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PCA Reduced Gaussian Mixture Models with Applications in Superresolution

dc.rights.licenseopenen_US
dc.contributor.authorHERTRICH, Johannes
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorNGUYEN, Lan
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierInstitut de Chimie de la Matière Condensée de Bordeaux [ICMCB]
dc.contributor.authorBERNARD, Dominique
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
dc.contributor.authorBERTHOUMIEU, Yannick
hal.structure.identifierInstitut de Chimie de la Matière Condensée de Bordeaux [ICMCB]
dc.contributor.authorSAADALDIN, Abdellatif
dc.contributor.authorSTEIDL, Gabriele
dc.date.accessioned2022-08-26T09:38:24Z
dc.date.available2022-08-26T09:38:24Z
dc.date.issued2022
dc.identifier.issn1930-8337en_US
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/140595
dc.description.abstractEnDespite the rapid development of computational hardware, the treatment of largeand high dimensional data sets is still a challenging problem. This paper providesa twofold contribution to the topic. First, we propose a Gaussian Mixture Model inconjunction with a reduction of the dimensionality of the data in each componentof the model by principal component analysis, called PCA-GMM. To learn the (lowdimensional) parameters of the mixture model we propose an EM algorithm whoseM-step requires the solution of constrained optimization problems. Fortunately,these constrained problems do not depend on the usually large number of samplesand can be solved efficiently by an (inertial) proximal alternating linearized mini-mization algorithm. Second, we apply our PCA-GMM for the superresolution of 2Dand 3D material images based on the approach of Sandeep and Jacob. Numericalresults confirm the moderate influence of the dimensionality reduction on the overallsuperresolution result.
dc.description.sponsorshipSuper-résolution d'images multi-échelles en sciences des matériaux avec des attributs géométriques - ANR-18-CE92-0050en_US
dc.language.isoENen_US
dc.subject.enGaussian mixture models
dc.subject.enexpectation maximization algorithm
dc.subject.endimensionality reduction
dc.subject.enprincipal component analysis
dc.subject.enmaximum likelihood estimation
dc.subject.ensuperresolution
dc.title.enPCA Reduced Gaussian Mixture Models with Applications in Superresolution
dc.typeArticle de revueen_US
dc.identifier.doi10.3934/ipi.2021053en_US
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]en_US
dc.subject.halInformatique [cs]/Traitement du signal et de l'imageen_US
dc.subject.halMathématiques [math]en_US
dc.identifier.arxiv2009.08670en_US
bordeaux.journalInverse Problems and Imagingen_US
bordeaux.page341-366en_US
bordeaux.volume16en_US
bordeaux.hal.laboratoriesLaboratoire d’Intégration du Matériau au Système (IMS) - UMR 5218en_US
bordeaux.issue2en_US
bordeaux.institutionUniversité de Bordeauxen_US
bordeaux.institutionBordeaux INPen_US
bordeaux.institutionCNRSen_US
bordeaux.peerReviewedouien_US
bordeaux.inpressnonen_US
bordeaux.import.sourcehal
hal.identifierhal-02941479
hal.version1
hal.exportfalse
workflow.import.sourcehal
dc.rights.ccPas de Licence CCen_US
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Inverse%20Problems%20and%20Imaging&rft.date=2022&rft.volume=16&rft.issue=2&rft.spage=341-366&rft.epage=341-366&rft.eissn=1930-8337&rft.issn=1930-8337&rft.au=HERTRICH,%20Johannes&NGUYEN,%20Lan&AUJOL,%20Jean-Fran%C3%A7ois&BERNARD,%20Dominique&BERTHOUMIEU,%20Yannick&rft.genre=article


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