Overlapping Domain Decomposition Method with Cascadic Multigrid for Image Restoration

Abstract

In the process of image restoration, it is usually necessary to solve large-scale inverse problems, where the computational cost is very high for large or high-resolution images. The domain decomposition method is one of the most effective algorithms to solve large-scale problems, which can effectively decrease the computational cost. The cascadic multigrid method has a good effect on the linear model of image restoration and can obtain high quality restored images. In this paper, the overlapping domain decomposition method (DDM) with the cascadic multigrid method (CMG) and the DDM with new extrapolation cascadic multigrid method (NECMG) are presented to solve the image restoration problems of denoising and deblurring. We first divide the image problem into some overlapping and independent subproblems. Then, each subproblem is solved independently by CMG or NECMG with the edge-preserving operator. Numerical experiments show that the new method is effective.