Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function

Recently, the tensor robust principal component analysis (TRPCA), aiming to recover the true low-rank tensor from noisy data, has attracted considerable attention. In this paper, we solve the TRPCA problem under the framework of the tensor singular value decomposition (t-SVD). Since the convex relaxation approaches have some limitations, we establish a new non-convex TRPCA model by introducing the non-convex tensor rank approximation based on the Laplace function via the weighted \(l_p\) $l_p$ -norm regularization. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed model. We further prove that the constructed sequence converges to the desirable Karush-Kuhn-Tucker point. Experimental results show that the proposed approach outperforms various latest approaches in the literature.