Symmetric orthogonal approximation to symmetric tensors with applications to image reconstruction

Junjun Pan, Kwok Po NG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


The main objective of this paper is to study an approximation of symmetric tensors by symmetric orthogonal decomposition. We propose and study an iterative algorithm to determine a symmetric orthogonal approximation and analyze the convergence of the proposed algorithm. Numerical examples are reported to demonstrate the effectiveness of the proposed algorithm. We also apply the proposed algorithm to represent correlated face images. We demonstrate better face image reconstruction results by combining principal components and symmetric orthogonal approximation instead of combining principal components and higher-order SVD results.

Original languageEnglish
Article numbere2180
JournalNumerical Linear Algebra with Applications
Issue number5
Publication statusPublished - Oct 2018

Scopus Subject Areas

  • Algebra and Number Theory
  • Applied Mathematics

User-Defined Keywords

  • cumulant tensors
  • polar decomposition
  • power method
  • symmetric orthogonal
  • symmetric tensors
  • tensor decomposition


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