Salt and pepper noise removal based on an approximation of l0 norm

In this paper, we present a novel variational model for salt and pepper noise removal, and an efficient numerical algorithm for solving it. The proposed model features the use of an approximating function of l0 norm to measure the closeness of the reconstructed and observed images at the pixels which are not the candidates of the noisy pixels. In addition, the total variation (TV) of the image on the entire image domain is minimized for edge-preserving smoothing. When solving the proposed minimization problem, to reduce the computational complexity from the expression of the approximating function, we use the dual forms of both TV and data terms, and find the solution of the corresponding primal-dual problem. Numerous experiments on real images, and comparisons with TV-L2, TV-L1, and adaptive median filter (AMF) indicate the effectiveness and robustness of the proposed method in salt and pepper noise removal.