Nonlinear Multi-grid Method For Adaptive Varaiational Model In Image Denoising

Image denoising is the preliminary work to provide high-quality images for subsequent image processing,and edge preserving is an important standard to measure the quality of denoised images.TV model can well preserve image edges,but it will produce ladder effect.Second-order adaptive variational model has realized the elimination of ladder effect of TV model by adaptively adjusting regular terms by using the structural features of images.In theory,the diffusion coefficient,corresponding to Euler-Lagrange equation has edge-preserving and smoothness-preserving effects,but the gradient descent method and fixed point method can only eliminate the ladder effect of TV model to a certain extent,and its edge-preserving effect is not as good as that of TV model.Nonlinear multigrid method is an important method to solve nonlinear equations by smoothing error.This paper constructs an effective nonlinear multigrid method for TVP and DTVP adaptive models,its main work is as follows:1.The differential curvature and residual arc restricted by using nine pixels on the fine grid which are close to the pixels on the coarse grid with reasonable weights,and the error is interpolated by using four pixels on the coarse grid which are close to the pixels on the fine grid with reasonable weights.Combining with the generalized global Gauss-Seidel iteration of lag diffusion coefficient as smoother,the error of the solution is calculated on the coarsest grid with the fixed point iteration method.An effective nonlinear multigrid(NMG1)method for solving TVP model is constructed.Experiments show that the peak signalto-noise ratio of denoised images obtained by NMG1 method is higher than that of semi-implicit gradient descent method and fixed point method,and NMG1 method not only has good edge preserving effect,but also can eliminate the step effect,and has high solving efficiency.2.When the semi-implicit gradient descent method is used to solve the TVP model,the relative error of the first five iterations can reach 10-4,but the relative error decreases more and more slowly with the increase of iteration times.We use the semi-implicit gradient descent method as a smoother,construct another nonlinear multigrid(NMG2)method,and make a local Fourier analysis of the smoother.The experiment shows that NMG2 method can improve the quality of denoised image as well as NMG1 method,and the calculation speed is fast.3.DTV model has a good denoising effect on directional texture images.We introduce differential curvature D into DTV model,establish DTVP model,and solve DTVP model with NMG1 and NMG2 methods.Experiments show that NMG1 and NMG2 methods can improve the denoising effect of directional texture images.