Nonlinear unmixing with multiple reflection for hyperspectral remote sensing imagery

Because of spatial resolution, each pixel in hyperspectral images usually contains more than one material. Linear mixture model is developed for this problem and has been widely studied. This model assumes the spectrum of a pixel is linearly combined by all the resident materials, and it ignores the interaction between materials. Nonlinear models have recently drawn lots of attentions for spectral unmixing. The generalized bilinear model (GBM) has been proposed for nonlinear mixture which considers the second order interactions between two different endmembers. However, it neglects the possibility of second order interactions between the same endmembers. In this study, we propose a modified GBM (MGBM) by considering second order reflection between all the endmembers. The positivity and sum-to-one constraints for the abundances are ensured by the proposed algorithms. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.