Quaternion Non-negative Matrix Factorization: a new tool for spectropolarimetric imaging

Quaternio n non-negative matrix factorization (QNMF) is a new tool which generalizes usual non-negative matrix factorization (NMF) to the case of polarized signals. The approach relies on two key features: (i) the algebraic representation of polarization information, namely Stokes parameters, thanks to quaternions and (ii) the exploitation of physical constraints linked to polarization generalizing non-negativity constraints. QNMF improves NMF model identifiability by revealing the key disambiguating role played by polarization information. A simple and numerically efficient algorithm is introduced for practical resolution of the QNMF problem. Numerical experiments on synthetic data validate the proposed approach and illustrate the potential of QNMF as a generic spectropolarimetric image unmixing tool.