Single Image Super-Resolution via Sparse Representation over Directionally Structured Dictionaries Based on the Patch Gradient Phase Angle

We propose a single-image super-resolution algorithm based on sparse representation over a set of cluster dictionary pairs. For each cluster, a directionally structured dictionary pair is designed. The dominant angle in the patch gradient phase matrix is employed as an approximately scale-invariant measure. This measure serves for patch clustering and sparse model selection. The dominant phase angle of each low resolution patch is found and used to identify its corresponding cluster. Then, the sparse coding coefficients of this patch with respect to the low resolution cluster dictionary are calculated. These coefficients are imposed on the high resolution dictionary of the same cluster to obtain a high resolution patch estimate. In experiments conducted on several images, the proposed algorithm is shown to out-perform the algorithm that uses a single universal dictionary pair, and to be competitive to the state-of-the art algorithm. This is validated in terms of PSNR, SSIM and visual comparison.