A weighted variational method for the removal of mixed noise

In this paper the authors present a novel variational method for the reconstruction of images corrupted by non-uniformly distributed noise. The additive noise model has been studied extensively, using variational techniques such as the Rudin, Osher and Fatemi model. However, the reconstruction of images corrupted by non-Gaussian noise has not yet been thoroughly studied. The proposed model includes a balance between the data term and the regularization term in the energy functional, taking into account the statistical control of the parameters and the position of the noisy points related to the edges presented in the image. The parameters are determined by the given observed noisy image. The obtained results have shown the effectiveness and robustness in restoring images with multiplicative noise or mixed Gaussian noise, while preserving edges and small structures belonging to the image.