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dc.contributor.authorParisotto, Simoneen
dc.contributor.authorMasnou, Sen
dc.contributor.authorSchönlieb, CBen
dc.date.accessioned2020-04-23T23:30:30Z
dc.date.available2020-04-23T23:30:30Z
dc.date.issued2019-01-01en
dc.identifier.issn1936-4954
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/304654
dc.description.abstractWe analyze a new notion of total anisotropic higher-order variation which, differently from total generalized variation in [K. Bredies, K. Kunisch, and T. Pock, SIAM J. Imaging Sci., 3 (2010), pp. 492--526], quantifies for possibly nonsymmetric tensor fields their variations at arbitrary order weighted by possibly inhomogeneous, smooth elliptic anisotropies. We prove some properties of this total variation and of the associated spaces of tensors with finite variations. We show the existence of solutions to a related regularity-fidelity optimization problem. We also prove a decomposition formula which appears to be helpful for the design of numerical schemes, as shown in a companion paper, where several applications to image processing are studied.
dc.publisherSociety for Industrial and Applied Mathematics
dc.rightsAll rights reserved
dc.rights.uri
dc.titleHigher-order total directional variation: Analysisen
dc.typeArticle
prism.endingPage496
prism.issueIdentifier1en
prism.publicationDate2019en
prism.publicationNameSIAM Journal on Imaging Sciencesen
prism.startingPage474
prism.volume13en
dc.identifier.doi10.17863/CAM.51733
dcterms.dateAccepted2020-01-06en
rioxxterms.versionofrecord10.1137/19M1239210en
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-01-01en
dc.contributor.orcidParisotto, Simone [0000-0003-0865-0289]
dc.identifier.eissn1936-4954
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (1513548)
pubs.funder-project-idEPSRC (EP/H023348/1)
pubs.funder-project-idEPSRC (EP/N014588/1)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (777826)
pubs.funder-project-idLeverhulme Trust (RPG-2018-121)
pubs.funder-project-idLeverhulme Trust (PLP-2017-275)
pubs.funder-project-idAlan Turing Institute (Unknown)
pubs.funder-project-idEPSRC (EP/S026045/1)
pubs.funder-project-idEPSRC (EP/M00483X/1)
pubs.funder-project-idEPSRC (EP/L016516/1)


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