Nonlinear Unmixing of Hyperspectral Data Using Semi-Nonnegative Matrix Factorization

Nonlinear spectral mixture models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel optimization method of nonlinear unmixing based on a generalized bilinear model (GBM), which considers the second-order scattering of photons in a spectral mixture model. Semi-nonnegative matrix factorization (semi-NMF) is used for the optimization to process a whole image in matrix form. When endmember spectra are given, the optimization of abundance and interaction abundance fractions converge to a local optimum by alternating update rules with simple implementation. The proposed method is evaluated using synthetic datasets considering its robustness for the accuracy of endmember extraction and spectral complexity, and shows smaller errors in abundance fractions rather than conventional methods. GBM-based unmixing using semi-NMF is applied to the analysis of an airborne hyperspectral image taken over an agricultural field with many endmembers, and it visualizes the impact of a nonlinear interaction on abundance maps at reasonable computational cost.