An Efficient Adaptive Total Variation Regularization for Image Denoising

In this paper, we propose an efficient adaptive total variation regularization scheme for ROF image denoising problem. By smoothing the non-differentiable convex function appearing in the traditional total variation by its Moreau envelope and selecting the smoothing factor to be inversely proportional to the likelihood of the presence of an edge at discrete image location, the proposed adaptive total variation can remove the stair casing effects caused by total variation as well as preserve sharp edges well in the restored image. Moreover, the proposed adaptive total variation facilitates us to employ some accelerated techniques to solve the generated ROF model. Our numerical experiments demonstrate the efficiency of the proposed method.