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Zhang, Z., Ely, G., Aeron, S., Hao, N. and Kilmer, M. (2014) Novel Methods for Multilinear Data Completion and De-Noising Based on Tensor-SVD. 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, 23-28 June 2014, 3842-3849.

has been cited by the following article:

• TITLE: Improved Robust Low-Rank Regularization Tensor Completion

  AUTHORS: Xiangyi Wang, Wei Jiang

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

  JOURNAL NAME: Open Access Library Journal, Vol.9 No.11, November 10, 2022

  ABSTRACT: 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.