Single-image super-resolution via patch-based and group-based local smoothness modeling

Local smoothness and nonlocal self-similarity of natural images are two main priors in the image restoration (IR) problem. Many IR methods have widely used patch-based modeling. Recently, the concept of grouping-based technique, the nonlocal patches with similar structures, has been introduced as the basic unit of sparse representation. In the group-based methods, the nonlocal self-similarity and the local sparsity properties are combined in a unified framework using the sparsity-based techniques. In this paper, a new model is proposed which utilizes both the patch and the group as the basic units of image modeling, called patch-based and group-based local smoothness modeling (PGLSM). More, precisely, in the proposed PGLSM scheme, the local smoothness in the patch-based unit is exploited by an isotropic total variation method and the local smoothness in the group-based unit is exploited by group-based sparse representation method. In this way, a novel technique for high-fidelity single-image super-resolution (SISR) via PGLSM is proposed, called SR-PGLSM. By adding nonlocal means (NLM) as the complementary regularization term to PGLSM, another technique for SISR is modeled, called SR_PGLSM_NLM. In order to efficiently solve the above variational problems, the split Bergman iterative technique has been leveraged. Extensive experimental results validate the effectiveness and robustness of the proposed methods. Our proposed schemes can recover more fine structures and achieve better results than the competing methods with the scaling factor of 2 and 3 and for noisy images both subjectively and objectively in most cases.