Cluster-based image super-resolution via jointly low-rank and sparse representation

• A novel algorithm for single image super-resolution uses the cluster as the basic unit.
• The algorithm can enforce global constraint and capture local structure.
• We research the appropriate numbers of exemplars for low and high frequency patches.

In this paper, we propose a novel algorithm for single image super-resolution by developing a concept of cluster rather than using patch as the basic unit. For the proposed algorithm, all patches are splitted into numerous subspaces, and the optimal representation problem is solved with jointly low-rank and sparse regularization for each subspace. By enforcing global consistency constraint of each subspace with nuclear norm regularization and capturing local linear structure of each patch with ℓ1ℓ1-norm regularization, effective matching functions for test and exemplar patches can be created. Accordingly, the desirable results with low computational complexity are obtained. Experimental results show that the proposed algorithm generates high-quality images in comparison with other state-of-the-art methods.