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The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTRAONMILIN, Yann
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLECLAIRE, Arthur
dc.date.accessioned2024-04-04T02:42:16Z
dc.date.available2024-04-04T02:42:16Z
dc.date.issued2022
dc.identifier.issn2049-8764
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191229
dc.description.abstractEnNon-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. We show how the size of the the basins of attraction of the minimizers of such problems is linked with the number of available measurements. This framework recovers known results about low-rank matrix estimation and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements. keywords: low-dimensional models, non-convex methods, low-rank matrix recovery, off-the-grid sparse recovery, Gaussian mixture model estimation from linear measurements.
dc.description.sponsorshipSuper-résolution d'images multi-échelles en sciences des matériaux avec des attributs géométriques - ANR-18-CE92-0050
dc.description.sponsorshipRégularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001
dc.language.isoen
dc.publisherOxford University Press (OUP)
dc.title.enThe basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
dc.typeArticle de revue
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.identifier.arxiv2009.08670
bordeaux.journalInformation and Inference
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02941814
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02941814v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Information%20and%20Inference&rft.date=2022&rft.eissn=2049-8764&rft.issn=2049-8764&rft.au=TRAONMILIN,%20Yann&AUJOL,%20Jean-Fran%C3%A7ois&LECLAIRE,%20Arthur&rft.genre=article


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