Cauchy Noise Removal by Weighted Nuclear Norm Minimization

Recently, weighted nuclear norm minimization (WNNM), which regularizes singular values of an input matrix with different strengths according to given weights, has demonstrated impressive results in low-level vision tasks such as additive Gaussian noise removal, deblurring and image inpainting [14, 15, 33]. In this study, we apply WNNM to remove additive Cauchy noise in images. A variational model is adopted based on maximum a posteriori estimate, which contains a data fidelity term that is appropriate for noise following the Cauchy distribution. Weighted nuclear norm is used as a regularizer in the proposed algorithm, and we utilized similar patches in the image by nonlocal similarity. We adopted the nonconvex alternating direction method of multiplier to solve the problem iteratively. Numerical experiments are presented to demonstrate the superior denoising performance of our algorithm compared with other existing methods in terms of quantitative measure and visual quality.