Combining synthesis sparse with analysis sparse for single image super-resolution

Abstract Sparse coding based-methods show great effectiveness in single image super-resolution (SR). Existing methods generally use only synthesis sparse coding. However, the analysis sparse coding model, which is an alternative to the synthesis sparse coding model, is typically neglected In this paper, we propose a novel single image SR method by combining synthesis sparse coding with analysis sparse coding. In contrast to the existing sparse coding-based SR methods, we replace synthesis sparse coding with analysis sparse coding in the low-resolution (LR) feature representation phase. Thus, we use an analysis dictionary to obtain the LR coefficients and use a synthesis dictionary to reconstruct the high-resolution (HR) patches. Due to the introducing of analysis sparse representation, the l 0 or l 1 optimization is replaced by soft threshold shrinkage, which is a more time-saving method. To improve the convergence of the training model, we introduce a linear mapping function that reveals the relationship between the HR coefficients and LR coefficients. An alternating optimization strategy is adopted to solve the improved training model. Furthermore, global and nonlocal constraints are taken into account to improve the quality of the reconstructed images. Compared with some existing SR methods, the experimental results demonstrate that our proposed method can obtain better performance.