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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChizat, Lénaïc
HAL ID: 19586
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSchmitzer, Bernhard
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierCentre de Mathématiques et de Leurs Applications [CMLA]
dc.contributor.authorVialard, François-Xavier
dc.date.accessioned2018-03-01T10:29:17Z
dc.date.available2018-03-01T10:29:17Z
dc.date.issued2010
dc.identifier.issn1615-3375
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17491
dc.language.isoenen
dc.subjectWassersteinen
dc.subjectOptimal Transporten
dc.subjectConvex optimizationen
dc.subjectFisher-Raoen
dc.subjectUnbalanced optimal transporten
dc.subjectWasserstein L2 metricen
dc.subjectFisher–Rao metricen
dc.subjectPositive Radon measuresen
dc.subject.ddc621.3en
dc.titleAn Interpolating Distance between Optimal Transport and Fisher-Raoen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper defines a new transport metric over the space of non-negative measures. This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses. It is defined as a generalization of the dynamical formulation of optimal transport of Benamou and Brenier, by introducing a source term in the continuity equation. The influence of this source term is measured using the Fisher-Rao metric, and is averaged with the transportation term. This gives rise to a convex variational problem defining our metric. Our first contribution is a proof of the existence of geodesics (i.e. solutions to this variational problem). We then show that (generalized) optimal transport and Fisher-Rao metrics are obtained as limiting cases of our metric. Our last theoretical contribution is a proof that geodesics between mixtures of sufficiently close Diracs are made of translating mixtures of Diracs. Lastly, we propose a numerical scheme making use of first order proximal splitting methods and we show an application of this new distance to image interpolation.en
dc.relation.isversionofjnlnameFoundations of Computational Mathematics
dc.relation.isversionofjnlvol18en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2018-02
dc.relation.isversionofjnlpages1–44en
dc.relation.isversionofdoi10.1007/s10208-016-9331-yen
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelTraitement du signalen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-03-01T10:20:14Z
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