Simultaneous sparse coding with Laplacian scale mixture prior for image restoration

Group-based sparse representation modeling of natural images codes each patch in a group as a sparse linear combination from an over-complete dictionary and assumes that the coding coefficients of each patch have a common set of nonzero support. This model has shown great success in image restoration (IR) applications; however, current group-based sparse models are simple extensions of traditional L0 or L1 sparse models and lack spatial adaption and principled fashion. We propose a group-based sparse model named as simultaneously sparse coding with Laplacian scale mixture (LSM) prior through probabilistic approach. In this model, the representation coefficients of each patch in group are characterized by the same LSM prior, which is dominated by the shared scale variables. By imposing a hyperprior distribution over the scale variables, the sparse coefficients and shared scale variables can be jointly estimated via alternating optimization. Furthermore, we generalize this model to process more general IR problems under the plug-and-play alternating direction method of multipliers framework. Extensive experiments on image denoising, deblurring, and single-image super-resolution demonstrate that the proposed method achieves notable objective and subjective improvements over many state-of-the-art restored methods.