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The structure of optimal parameters for image restoration problems

dc.creatorde, los Reyes JC
dc.creatorSchönlieb, CB
dc.creatorValkonen, T
dc.date.accessioned2018-11-24T23:18:23Z
dc.date.available2015-09-16T10:41:44Z
dc.date.available2018-11-24T23:18:23Z
dc.date.issued2015-09-16
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/250589
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3266
dc.description.abstractWe study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general type of regulariser is considered, which encompasses total variation (TV), total generalized variation (TGV) and infimal-convolution total variation (ICTV). We prove that under certain conditions on the given data optimal parameters derived by bilevel optimisation problems exist. A crucial point in the existence proof turns out to be the boundedness of the optimal parameters away from 0 which we prove in this paper. The analysis is done on the original -- in image restoration typically non-smooth variational problem -- as well as on a smoothed approximation set in Hilbert space which is the one considered in numerical computations. For the smoothed bilevel problem we also prove that it Γ converges to the original problem as the smoothing vanishes. All analysis is done in function spaces rather than on the discretised learning problem.
dc.languageen
dc.publisherElsevier
dc.publisherJournal of Mathematical Analysis and Applications
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsCreative Commons Attribution 4.0 International License
dc.subjecttotal variation
dc.subjecttotal generalised variation
dc.subjectbi-level optimisation
dc.subjectoptimality
dc.subjectparameter choice
dc.titleThe structure of optimal parameters for image restoration problems
dc.typeArticle


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