A Semi-Supervised Method for Nonlinear Hyperspectral Unmixing

As the interaction of light with the Earth surface is very complex, spectral reflectances are composed of nonlinear mixtures of the observed materials. Nonlinear mixing models have the disadvantage that not all spectra of a hyperspectral dataset necessarily follow the same particular mixing model. Moreover, most models lack a proper interpretation of the estimated parameters in terms of fractional abundances. In this paper, we present a semi-supervised nonlinear unmixing technique that overcomes these problems. In a first step, we apply a kernelized simplex volume maximization to select an overcomplete set of endmembers that precisely describe the hyperspectral data manifold. In a second step, this set is used as ground truth data in a supervised learning approach to generate fractional abundance maps from the entire dataset. For this, three methods are presented, based on kernelized sparse unmixing, feedforward neural networks, and gaussian processes. The proposed method is validated on simulated data, a dataset obtained by ray tracing, and a real hyperspectral image.