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Rayleigh quotient minimization for absolutely one-homogeneous functionals

hal.structure.identifierDepartment of Electrical Engineering - Technion [Haïfa] [EE-Technion]
dc.contributor.authorFELD, Tal
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierDepartment of Electrical Engineering - Technion [Haïfa] [EE-Technion]
dc.contributor.authorGILBOA, Guy
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
dc.date.accessioned2024-04-04T03:00:24Z
dc.date.available2024-04-04T03:00:24Z
dc.date.issued2019
dc.identifier.issn0266-5611
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192814
dc.description.abstractEnIn this paper we examine the problem of minimizing generalized Rayleigh quotients of the form J(u)/H(u), where both J and H are absolutely one-homogeneous functionals. This can be viewed as minimizing J where the solution is constrained to be on a generalized sphere with H(u) = 1, where H is any norm or semi-norm. The solution admits a nonlinear eigenvalue problem, based on the subgradients of J and H. We examine several flows which minimize the ratio. This is done both by time-continuous flow formulations and by discrete iterations. We focus on a certain flow, which is easier to analyze theoretically, following the theory of Brezis on flows with maximal monotone operators. A comprehensive theory is established, including convergence of the flow. We then turn into a more specific case of minimizing graph total variation on the L1 sphere, which approximates the Cheeger-cut problem. Experimental results show the applicability of such algorithms for clustering and classification of images.
dc.description.sponsorshipGeneralized Optimal Transport Models for Image processing - ANR-16-CE33-0010
dc.language.isoen
dc.publisherIOP Publishing
dc.title.enRayleigh quotient minimization for absolutely one-homogeneous functionals
dc.typeArticle de revue
dc.identifier.doi10.1088/1361-6420/ab0cb2
dc.subject.halInformatique [cs]/Traitement des images
dc.description.sponsorshipEuropeNonlocal Methods for Arbitrary Data Sources
bordeaux.journalInverse Problems
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01864129
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01864129v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Inverse%20Problems&rft.date=2019&rft.eissn=0266-5611&rft.issn=0266-5611&rft.au=FELD,%20Tal&AUJOL,%20Jean-Fran%C3%A7ois&GILBOA,%20Guy&PAPADAKIS,%20Nicolas&rft.genre=article


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