Dictionary Learning With Low-Rank Coding Coefficients for Tensor Completion

Tai Xiang Jiang, Xi Le Zhao, Hao Zhang, Michael K. Ng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


In this article, we propose a novel tensor learning and coding model for third-order data completion. The aim of our model is to learn a data-adaptive dictionary from given observations and determine the coding coefficients of third-order tensor tubes. In the completion process, we minimize the low-rankness of each tensor slice containing the coding coefficients. By comparison with the traditional predefined transform basis, the advantages of the proposed model are that: 1) the dictionary can be learned based on the given data observations so that the basis can be more adaptively and accurately constructed and 2) the low-rankness of the coding coefficients can allow the linear combination of dictionary features more effectively. Also we develop a multiblock proximal alternating minimization algorithm for solving such tensor learning and coding model and show that the sequence generated by the algorithm can globally converge to a critical point. Extensive experimental results for real datasets such as videos, hyperspectral images, and traffic data are reported to demonstrate these advantages and show that the performance of the proposed tensor learning and coding method is significantly better than the other tensor completion methods in terms of several evaluation metrics.

Original languageEnglish
Pages (from-to)932-946
Number of pages15
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number2
Early online date31 Aug 2021
Publication statusPublished - Feb 2023

Scopus Subject Areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

User-Defined Keywords

  • Dictionary learning
  • low-rank coding
  • tensor completion
  • tensor singular value decomposition (t-SVD)


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