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


Type

Article

Change log

Authors

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

Abstract

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 problems 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 poses severe problems. In the present paper we prove uniqueness for a larger class of problems and in particular independent of the image size. Moreover, we provide a numerical algorithm with proved convergence. Experimental results support our theoretical findings.

Description

Keywords

quasi-variational inequalities, denoising, deblurring, adaptive regularization, total variation regularization, non-convex

Journal Title

SIAM Journal on Imaging Sciences

Conference Name

Journal ISSN

1936-4954
1936-4954

Volume Title

7

Publisher

Society for Industrial & Applied Mathematics (SIAM)

Rights

DSpace@Cambridge license
Sponsorship
Engineering and Physical Sciences Research Council (EP/M00483X/1)
Engineering and Physical Sciences Research Council (EP/J009539/1)
The work of J.L. was supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST), EPSRC first grant No. EP/J009539/1, and Royal Society International Exchange Award No. IE110314.