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On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds

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.authorBÉNARD, Pierre-Jean
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLECLAIRE, Arthur
dc.date.accessioned2024-04-04T02:34:45Z
dc.date.available2024-04-04T02:34:45Z
dc.date.issued2023-09-28
dc.identifier.issn0924-9907
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190574
dc.description.abstractEnIn this article, we study the size of strong basins of attractions for the non-convex sparse spike estimation problem. We first extend previous results to obtain a lower bound on the size of sets where gradient descent converges with a linear rate to the minimum of the non-convex objective functional. We then give an upper bound that shows that the dependency of the lower bound with respect to the number of measurements reflects well the true size of basins of attraction for random Gaussian Fourier measurements. These theoretical results are confirmed by experiments.
dc.description.sponsorshipRégularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enOn strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie de l'information et codage [math.IT]
dc.subject.halInformatique [cs]
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
bordeaux.journalJournal of Mathematical Imaging and Vision
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-04047677
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04047677v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Imaging%20and%20Vision&rft.date=2023-09-28&rft.eissn=0924-9907&rft.issn=0924-9907&rft.au=TRAONMILIN,%20Yann&AUJOL,%20Jean-Fran%C3%A7ois&B%C3%89NARD,%20Pierre-Jean&LECLAIRE,%20Arthur&rft.genre=article


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