PCA Reduced Gaussian Mixture Models with Applications in Superresolution

Johannes Hertrich; Dang Phoung Lan Nguyen; Jean-Fancois Aujol; Dominique Bernard; Yannick Berthoumieu; Abdellatif Saadaldin; Gabriele Steidl

doi:10.3934/ipi.2021053

arXiv · 2009.07520

PCA Reduced Gaussian Mixture Models with Applications in Superresolution

Johannes Hertrich·Dang Phoung Lan Nguyen·Jean-Fancois Aujol·Dominique Bernard·Yannick Berthoumieu·Abdellatif Saadaldin·Gabriele Steidl

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Abstract

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, called PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.

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BibTeX RIS

Johannes Hertrich, Dang Phoung Lan Nguyen, Jean-Fancois Aujol, Dominique Bernard, Yannick Berthoumieu, Abdellatif Saadaldin, Gabriele Steidl. 2020-09-16. PCA Reduced Gaussian Mixture Models with Applications in Superresolution. https://doi.org/10.3934/ipi.2021053

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