Mathematics (May 2023)

Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion

  • Jiang-Feng Chen,
  • Qing-Wen Wang,
  • Guang-Jing Song,
  • Tao Li

DOI
https://doi.org/10.3390/math11092144
Journal volume & issue
Vol. 11, no. 9
p. 2144

Abstract

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The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation and Tikhonov regularization to the factor quaternion matrices to preserve the spatial/temporal smoothness. Moreover, a proximal alternating minimization (PAM) algorithm was proposed to tackle the corresponding optimal problem. Numerical results on color images indicate the advantages of our method.

Keywords