A fast 1-TV algorithm for image restoration

Abstract. Image restoration problems are often solved by finding the minimizer of a suitable objective function consisting of a data-fitting term and a regularization term. In this paper, we consider the data-fitting term measured in the `1 norm to handle non-Gaussian additive noise, and the regularization term given by the total variation to restore image edges. We propose a new objective function for this image restoration problem by making use of new variables to modify the data-fitting term and the total variation regularization term. An alternating minimization algorithm based on the new objective function is employed to restore blurred and noisy images. Our experimental results show that the quality of restored images by the proposed method is competitive with those restored by the other tested methods. We also show the convergence of the alternating minimization algorithm and demonstrate that the proposed algorithm is very efficient