Blind nonlinear hyperspectral unmixing based on constrained kernel nonnegative matrix factorization

Spectral unmixing has been a useful technique for hyperspectral data exploration since the earliest days of imaging spectroscopy. As nonlinear mixing phenomena are often observed in hyperspectral imagery, linear unmixing methods are often unable to unmix the nonlinear mixtures appropriately. In this paper, we propose a novel blind unmixing algorithm, constrained kernel nonnegative matrix factorization, which obtains the endmembers and corresponding abundances under nonlinear mixing assumptions. The proposed method exploits the nonlinear structure of the original data through kernel-induced nonlinear mappings and one need not know the nonlinear model. In order to improve its performance further, two auxiliary constraints, namely simplex volume constraint and abundance smoothness constraint, are also introduced into the algorithm. Experiments based on synthetic datasets and real hyperspectral images were performed to evaluate the validity of the proposed method.