Nonlocal low-rank regularized two-phase approach for mixed noise removal

Removing mixed noise in images is a difficult problem which has been discussed in many recent papers. In this paper, we tackle the problem of having mixed additive Gaussian white noise and impulse noise. We propose to remove this mixed noise through a nonlocal low-rank regularized two-phase approach. In the first phase, we identify and label the pixels that are likely to be corrupted by the impulse noise. In the second phase, the image is restored through the unlabeled observed data. The restored image is achieved via solving an optimization problem whose objective function has an ℓ 1/ℓ 2 combined content-dependent fidelity term and a nonconvex nonlocal low-rank regularization term. Both terms are built on patch matrices formed from similar patches. Each patch matrix is considered to be low-rank according to the prior knowledge of images. We solve this nonconvex optimization through an iterative adaptive nuclear norm minimization algorithm and provide its convergence analysis. Our experiments show the proposed method outperforms the existing state-of-the-art algorithms in terms of three quantitative metrics, namely, the peak signal-to-noise ratio, the structural similarity and the feature similarity, and visual quality of the restored images.