Efficient algorithms for mixed noise removal via nonlocal low-rank regularization

This paper addresses an image denoising problem where observed images are contaminated by a mix of Gaussian and impulse noise. The proposed approach involves solving an optimization problem with an objective function that combines a convex content-dependent fidelity term and a nonlocal low-rank regularization term. Both terms are constructed using patch matrices formed from similar patches of the image. Based on the unique properties of these terms, we propose two different strategies to efficiently solve the problem. We also provide convergence analysis for both methods. Our numerical experiments demonstrate that the proposed two-phase approach performs well in terms of three quantitative metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and feature similarity (FSIM), as well as in the visual quality of the restored images.