Image denoising based on nonconvex anisotropic total-variation regularization

摘要

Image denoising models based on the total variation (TV) regularization have been used in many fields of image processing. The main advantage of the TV regularization can preserve the edge efficiently when restoring the degraded image. However, the main flaw can not describe the local feature due to the same weight for the gradient subvariable in the TV term. To this end, we propose a nonconvex anisotropic total variation (NCATV)-based image denoising model. In the proposed model, the weighted matrix depends on the restored image, so we can expect that it can describe local features to be more robust. Due to the nonconvexity of the proposed model, first we need to use the successive replacement scheme to decouple with the weighted matrix from the TV term. With this operation, the proposed model is transformed into the nonsmooth and convex optimization problem. Then we can employ the alternating direction method of multipliers (ADMM) to transform this problem into several easily solvable subproblems. Numerical experiments show that our proposed model yields an improvement in performance both visually and quantitatively compared with some state-of-the-art methods.