Show simple item record

dc.contributor.authorGrimm, V
dc.contributor.authorMcLachlan, RI
dc.contributor.authorMcLaren, DI
dc.contributor.authorQuispel, GRW
dc.contributor.authorSchönlieb, CB
dc.date.accessioned2019-05-13T13:00:45Z
dc.date.available2019-05-13T13:00:45Z
dc.date.issued2017-06-28
dc.identifier.issn1751-8113
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/292706
dc.description.abstractDiscrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting.
dc.publisherIOP Sciences
dc.titleDiscrete gradient methods for solving variational image regularisation models
dc.typeArticle
prism.issueIdentifier29
prism.number295201
prism.publicationDate2017
prism.publicationNameJournal of Physics A: Mathematical and Theoretical
prism.volume50
dc.identifier.doi10.17863/CAM.39859
dcterms.dateAccepted2017-05-22
rioxxterms.versionofrecord10.1088/1751-8121/aa747c
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2017-06-28
dc.identifier.eissn1751-8121
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/N014588/1)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/M00483X/1)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/J009539/1)
pubs.funder-project-idAlan Turing Institute (unknown)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
pubs.funder-project-idLeverhulme Trust (RPG-2015-250)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/H023348/1)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (777826)
cam.issuedOnline2017-06-28


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record