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Polarization is a unique characteristic of transverse wave and is representedby Stokes parameters. Analysis of polarization states can reveal valuableinformation about the sources. In this paper, we propose a separable low-rankquaternion linear mixing model to polarized signals: we assume each column ofthe source factor matrix equals a column of polarized data matrix and refer tothe corresponding problem as separable quaternion matrix factorization (SQMF).We discuss some properties of the matrix that can be decomposed by SQMF. Todetermine the source factor matrix in quaternion space, we propose a heuristicalgorithm called quaternion successive projection algorithm (QSPA) inspired bythe successive projection algorithm. To guarantee the effectiveness of QSPA, anew normalization operator is proposed for the quaternion matrix. We use ablock coordinate descent algorithm to compute nonnegative factor activationmatrix in real number space. We test our method on the applications ofpolarization image representation and spectro-polarimetric imaging unmixing toverify its effectiveness.

Separable Quaternion Matrix Factorization for Polarization Images