Cascadic Multigrid Methods For Image Restoration Problems

In the process of transmission and processing,image quality is easy to be affected by external factors,such as noise,blur and so on.It is very important to recover more real image from noise and blur data.Therefore,the study of fast and effective image restoration methods has become one of the most significant research hotspots in the field of image processing.Based on cascadic multigrid method and domain decomposition method,this paper constructs two kinds of fast and effective image restoration algorithms.(1)For the image restoration model,this paper proposes a new extrapolation economy cascadic multigrid method.This method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator,which provides more accurate initial values for the fine grid level.In order to improve the effect of removing noise and preserving image edges,an edge preserving denoising operator is constructed.In order to reduce the influence of step effect,a local smoothing operator is constructed.Numerical experiments show that the new extrapolated economic cascadic multigrid method can not only produce good image restoration quality but also improve the computational efficiency.(2)This paper combines the overlapping domain decomposition method with the cascadic multigrid method,and proposes the parallel new extrapolated cascadic multigrid method for image restoration.In the process of image restoration,it is usually necessary to solve large-scale inverse problems.For large-scale images or high-resolution images,the computational cost is very high.Domain decomposition method is one of the most effective algorithms to solve large-scale problems,which can effectively save computing cost.Cascadic multigrid method has good effect on linear model image restoration and can obtain high quality restored images.The image problem is transformed into multiple overlapping and independent subproblems by the parallel new extrapolated cascadic multigrid method,and then each subproblem is solved by the new extrapolated cascadic multigrid method.Numerical experiments show that this method can effectively remove the noise and blur of the high-resolution images,and the parallel algorithm saves computing time and memory usage.