# Separable Quaternion Matrix Factorization for Polarization Images

arXiv: https://arxiv.org/abs/2207.14039 · HTML: https://mlsanity.com/paper/2207.14039/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related](https://mlsanity.com/paper/1409.4320/) (2014)
- [Generalized Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1905.12995/) (2019)
- [Quaternion Non-negative Matrix Factorization: definition, uniqueness and algorithm](https://mlsanity.com/paper/1903.10593/) (2019)
- [Co-Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/2109.00749/) (2021)

## Built on by (most cited first, 2 of 2)

- [Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion](https://mlsanity.com/paper/2504.21468/) (2025)
- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)

## Abstract (arXiv)

Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion linear mixing model to polarized signals: we assume each column of the source factor matrix equals a column of 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 factor 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.