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PCA Reduced Gaussian Mixture Models with Applications in Superresolution

hal.structure.identifierTechnical University of Berlin / Technische Universität Berlin [TUB]
dc.contributor.authorHERTRICH, Johannes
hal.structure.identifierUniversité de Bordeaux [UB]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLaboratoire de l'intégration, du matériau au système [IMS]
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
hal.structure.identifierTechnical University of Berlin / Technische Universität Berlin [TUB]
dc.contributor.authorSTEIDL, Gabriele
dc.date.accessioned2024-04-04T02:49:45Z
dc.date.available2024-04-04T02:49:45Z
dc.date.issued2022
dc.identifier.issn1930-8337
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191847
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-CE92-0050
dc.language.isoen
dc.publisherAIMS American Institute of Mathematical Sciences
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 revue
dc.identifier.doi10.3934/ipi.2021053
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.subject.halMathématiques [math]
dc.identifier.arxiv2009.08670
bordeaux.journalInverse Problems and Imaging
bordeaux.page341-366
bordeaux.volume16
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02941479
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02941479v1
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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