Impulse Noise Removal by L1 Weighted Nuclear Norm Minimization (Journal of Computational Mathematics, 2023)
In recent years, the nuclear norm minimization (NNM) as a convex relaxation of therank minimization has attracted great research interest. By assigning different weightsto singular values, the weighted nuclear norm minimization (WNNM) has been utilizedin many applications. However, most of the work on WNNM is combined with the $l^2$-data-fidelity term, which is under additive Gaussian noise assumption. In this paper,we introduce the L1-WNNM model, which incorporates the $l^1$-data-fidelity term and theregularization from WNNM. We apply the alternating direction method of multipliers(ADMM) to solve the non-convex minimization problem in this model. We exploit the lowrank prior on the patch matrices extracted based on the image non-local self-similarity andapply the L1-WNNM model on patch matrices to restore the image corrupted by impulsenoise. Numerical results show that our method can effectively remove impulse noise.
Keywords: Image denoising; Weighted nuclear norm minimization; $l^1$-data-fidelity term; Low rank analysis; Impulse noise.