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

Abstract

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 $l_p$-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.

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Keywords

Tensor robust principal component analysis (TRPCA) / Laplace function / $l_{p}$-norm')">Weighted $l_{p}$-norm / Alternating direction method of multipliers (ADMM) / Tensor singular value decomposition (t-SVD) / 15A69 / 65K05

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Funding

Innovative Research Group Project of the National Natural Science Foundation of China(12071159)

Natural Science Foundation of Guangdong Province(2021A1515012032)

RIGHTS & PERMISSIONS

Shanghai University