Image super-resolution with PCA reduced generalized Gaussian mixture models in materials science
Dang-Phuong-Lan Nguyen, Univ. Bordeaux, Bordeaux INP, CNRS, IMB, UMR 5251, F-33400 Talence, France, Johannes Hertrich, Jean–François Aujol, Yannick Berthoumieu, Univ. Bordeaux, Bordeaux INP, CNRS, IMS, UMR 5218, F-33400 Talence, France, TU Berlin, Straße des 17. Juni 136, D-10587 Berlin, Germany · Inverse Problems and Imaging · 2023
Single Image Super-Resolution algorithms based on patches have been noticed and widely used over the past decade. Recently, generalized Gaussian mixture models (GGMMs) have been shown to be a suitable tool for many image processing problems because of the flexible shape parameter. In this work, we introduce a supervised GGMM-based approach for super-resolution of two- and three-dimensional images, in particular materials images. We first propose to use a joint GGMM learned from concatenated vectors of high- and low-resolution training patches. For each low-resolution patch, we compute the minimum mean square error (MMSE) estimator and generate the high-resolution image by averaging these estimates. We select the MMSE approach using GGMM as the method is invariant to affine contrast change and also invariant to a linear super-resolution operator. Unfortunately, the large dimension of the concatenated high- and low-resolution patches leads to instabilities and an intractable computational effort when estimating the parameters of the GGMM. Thus, we propose to combine a GGMM with a principal component analysis and derive an EM algorithm for estimating the parameters of the arising model. We demonstrate the performance of our model by numerical examples on synthetic and real images of material microstructure.