Total variation image restoration using hyper-Laplacian prior with overlapping group sparsity

• A total variation based image restoration method is proposed that using hyper-Laplacian prior for image gradient and the overlapping group sparsity prior for sparser image representation constraint.
• The alternating direction method of multipliers (ADMM) method is adopted to optimize the complex object function of the proposed model. Parameter selection criterions are discussed for the complex formulation.
• The method has good performance in convergence and suppressing staircase artifacts, which makes a good balance between alleviating staircase effects and preserving image details.
• An image restoration method using hyper-Laplacian prior and overlapping group sparsity.

Image restoration is a highly ill-posed problem and requires to be regularized. Many common image priors aim to make full use of natural image prior information. Total variation (TV) regularize prior has good performance of preserving edges but also has drawbacks in arising In this paper, we propose a total variation based image restoration method using hyper-Laplacian prior for image gradient and the overlapping group sparsity prior for sparser image representation constraint. We adopt the alternating direction method of multipliers (ADMM) method to optimize the object function of the proposed model and discuss the parameter selection criterion in the complex formulation. Finally, we carry out experiments on various degrade images and compare our method with several classical state-of-the-art methods. Experimental results show that our method has good performance in convergence and suppressing staircase artifacts, which makes a good balance between alleviating staircase effects and preserving image details.