1. Beijing Normal Univ, State Key Lab Earth Surface Proc & Resource Ecol, Beijing 100875, Peoples R China

2. Nagoya Univ, Grad Sch Environm Studies, Nagoya, Aichi 4648601, Japan

3. Univ New S Wales, Sch Engn & Informat Technol, Univ Coll, Australian Def Force Acad, Canberra, ACT, Australia

4. Katholieke Univ Leuven, Div Measure Model & Manage Bioresponses, Dept Biosyst, B-3001 Louvain, Belgium

Abstract: In the past decades, spectral unmixing has been studied for deriving the fractions of spectrally pure materials in a mixed pixel. However, limited attention has been given to the collinearity problem in spectral mixture analysis. In this paper, quantitative analysis and detailed simulations are provided, which show that the high correlation between the endmembers, including the virtual endmembers introduced in a nonlinear model, has a strong impact on unmixing errors through inflating the Gaussian noise. While distinctive spectra with low correlations are often selected as true endmembers, the virtual endmembers formed by their product terms can be highly correlated. It is found that a virtual-endmember-based nonlinear model generally suffers more from collinearity problems compared to linear models and may not perform as expected when the Gaussian noise is high, despite its higher modeling power. Experiments were conducted on a set of in situ measured data, and the results show that the linear mixture model performs better in 61.5% of the cases.

Keywords: Collinearity problem; hyperspectral data; linear spectral mixture analysis (LSMA); nonlinear spectral mixture analysis (NSMA); spectral mixture analysis (SMA)