Abstract: In order to integrative deal with staircasing effect of ROF model and over-smoothing of high-order regularization,a new model for image denoising was proposed by using second-order symmetric gradient to construct the regularization term in the symmetric tensor space．By analyzing the properties of new model,an efficient primal-dual algorithm is introduced．The new model can effectively reduce the staircase effect because the second-order symmetric gradient is higher than first derivative．Meanwhile,it can maintain the edge because the norm of second-order symmetric gradient is smaller than the norm of Hessian matrix．Both theoretical analysis and simulated results show that the new algorithm has a high converge speed and stability.

Key words: Image restoration,Tensor space,Second-order symmetric gradient