A coupled variational model for image denoising using a duality strategy and split Bregman

To reduce the staircase effect, high-order diffusion equations are used with high computational cost. Recently, a two-step method with two energy functions has been introduced to alleviate the staircase effect successfully. In the two-step method, firstly, the normal vector of noisy image is smoothed, and then the image is reconstructed from the smoothed normal field. In this paper, we propose a new image restoration model with only one energy function. When the alternating direction method is used, the estimation of the vector field and the reconstruction of the image are interlaced, which makes the new vector field can utilize sufficiently the information of the restored image, thus the constructed vector field is more accurate than that generated by the two-step method. To speed up the computation, the dual approach and split Bregman are employed in our numerical algorithm. The experimental results show that the new model is more effective to filter out the Gaussian noise than the state-of-the-art models.