Show simple item record

Total Variation Denoising and Support Localization of the Gradient

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDuval, Vincent
HAL ID: 7243
ORCID: 0000-0002-7709-256X
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
hal.structure.identifierDepartment of Applied Mathematics and Theoretical Physics [Cambridge] [DAMTP]
dc.contributor.authorPoon, Clarice
dc.date.accessioned2023-01-13T13:42:12Z
dc.date.available2023-01-13T13:42:12Z
dc.date.issued2016
dc.identifier.issn1742-6588
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23712
dc.language.isoenen
dc.subject.ddc510en
dc.titleTotal Variation Denoising and Support Localization of the Gradienten
dc.typeCommunication / Conférence
dc.description.abstractenThis paper describes the geometrical properties of the solutions to the total variation denoising method. A folklore statement is that this method is able to restore sharp edges, but at the same time, might introduce some staircasing (i.e. “fake” edges) in flat areas. Quite surprisingly, put aside numerical evidences, almost no theoretical result are available to backup these claims. The first contribution of this paper is a precise mathematical definition of the “extended support” (associated to the noise-free image) of TV denoising. This is intuitively the region which is unstable and will suffer from the staircasing effect. Our main result shows that the TV denoising method indeed restores a piece-wise constant image outside a small tube surrounding the extended support. Furthermore, the radius of this tube shrinks toward zero as the noise level vanishes and in some cases, an upper bound on the convergence rate is given.en
dc.relation.ispartoftitleJournal of Physics: Conference Series, Volume 756, 6th International Workshop on New Computational Methods for Inverse Problems 20 May 2016, Cachan, Franceen
dc.relation.ispartofpublnameJournal of Physics. Conference Seriesen
dc.subject.ddclabelMathématiquesen
dc.relation.conftitle6th International Workshop on New Computational Methods for Inverse Problemsen
dc.relation.confdate2016-05
dc.relation.confcityCachanen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen
dc.identifier.doi10.1088/1742-6596/756/1/012007en
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2023-01-13T13:36:21Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


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