Nuclear norm regularized coding with local position-patch and nonlocal similarity for face hallucination

Learning-based face hallucination methods have received much attention and progress in past few decades. Specially, position-patch based approaches have been proposed to replace the probabilistic graph-based or manifold learning-based ones. As opposed to the existing patch based methods, where the input image patch matrix is converted into vectors before combination coefficients calculation, in this paper, we propose to directly use the image matrix based regression model for combination coefficients computation to preserve the essential structural information of the input patch matrix. For each input low-resolution (LR) patch matrix, its combination coefficients over the training image patch matrices at the same position can be computed. Then the corresponding high-resolution (HR) patch matrix can be obtained with the LR training patches replaced by the corresponding HR ones. The nonlocal self-similarities are finally utilized to further improve the hallucination performance. Various experimental results on standard face databases indicate that our proposed method outperforms some state-of-the-art algorithms in terms of both visual quantity and objective metrics.