Separable Quaternion Matrix Factorization for Polarization Images

TL;DR

This paper introduces a novel separable quaternion matrix factorization model for polarization images, along with a heuristic algorithm and normalization technique, demonstrating effectiveness in polarization image analysis and spectro-polarimetric unmixing.

Contribution

It proposes a new separable quaternion matrix factorization model and a heuristic algorithm for polarization data analysis, addressing challenges in polarization image representation.

Findings

Effective polarization image representation demonstrated

Successful spectro-polarimetric unmixing results

Proposed algorithms outperform existing methods

Abstract

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.