Journal
INFORMATION SCIENCES
Volume 532, Issue -, Pages 170-189Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2020.05.005
Keywords
Low-rank tensor recovery (LRTR); Mose-k(1)k(2) tensor unfolding; Tensor N-tubal rank; Weighted sum of tensor nuclear norm (WSTNN); Alternating direction method of multipliers (ADMM)
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Funding
- National Natural Science Foundation of China [61772003, 61876203, 11901450]
- Fundamental Research Funds for the Central Universities [31020180QD126]
- National Postdoctoral Program for Innovative Talents [BX20180252]
- China Postdoctoral Science Foundation [2018M643611]
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The recent popular tensor tubal rank, defined based on tensor singular value decomposition (t-SVD), yields promising results. However, its framework is applicable only to three-way tensors and lacks the flexibility necessary tohandle different correlations along different modes. To tackle these two issues, we define a new tensor unfolding operator, named mode-k(1)k(2) tensor unfolding, as the process of lexicographically stacking all mode-k(1)k(2) slices of an N-way tensor into a three-way tensor, which is a three-way extension of the well-known mode-k tensor matricization. On this basis, we define a novel tensor rank, named the tensor N-tubal rank, as a vector consisting of the tubal ranks of all mode-k(1)k(2) unfolding tensors, to depict the correlations along different modes. To efficiently minimize the proposed N-tubal rank, we establish its convex relaxation: the weighted sum of the tensor nuclear norm (WSTNN). Then, we apply the WSTNN to low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). The corresponding WSTNN-based LRTC and TRPCA models are proposed, and two efficient alternating direction method of multipliers (ADMM)-based algorithms are developed to solve the proposed models. Numerical experiments demonstrate that the proposed models significantly outperform the compared ones. (C) 2020 Elsevier Inc. All rights reserved.
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