Tensor completion by multi-rank via unitary transformation

Guang Jing Song, Michael K. Ng, Xiongjun Zhang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study n1×n2×n3 third-order tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries. Our approach is to make use of the multi-rank of the underlying tensor instead of its tubal rank in the bound. In numerical experiments on synthetic and imaging data sets, we demonstrate the effectiveness of our proposed bound for the number of sample entries. Moreover, our theoretical results are valid to any unitary transformation applied to n3-dimension under transformed tensor singular value decomposition.

Original languageEnglish
Pages (from-to)348-373
Number of pages26
JournalApplied and Computational Harmonic Analysis
Early online date31 Mar 2023
Publication statusPublished - Jul 2023

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Sampling sizes
  • Tensor completion
  • Transformed tensor nuclear norm
  • Transformed tensor singular value decomposition


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