Show simple item record

dc.contributor.authorChambolle, Antonin
dc.contributor.authorDuval, Vincent
dc.contributor.authorPeyré, Gabriel
dc.contributor.authorPoon, Clarice
dc.date.accessioned2017-11-02T14:53:19Z
dc.date.available2017-11-02T14:53:19Z
dc.date.issued2016
dc.identifier.issn0266-5611
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16903
dc.language.isoenen
dc.subjectcalibrable set
dc.subjectdenoising
dc.subjectoptimization
dc.subjectTotal variation
dc.subject.ddc519en
dc.titleGeometric properties of solutions to the total variation denoising problem
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first contribution of this paper is a precise mathematical definition of the “extended support” (associated to the noise-free image) of TV denoising. It is intuitively the region which is unstable and will suffer from the staircasing effect. We highlight in several practical cases, such as the indicator of convex sets, that this region can be determined explicitly. Our second and main contribution is a proof that the TV denoising method indeed restores an image which is exactly constant outside a small tube surrounding the extended support. The radius of this tube shrinks toward zero as the noise level vanishes, and are able to determine, in some cases, an upper bound on the convergence rate. For indicators of so-called “calibrable” sets (such as disks or properly eroded squares), this extended support matches the edges, so that discontinuities produced by TV denoising cluster tightly around the edges. In contrast, for indicators of more general shapes or for complicated images, this extended support can be larger. Beside these main results, our paper also proves several intermediate results about fine properties of TV regularization, in particular for indicators of calibrable and convex sets, which are of independent interest.
dc.relation.isversionofjnlnameInverse Problems
dc.relation.isversionofjnlvol33
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2016
dc.relation.isversionofdoihttps://doi.org/10.1088/0266-5611/33/1/015002
dc.identifier.urlsitehttps://arxiv.org/abs/1602.00087
dc.relation.isversionofjnlpublisherIOP Science
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T09:18:46Z
hal.person.labIds89626*
hal.person.labIds60*
hal.person.labIds60*
hal.person.labIds54798$$$60*


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record