Dual-sparsity regularized sparse representation for single image super-resolution

• Row nonlocal similarity regularization term with l1-norm constraint is explored.
• Dual-sparsity regularized sparse representation model is presented for SISR.
• Iterative shrinkage algorithm is extended to solve dual l1-norm constraints model.

Recently, by exploring the column nonlocal similarity prior among the sparse representation coefficients, the column nonlocal similarity sparse representation models for solving the ill-posed single image super-resolution (SISR) problem are attracting more and more attention. However, these conventional models consider only the prior among nonlocal similar sparse representation coefficients, and fail to consider the prior among all entries (or rows) of the sparse representation coefficient. Hence the modeling capability may be limited. In fact, if a cluster of similar representation coefficients is rearranged into a matrix in the sparse representation coefficient space, the nonlocal similarity priors exist both among columns and rows. Using the row nonlocal similarity prior, a row nonlocal similarity regularization term with l1-norm constraint is explored. By introducing it to the conventional column nonlocal similarity sparse representation model, we present a dual-sparsity regularized sparse representation (DSRSR) model. A surrogate function based iterative shrinkage algorithm is introduced to effectively solve the proposed model. Extensive experiments on SISR demonstrate that the presented model can effectively reconstruct the edge structures and suppress the noise, achieving convincing improvement over many state-of-the-art example-based methods in terms of PSNR, SSIM and visual quality.