Author(s)

Yujie Luan¹, Wei Jiang²

¹School of Mathematics, Liaoning Normal University, Dalian, China.
²College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, China.

This paper mainly studies the problem of tensor robust principal component analysis (TRPCA), in order to accurately recover the low rank and sparse components from the observed signals. Most of the existing robust principal component analysis (RPCA) methods are based on nuclear norm minimizationss. These methods minimize all singular values at the same time, so they can not approach the rank well in practice. In this paper, the idea of truncated nuclear norm regularization is extended to RPCA. At the same time, in order to improve the stability of the model, the tensor truncated Frobenius norm is newly defined. Truncated nuclear norm and truncated Frobenius norm are considered at the same time called hybrid truncated model of tensor. This method minimizes min singular values. In addition, this paper also gives an effective method to determine the contraction operator, and develops an effective iterative algorithm based on alternating direction to solve this optimization problem. Experimental results show the effectiveness and accuracy of this method.

Tensor Robust Principal Component Analysis (TRPCA), Hybrid Truncation Norm , Alternating Direction Multiplier Method (ADMM)

Luan, Y.J. and Jiang, W. (2022) Tensor Robust Principal Component Analysis via Hybrid Truncation Norm. Open Access Library Journal, 9, 1-22. doi: 10.4236/oalib.1109412.