Nonlinear Unmixing with Multiple Reflection for Hyperspectral Remote Sensing Imagery

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Remote sensing is to measure the object properties on the earth’s surface using data acquire from aircrafts and satellites. Hyperspectral imaging spectrometers record electromagnetic energy scattered in their instantaneous field of view with hundreds or thousands of spectral channels. This high spectral resolution improves the capability for material identification via spectroscopic analysis. However, because of spatial resolution, each pixel in hyperspectral images usually contains more than one material. Linear mixture model (LMM) is developed for this problem and has been widely studied. This model assumes that the spectrum of a pixel is linearly combined by all the resident materials with their corresponding abundance, and it ignores the reflection 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 non-negativity and sum-to-one constraints for the abundances are ensured by the proposed algorithms.