For non-differential characteristics and easily producing stair effect of total variation in image restoration

the paper presents a second order differential primal-dual model and Newton iterative algorithm.The characteristics of pseudo Huber function are analyzed

primal model is converted into primal-dual model resort to Fenchel transform

Newton iterative algorithm based on the different step length update schemes of primal and dual variables are proposed

and the generalized cross validation principle is given to determine the weight.Synthesized and real images are blurred by point spread function and Gaussian noise

the comparison experiments among the proposed scheme with fast Fourier transform algorithm

fast shrinkage-thresholding algorithm

alternating projection algorithm and quasi-Newton algorithm are carried out.Simulation results show the proposed algorithm can protect image edges

alleviate stair effect

and achieve lower relative error and deviation

higher peak signal to noise ratio and structural similarity index measure

and better visual effect.