First-order Forward Backward Algorithm For Image Restoration Based On Total Variational Model

Image noise and image blur often affect the post-processing image,such as image segmentation,feature extraction,target tracking and so on.So the effective removal of image noise and image blur becomes a key problem in the field of digital image processing.The purpose of image denoising and restoration is to recover the original image with clear boundary and clear texture as far as possible from the degraded image.Therefore,the key to image denoising and image restoration is to preserve the edge information Texture.Because the full variational model can preserve the image edge information to obtain better image restoration effect.So this paper focuses on the image restoration algorithm under the full variational model.According to the bounded variational image processing,the whole variational image restoration problem is decomposed into two convex function minimization problems.The first and second order methods can be solved.Because the second-order iterative computation is large,It is not suitable for solving image restoration problems of large-scale data.The first-order method only involves the gradient and the objective function value information,so the algorithm is small in computation and iterative efficiency is high,which is suitable for solving large-scale practical problems.Therefore,this paper studies the first-order method of full variational image restoration.Based on the above description,the main content of this paper for the following points:Firstly,this paper applies the forward backward splitting algorithm to solve the full variational image restoration model.The fixed step size of the algorithm limits the shortcoming of the convergence rate of the algorithm,and proposes a fast forward backward Split algorithm.The algorithm combines the forward backward splitting algorithm with the Barzilai-Borwein adaptive step selection operator.In the algorithm iteration,the update step size factor is selected to obtain a faster algorithm convergence effect.Numerical experiments show that the adaptive step size fast forward backward splitting algorithm not only improves the convergence rate of the algorithm,but also improves the quality of image restoration.Secondly,the improved fast forward backward splitting algorithm is further studied.It is found that the new algorithm using Barzilai-Borwein spectral step length does not always guarantee the strict convergence of the algorithm in numerical experiments.In this paper,The idea of monotonic linear search is introduced into the improved fast forward backward splitting algorithm,and a fast forward backward splitting algorithm is proposed for nonmonotone linear search,which avoids thelocal optimization of the algorithm.So that the algorithm in the computing accuracy and time complexity to achieve the best.Numerical experiments administrate that the effectiveness of the proposed algorithm.Finally,through the in-depth study of the fast forward backward splitting algorithm,the objective function exhibits a certain "concussion" phenomenon: the objective function value increases and the convergence of the objective function is slowed down.It is found that the algorithm has a strong sensitivity to the selection of decision factors.Based on this,this paper proposes a fast forward backward splitting algorithm for adaptive restart.By adding the judgment factor to judge,timely restart the algorithm,so that the objective function presents a monotonically decreasing phenomenon.Numerical experiments show that the adaptive back-to-back algorithm improves the convergence of the algorithm,reduces the oscillation of the objective function,and improves the recovery quality of the algorithm for image denoising and image deblur.