Fast Single-Image Super-Resolution Via Tangent Space Learning of High-Resolution-Patch Manifold

Manifold assumption has been used in example-based super-resolution (SR) reconstruction from a single frame. Previous manifold- based SRapproaches (more generally example-based SR) mainly focus on analyzing the co-occurrence properties of low-resolution and high-resolution patches. This paper develops a novel single-image SR approach based on linear approximation of the high-resolution-patch space using a sparse subspace clustering algorithm. The approach exploits the underlying high-resolution patches nonlinear space by considering it as a low-dimensional manifold in a high-dimensional Euclidean space, and by considering each training high-resolution-patch as a sample from the manifold. We utilize the sparse subspace clustering algorithm to create the set of low-dimensional linear spaces that are considered, approximately, as tangent spaces at the high-resolution samples. Furthermore, we consider and analyze each tangent space as one point in a Grassmann manifold, which helps to compute geodesic pairwise distances among these tangent spaces. An optimal subset of these tangent spaces is then selected using a min-max algorithm. The optimal subset reduces the computational cost in comparison with using the full set of tangent spaces while still preserving the quality of the high-resolution image reconstruction. In addition, we perform hierarchical clustering on the optimal subset based on the geodesic distance, which helps to further achieve much faster SR algorithm. We also analytically prove the validity of the geodesic distance based clustering under the proposed framework. A comparison of the obtained results with other related methods in both high-resolution image quality and computational complexity clearly indicates the viability of the proposed framework.