Single image super resolution via manifold linear approximation using sparse subspace clustering

This paper considers the problem of single image super-resolution (SR). Previous example-based SR approaches mainly focus on analyzing the co-occurrence property of low resolution (LR) and high resolution (HR) patches via dictionary learning. In this paper, we propose a novel approach based on local linear approximation of the HR patch space using a sparse subspace clustering (SSC) algorithm. Our approach exploits the underlying HR patches´ non-linear space by considering it as a low dimensional manifold in a high dimensional Euclidean space, and by employing each training HR patch as a sample from the manifold. We utilize the SSC algorithm to create the set of low dimensional linear spaces that are considered, approximately, as tangent spaces at the HR samples. Based on the obtained approximated tangent spaces, we examine the structure of the underlying HR manifold that allows locating the co-occurrence HR patch for a given LR one. The proposed approach requires a small number of training HR samples (about 1000 patches), without any prior assumption about the LR images. A comparison of the obtained results with other state-of-the-art methods clearly indicates the viability of the proposed approach.