Randomized low rank approximation for nonnegative pure quaternion matrices

Chengyao Lyu, Junjun Pan, Michael K. Ng*, Xile Zhao

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Pure quaternion matrix has been widely employed to represent data in real-world applications, such as colour images. Additionally, the imaginary part of quaternion matrix is usually nonnegative due to the natural nonnegativity of real-world data. In this paper, we propose an alternating projection-based algorithm for low rank nonnegative pure quaternion matrix approximation, which can exactly calculate the optimal fixed rank approximation while preserve the pure and nonnegative properties from the given data. More concretely, the proposed algorithm alternatively projects the given quaternion matrix onto the fixed rank quaternion matrix set and nonnegative pure quaternion matrix set in an iterative fashion. Moreover, we establish the theoretical convergence guarantee of the proposed algorithm. To extend the proposed algorithm to large-scaled data, we further propose a randomized algorithm with significant lower computational complexity and comparable accuracy. Numerical experiments on colour images show that our algorithms outperform the other state-of-the-art algorithms.

Original languageEnglish
Article number108940
JournalApplied Mathematics Letters
Early online date2 Dec 2023
Publication statusE-pub ahead of print - 2 Dec 2023

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Alternating projection algorithm
  • Low rank
  • Nonnegative pure quaternion matrix
  • Randomized algorithm


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