Separable Quaternion Matrix Factorization for Polarization Images

Junjun Pan*, Michael K. Ng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


A transverse wave is a wave in which the particles are displaced perpendicular to the direction of the wave's advance. Examples of transverse waves include ripples on the surface of water and light waves. Polarization is one of the primary properties of transverse waves. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion linear mixing model for polarized signals: we assume each column of the source factor matrix equals a column of the polarized data matrix and refer to the corresponding problem as separable quaternion matrix factorization (SQMF). We discuss some properties of the matrix that can be decomposed by SQMF. To determine the source factor matrix in quaternion space, we propose a heuristic algorithm called quaternion successive projection algorithm (QSPA) inspired by the successive projection algorithm. To guarantee the effectiveness of QSPA, a new normalization operator is proposed for the quaternion matrix. We use a block coordinate descent algorithm to compute nonnegative activation matrix in real number space. We test our method on the applications of polarization image representation and spectro-polarimetric imaging unmixing to verify its effectiveness.

Original languageEnglish
Pages (from-to)1281-1307
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number3
Early online date26 Jul 2023
Publication statusPublished - Sept 2023

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • polarization
  • quaternion
  • matrix factorization
  • polarization image
  • separability


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