Color video recovery through low-rank quaternion tensor completion with nonconvex weighted Laplace regularization

Low-rank quaternion tensor completion, which recovers color videos from incomplete observations by representing them as quaternion tensors, has been extensively studied. Conventional approaches often rely on the convex nuclear norm to characterize low-rankness, which can lead to suboptimal rank approximations. To achieve a more accurate approximation of the Tucker rank, this paper introduces a novel nonconvex model for quaternion tensor completion, utilizing a weighted Laplace function as a rank surrogate. We optimize the model within the Alternating Direction Method of Multipliers (ADMM) framework and provide a convergence analysis for the algorithm. Experimental evaluations on benchmark color video datasets confirm the advantages of the proposed approach in terms of recovery quality.