Primal-dual method for the coupled variational model

Abstract

Total variation method has been widely used in image processing, however, it produces undesirable staircase effect. Recently, the two-step method has been used to alleviate the staircase effect successfully. Combined with a new vector field and an edge indicator function, a novel variational model is proposed in this paper. Unlike the two-step method, the proposed model contains only one energy functional, that is to say, the new vector field and the reconstructed image are interwoven. Due to using the information of the restored image fully, the new vector field is more accurate than the normal vector field, and the reconstructed image is also better than that in the two-step method. To solve the new model, we design a primal-dual method to simulate the minimization problem. The numerical experiments show that the new model can obtain significant improvement not only in noise removal but also in avoiding staircase effect.