A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion

Xiongjun Zhang, Michael K. Ng

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)
13 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1231-1273
Number of pages43
JournalSIAM Journal on Imaging Sciences
Issue number2
Publication statusPublished - 27 Jun 2019

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Error bound
  • Low-rank tensor recovery
  • Tensor nuclear norm
  • Tensor singular value decomposition
  • Tubal rank


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