An improved model for image denoising

In this paper, we propose an improved model for image denoising, which combines the second-order ROF model and the fourth-order partial differential equations (PDE), and it is solved by the combination algorithm of the split Bregman method, an algebraic multigrid method and Krylov subspace acceleration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to verify the efficiency of the model and combination algorithm. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.