  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.
