Impact of collinearity on linear and nonlinear spectral mixture analysis

Abstract

Linear and nonlinear spectral mixture analysis has been studied for deriving the fractions of spectrally pure materials in a mixed pixel in the past decades. However, not much attention has been given to the collinearity problem in spectral unmixing. 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 with others. Therefore, it is found that a nonlinear model generally suffers the collinearity problem more in comparison with a linear model and may not perform as expected when the Gaussian noise is high, despite its higher modeling power. Experiments were conducted to illustrate the effects.