Robust Sparse Image Denoising

In this paper, we propose a novel method for denoising images corrupted by the mixture of the additive white Gaussian noise and the heavy tailed noise. The proposed method is based on robust statistical approach, i.e. application of M-estimators in the combination with l(1) sparse regularization technique. Thus, we perform the denoising by numerical solving of the convex optimization problem. Additionally, the developed method performs denoising adaptively in order to preserve the image details, by adjusting regularization coefficients according to the local variance. The proposed denoising scheme produces excellent results, both objectively (in terms of PSNR and MSSIM) and subjectively and outperforms state-of-the-art filters for denoising heavy tailed noise in images.