Hybrid non-convex second-order total variation with applications to non-blind image deblurring

Total variation is a very popular method for image restoration, yet it produces undesirable staircase artifacts. In this paper, a combined second-order non-convex total variation with overlapping group sparse regularizer for staircase artifact removal is proposed. The non-convex higher-order TV regularizer is introduced to model the observation that the staircase effect must be appropriately smoothen out in the restored image while preserving its edges. However, using the non-convex higher-order TV alone tends to smoothen the image while amplifying speckle artifacts. To deal with this, the overlapping group sparse regularizer is added to balance the effects produced by the non-convex higher-order TV regularizer. An efficient re-weighted l1 alternating direction method is formulated to solve the corresponding iterative scheme. Comparative analysis with three algorithms, namely overlapping group sparse total variation, total generalized variation and the fast non-smooth non-convex method, with two different blur kernels is carried out. The results from peak signal-to-noise ratio and structural similarity index measure show the effectiveness of our proposed method when compared to the mentioned algorithms.