Robust Tensor SVD and Recovery With Rank Estimation

Qiquan Shi, Yiu Ming Cheung*, Jian Lou

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

10 Citations (Scopus)


Tensor singular value decomposition (t-SVD) has recently become increasingly popular for tensor recovery under partial and/or corrupted observations. However, the existing t-SVD-based methods neither make use of a rank prior nor provide an accurate rank estimation (RE), which would limit their recovery performance. From the practical perspective, the tensor RE problem is nontrivial and difficult to solve. In this article, we, therefore, aim to determine the correct rank of an intrinsic low-rank tensor from corrupted observations based on t-SVD and further improve recovery results with the estimated rank. Specifically, we first induce the equivalence of the tensor nuclear norm (TNN) of a tensor and its f-diagonal tensor. We then simultaneously minimize the reconstruction error and TNN of the f-diagonal tensor, leading to RE. Subsequently, we relax our model by removing the TNN regularizer to improve the recovery performance. Furthermore, we consider more general cases in the presence of missing data and/or gross corruptions by proposing robust tensor principal component analysis and robust tensor completion with RE. The robust methods can achieve successful recovery by refining the models with correct estimated ranks. Experimental results show that the proposed methods outperform the state-of-the-art methods with significant improvements.

Original languageEnglish
Pages (from-to)10667-10682
Number of pages16
JournalIEEE Transactions on Cybernetics
Issue number10
Early online date19 Apr 2021
Publication statusPublished - Oct 2022

Scopus Subject Areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

User-Defined Keywords

  • Rank estimation (RE)
  • robust tensor PCA (RTPCA)
  • robust tensor recovery
  • tensor completion (TC)
  • tensor singular value decomposition (t-SVD)


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