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

Handle URI:
http://hdl.handle.net/10754/599672
Title:
Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets
Authors:
Lenzen, F.; Lellmann, J.; Becker, F.; Schnörr, C.
Abstract:
© 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.
Citation:
Lenzen F, Lellmann J, Becker F, Schnörr C (2014) Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets. SIAM Journal on Imaging Sciences 7: 2139–2174. Available: http://dx.doi.org/10.1137/130938347.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Imaging Sciences
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2014
DOI:
10.1137/130938347
Type:
Article
ISSN:
1936-4954
Sponsors:
DAMTP/CIA, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, UK (j.lellmann@damtp.cam.ac.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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLenzen, F.en
dc.contributor.authorLellmann, J.en
dc.contributor.authorBecker, F.en
dc.contributor.authorSchnörr, C.en
dc.date.accessioned2016-02-28T06:07:13Zen
dc.date.available2016-02-28T06:07:13Zen
dc.date.issued2014-01en
dc.identifier.citationLenzen F, Lellmann J, Becker F, Schnörr C (2014) Solving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Sets. SIAM Journal on Imaging Sciences 7: 2139–2174. Available: http://dx.doi.org/10.1137/130938347.en
dc.identifier.issn1936-4954en
dc.identifier.doi10.1137/130938347en
dc.identifier.urihttp://hdl.handle.net/10754/599672en
dc.description.abstract© 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.en
dc.description.sponsorshipDAMTP/CIA, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, UK (j.lellmann@damtp.cam.ac.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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdaptive regularizationen
dc.subjectDeblurringen
dc.subjectDenoisingen
dc.subjectNonconvexen
dc.subjectQuasi-variational inequalitiesen
dc.subjectTotal variation regularizationen
dc.titleSolving Quasi-Variational Inequalities for Image Restoration with Adaptive Constraint Setsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Imaging Sciencesen
dc.contributor.institutionUniversitat Heidelberg, Heidelberg, Germanyen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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