A Combination Algorithm for Image Denoising and Deblurring

In this paper, we propose an efficient combination algorithm of split Bregman method, algebraic multigrid method and Krylov acceleration method for image denoising and deblurring. The split Bregman method is used to convert nonlinear TV model into linear systems. The linear systems with the blur operator are difficult for solving. We apply an algebraic multigrid(AMG) method and Krylov acceleration method to solve the linear systems in the inner iteration. For the linear systems, we have added an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. The inclusion of the linear stabilizing term plays a crucial role in our algorithm. We have also conducted numerical experiments. The results show that our algorithm is efficient and robust. The results of numerical experiments are given and compared with ones of.