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• W3022425365 abstract "Abstract 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." @default.
• W3022425365 created "2020-05-13" @default.
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• W3022425365 date "2020-09-01" @default.
• W3022425365 modified "2023-10-17" @default.
• W3022425365 title "Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery" @default.
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• W3022425365 doi "https://doi.org/10.1016/j.ins.2020.05.005" @default.
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