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Article Dans Une Revue Inverse Problems and Imaging Année : 2022

PCA Reduced Gaussian Mixture Models with Applications in Superresolution

Résumé

Despite 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.
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Dates et versions

hal-02941479 , version 1 (17-09-2020)

Identifiants

Citer

Johannes Hertrich, Lan Dang Phuong Nguyen, Jean-François Aujol, Dominique Bernard, Yannick Berthoumieu, et al.. PCA Reduced Gaussian Mixture Models with Applications in Superresolution. Inverse Problems and Imaging , 2022, 16 (2), pp.341-366. ⟨10.3934/ipi.2021053⟩. ⟨hal-02941479⟩
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