A novel adaptive non-convex TV<inline-formula><tex-math id="M1">$ ^{p,q} $</tex-math></inline-formula> model in image restoration

In this paper, we propose a novel adaptive non-convex TV$ ^{p, q} $ model. The model combines a non-convex regularization with a convex regularization, which can inherit the advantages of the two regularizations, and has a remarkable effect in enhancing image edges and avoiding over-smooth. Simultaneously, the model can eliminate the staircase effect. Moreover, we extend the model to an adaptive form which divides the image into a edge region and a piecewise constant region. In this model, the parameters adaptively change. In terms of algorithm, we employ the iterative support shrinking algorithm to solve these two proposed models. The convergence is also established. Experimental results show that the new non-convex TV$ ^{p, q} $ model and algorithm are effective for image restoration.