Dang-Phuong-Lan Nguyen

Dang-Phuong-Lan Nguyen, Jean-François Aujol, Yannick Berthoumieu

Single Image Super Resolution (SISR) methods aim to recover the clean images in high resolution from low resolution observations.A family of patch-based approaches have received considerable attention and development. The minimum mean square error (MMSE) methodis a powerful image restoration method that uses a probability model on the patches of images. This paper proposes an algorithm to learn a jointgeneralized Gaussian mixture model (GGMM) from a pair of the low resolution patches and the corresponding high resolution patches fromthe reference data. We then reconstruct the high resolution image based on the MMSE method. Our numerical evaluations indicate that theMMSE-GGMM method competes with other state of the art methods.

Johannes Hertrich, Dang Phoung Lan Nguyen, Jean-Fancois Aujol et al.

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.