Show simple item record

dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.date.accessioned2009-06-19T08:57:48Z
dc.date.available2009-06-19T08:57:48Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/365
dc.language.isoenen
dc.subjectadapted basesen
dc.subjectnon-local denoisingen
dc.subjectmanifolden
dc.subjectImage processingen
dc.subject.ddc519en
dc.titleImage Processing with Non-local Spectral Basesen
dc.typeArticle accepté pour publication ou publiéen_US
dc.description.abstractenThis article studies regularization schemes that are defined using a lifting of the image pixels in a high dimensional space. For some specific classes of geometric images, this discrete set of points is sampled along a low dimensional smooth manifold. The construction of differential operators on this lifted space allows one to compute PDE flows and perform variational optimizations. All these schemes lead to regularizations that exploit the manifold structure of the lifted image. Depending on the specific definition of the lifting, one recovers several well-known semi-local and non-local denoising algorithms that can be interpreted as local estimators over a semi-local or a non-local manifold. This framework also allows one to define thresholding operators in adapted orthogonal bases. These bases are eigenvectors of the discrete Laplacian on a manifold adapted to the geometry of the image. Numerical results compare the efficiency of PDE flows, energy minimizations and thresholdings in the semi-local and non-local settings. The superiority of the non-local computations is studied through the performance of non-linear approximation in orthogonal bases.en
dc.relation.isversionofjnlnameMultiscale Modeling & Simulation
dc.relation.isversionofjnlvol7en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2008-06
dc.relation.isversionofjnlpages703-730en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/07068881Xen
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00359721/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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