Efficient removing of impulsive noise based on an l1-l2 cost-function

In this paper, we consider images corrupted by impulsive noise (outliers). A large variety of methods are based on order statistic filters. Other methods use state-conditioned filters. We propose a different approach, consisting of two stages. First, outliers are detected based on the minimizer of a cost-function composed of an l₁ data-fidelity and an l₂ regularization term. The computation of this minimizer is speed and the detection of outliers reliable. Then, only outliers are removed and replaced by the median of the nearest neighboring regular (uncorrupted) data samples. This method is justified by some recent theoretical result. The numerical experiments show that our method is very efficient in a broad range of situations, including highly corrupted images.