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Despite the rapid development of computational hardware, the treatment oflarge and high dimensional data sets is still a challenging problem. This paperprovides a twofold contribution to the topic. First, we propose a GaussianMixture Model in conjunction with a reduction of the dimensionality of the datain 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 EMalgorithm whose M-step requires the solution of constrained optimizationproblems. Fortunately, these constrained problems do not depend on the usuallylarge number of samples and can be solved efficiently by an (inertial) proximalalternating linearized minimization algorithm. Second, we apply our PCA-GMM forthe superresolution of 2D and 3D material images based on the approach ofSandeep and Jacob. Numerical results confirm the moderate influence of thedimensionality reduction on the overall superresolution result.

PCA Reduced Gaussian Mixture Models with Applications in Superresolution