Solving quasi-variational inequalities for image restoration with adaptive constraint sets

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

*Corresponding author for this work
6 Citations (Scopus)


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
JournalSIAM Journal on Imaging Sciences
Issue number4
Pages (from-to)2139-2174
Number of pages36
Publication statusPublished - 11.11.2014


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