Group-based weighted nuclear norm minimization for Cauchy noise removal with TV regularization

Cauchy noise, as a kind of impulsive and non-Gaussian noise, has recently received a lot of attention in the image processing. In this paper, we combine group-based low rank regularization and total variation (TV) regularization to propose a new hybrid variational model for Cauchy noise removal. In order to solve the proposed model, we develop an efficient alternating minimization method by incorporating the Chambolle projection algorithm, the weighted nuclear norm minimization algorithm, and Newton method. Numerical experiments demonstrate that the proposed method is superior to the existing state-of-the-art methods in terms of visual quality and quantitative measures.