Department of Computer Science
In this paper, we study the problem of low-rank tensor recovery from limited sampling with noisy observations for third-order tensors. A tensor nuclear norm method based on a convex relaxation of the tubal rank of a tensor has been used and studied for tensor completion. In this paper, we propose to incorporate a corrected term in the tensor nuclear norm method for tensor completion. Theoretically, we provide a nonasymptotic error bound of the corrected tensor nuclear norm model for low-rank tensor completion. Moreover, we develop and establish the convergence of a symmetric Gauss--Seidel based multiblock alternating direction method of multipliers to solve the proposed correction model. Extensive numerical examples on both synthetic and real-world data are presented to validate the superiority of the proposed model over several state-of-the-art methods.
low-rank tensor recovery, tensor nuclear norm, tensor singular value decomposition, tubal rank, error bound
Source Publication Title
SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Zhang, X., & Ng, M. (2019). A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion. SIAM Journal on Imaging Sciences, 12 (2), 1231-1273. https://doi.org/10.1137/18M1202311
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