Author(s)

Xiangyi Wang¹, Wei Jiang^1,2

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

In recent years, there are many surrogates for tensor tubal rank. In this paper, we propose a hybrid norm consisting of the weighted nuclear norm and the weighted Frobenius norm (WTNFN) of a tensor. The WTNFN is a surrogate for tensor tubal rank, and studies the weighted tensor nuclear and Frobenius norm minimization (WTNFNM) problem. The aim is to enhance the stability of the solution and improve the shortcomings of the traditional method of minimizing approximate rank functions based on the tensor nuclear norm (TNN) in the field of low-rank tensor recovery. Based on this definition, we build a novel model for typical tensor recovery problems i.e. the weighted tensor nuclear and Frobenius tensor completion (WTNFNTC). The experimental results on synthetic data and real data show that the stability and recovery effects of the model are improved compared with related algorithms.

Low-Rank Recovery, T-SVD, Weighted Tensor Nuclear, Weighted Tensor Frobenius Norm

Wang, X.Y. and Jiang, W. (2022) Improved Robust Low-Rank Regularization Tensor Completion. Open Access Library Journal, 9, 1-25. doi: 10.4236/oalib.1109425.