Image Restoration Problem Based On Smoothing Total Variation-type Models

Image restoration is of recovering image degraded by noise and blur.Among the restored models,the Rudin-Osher-Fatemi(ROF)model and high-order total variationbased model are effective and popular restored model.However,these two models have their advantages and disadvantages.In order to overcome their shortcomings,we propose a smoothing TV-L~1 model to deal with contaminated image by the salt and pepper noise.To the high-order model,we also use the smoothing scheme to restore contaminated image by Gaussian noise and blur.Since proposed models can be written as the min-max problem,we can employ the primal-dual method to solve it.The main comments are summarized as follows:· The TV-L~1 model can efficiently restore the image contaminated by the pepper-salt noise.However this model also generates the staircase effect in the smoothing region of image.In order to overcome this drawback,we employ the smoothing scheme to penalize the TV-regularization term.This smoothing can be looked at as the approximations of ||?u|| 2 in the small gradient regions,so it can keep the smoothing regions.We also transform the proposed model transform into the saddle point problem,so we can employ the primal-dual method to solve it and the convergence can be kept due to the convexity of the proposed model.· We also extend to the smoothing scheme to the high-order total variation image restoration problem.Numerical comparisons verify effectiveness of the proposed model and numerical method.