Generalized nonconvex nonsmooth four-directional total variation with overlapping group sparsity for image restoration

In this paper, we address the challenge of image deblurring in the presence of Gaussian noise. To achieve high-quality image restoration, we introduce an optimization framework that integrates four-directional total variation regularization, overlapping group sparsity, and a range of nonconvex penalties. This novel model effectively mitigates the staircase artifacts associated with total variation regularization and enhances restoration quality by leveraging domain-specific information about image pixels. Compared to the l(1) norm, the nonconvex penalty applied to overlapping groups promotes sparsity in image gradients at the group level. To solve this nonconvex optimization problem, we propose a proximal alternating reweighted minimization algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. Theoretically, we establish that the sequences generated by the proposed algorithm converge to a critical point using the Kurdyka-Lojasiewicz property. Experimental results validate the superiority of our approach over competing methods.