Single Image Super-Resolution using Compressive Sensing with Learned Overcomplete Dictionary

This paper proposes a novel framework that unifies the concept of sparsity of a signal over a properly chosen basis set and the theory of signal reconstruction via compressed sensing in order to obtain a high-resolution image derived by using a single down-sampled version of the same image. First, we enforce sparse overcomplete representations on the low-resolution patches of the input image. Then, using the sparse coefficients as obtained above, we reconstruct a high-resolution output image. A blurring matrix is introduced in order to enhance the incoherency between the sparsifying dictionary and the sensing matrices which also resulted in better preservation of image edges and other textures. When compared with the similar techniques, the proposed method yields much better result both visually and quantitatively.