Assessing the impact of endmember variability on linear Spectral Mixture Analysis (LSMA): A theoretical and simulation analysis

The extensive existence of mixed pixels in satellite imagery is challenging for accurate land surface interpretation and parametric inversion. Spectral mixture analysis (SMA) addresses the issue by providing valuable sub-pixel information. However, it is affected by endmember variability exhibiting diverse spectral characteristics for the same endmember, inducing substantial uncertainties in model estimations. A number of approaches have been proposed to reduce the uncertainties, but theoretical explanations of how endmember variability affects model estimation and how these approaches perform successfully have not yet been derived. In this study, error propagation caused by endmember variability in linear SMA (LSMA) was investigated using theoretical analysis and simulation experiments. The major findings are as follows: (1) the impact of endmember variability on LSMA unmixing error depends on the interactions between deviation signal and gain vectors in a multiplicative way. (2) Unmixing error originates from the deviation signal that is governed jointly by spectral variability within an endmember class (i.e., intra-class variability) and endmember abundances, while spectra magnitude and spectral similarity among different endmember classes (i.e., inter-class variability) can amplify or reduce the deviation signal. (3) The typical approaches for mitigating endmember variability could not only change the deviation signal but also affect gain vectors, resulting in improved performance of LSMA to some extent. Based on these results, we recommend Multiple Endmember Spectral Mixture Analysis (MESMA) to be used in most applications considering its robustness in mitigating endmember variability. The results of this study will be of benefit to the application of LSMA in practice.