PCA Reduced Gaussian Mixture Models with Applications in Superresolution
NGUYEN, Lan
Laboratoire de l'intégration, du matériau au système [IMS]
Institut de Mathématiques de Bordeaux [IMB]
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Laboratoire de l'intégration, du matériau au système [IMS]
Institut de Mathématiques de Bordeaux [IMB]
NGUYEN, Lan
Laboratoire de l'intégration, du matériau au système [IMS]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Laboratoire de l'intégration, du matériau au système [IMS]
Institut de Mathématiques de Bordeaux [IMB]
Language
EN
Article de revue
This item was published in
Inverse Problems and Imaging. 2022, vol. 16, n° 2, p. 341-366
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Gaussian mixture models
expectation maximization algorithm
dimensionality reduction
principal component analysis
maximum likelihood estimation
superresolution
ANR Project
Super-résolution d'images multi-échelles en sciences des matériaux avec des attributs géométriques - ANR-18-CE92-0050