Two-Step Constrained Nonlinear Spectral Mixture Analysis Method for Mitigating the Collinearity Effect

Spectral mixture analysis (SMA) is widely used to quantify the fraction of each component (endmember) of mixed pixels that contain spectral signals from more than one land surface type. Generally, nonlinear SMA (NSMA) outperforms linear SMA (LSMA) in the vegetation (tree, shrub, crop, and grass) and soil mixture case because NSMA considers the significant multiple scattering that exists for these mixtures. However, compared to LSMA, the bilinear NSMA method, which is a typical physical-based NSMA method, is undermined by its susceptibility to the collinearity effect. In this paper, a two-step constrained NSMA method (referred to as TsC-NSMA) is proposed to mitigate the collinearity effect in the bilinear NSMA method. The theoretical maximum likelihood range is mathematically derived for each endmember fraction, and the ranges are used as additional constraints for the bilinear NSMA method to optimize the unmixing results. Three different data sets, including simulated spectral data, an in situ ground plot spectral measurement, and a Landsat8 Operational Land Imager image, were used to assess the performance of the TsC-NSMA method. The results indicated that TsC-NSMA achieved the highest estimation accuracy for all mixed scenarios which either contain severe endmember collinearity or high noise levels, thereby suggesting its ability to mitigate the collinearity effect in the bilinear NSMA method with the potential to improve the estimation of endmember fractions in practical applications.