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.

翻译：尽管计算硬件的迅速发展,大型和高维数据集的处理仍是一个具有挑战性的问题,本文件对这一专题作出了双重贡献。首先,我们提议采用高山混合模型,同时通过主要组成部分分析,减少模型每个组成部分的数据的维度,称为PCC-GMM。要了解混合物模型的(低维)参数,我们提议采用EM算法,其M步法需要解决限制优化的问题。幸运的是,这些受限制的问题并不取决于通常的大量样本,而可以通过一种(自然的)准氧化物交替线性最小化算法来有效解决。第二,我们运用我们的五氯苯甲醚-GMMM法,根据Sandep和Jacob的方法,对2D和3D材料图像的超分辨率进行应用。数字结果证实了维度减少对总体超分辨率结果的适度影响。