptive image restoration, where the adaptivity is described via solution-dependent constraint sets. In previous work we studied both theoretical and numerical issues. While we were able to show the existence of solutions for a relatively broad class of problems, we encountered difficulties concerning uniqueness of the solution as well as convergence of existing algorithms for solving QVIs. In particular, it seemed that with increasing image size the growing condition number of the involved differential operator posed severe problems. In the present paper we prove uniqueness for a larger class of problems, particularly independent of the image size. Moreover, we provide a numerical algorithm with proved convergence. Experimental results support our theoretical findings.
Original languageEnglish (US)
Pages (from-to)2139-2174
Number of pages36
JournalSIAM Journal on Imaging Sciences
Issue number4
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: DAMTP/CIA, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, UK ( The work of this author was supported by Award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST), by EPSRC first grant EP/J009539/1, and by Royal Society International Exchange Award IE110314.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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