Rayleigh quotient minimization for absolutely one-homogeneous functionals
| hal.structure.identifier | Department of Electrical Engineering - Technion [Haïfa] [EE-Technion] | |
| dc.contributor.author | FELD, Tal | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| hal.structure.identifier | Department of Electrical Engineering - Technion [Haïfa] [EE-Technion] | |
| dc.contributor.author | GILBOA, Guy | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| dc.date.accessioned | 2024-04-04T03:00:24Z | |
| dc.date.available | 2024-04-04T03:00:24Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0266-5611 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192814 | |
| dc.description.abstractEn | In 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.sponsorship | Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010 | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.title.en | Rayleigh quotient minimization for absolutely one-homogeneous functionals | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1361-6420/ab0cb2 | |
| dc.subject.hal | Informatique [cs]/Traitement des images | |
| dc.description.sponsorshipEurope | Nonlocal Methods for Arbitrary Data Sources | |
| bordeaux.journal | Inverse Problems | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01864129 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01864129v1 | |
| bordeaux.COinS | ctx_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 |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||