2022/07/28 by Junjun Pan, Michael K. Ng, Pan, Junjun +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Fractal and DNA sequence analysis #Molecular spectroscopy and chirality #Numerical Analysis (math.NA) #Optical Polarization and Ellipsometry
paper · pdf · doi:10.48550/arxiv.2207.14039
openalex publication_date 2022/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.