Linear-Quadratic Blind Source Separation Using NMF to Unmix Urban Hyperspectral Images

Abstract

In this work, we propose algorithms to perform Blind Source Separation (BSS) for the linear-quadratic mixing model. The linear-quadratic model is less studied in the literature than the linear one. In this paper, we propose original methods that are based on Non-negative Matrix Factorization (NMF). This class of methods is well suited to many applications where the data are non-negative. We are here particularly interested in spectral unmixing (extracting reflectance spectra of materials present in pixels and associated abundance fractions) for urban hyperspectral images. The originality of our work is that we developed extensions of NMF, which is initially suited to the linear model, for the linear-quadratic model. The proposed algorithms are tested with simulated hyperspectral images using real reflectance spectra and the obtained results are very satisfactory.