A Nonlinear Spectral Unmixing Method for Abundance Retrieval of Mineral Mixtures

摘要

Minerals are generally present as intimate mixtures. The spectra of intimate mixtures in visible-infrared are complex function of abundance, grain size, and optical constants et.al, making the linear spectral unmixing model inapplicable. In this paper, we presented a nonlinear unmixing method by combining Shkuratov model (SK99) and Hapke model (H81) to unmix the mineral mixtures. For obtaining the abundances of mineral endmembers, we built up a look-up table (LUT) in the following steps: First, the optical constants were derived by SK99 model and then single scattering albedos of endmembers were computed. Second, the approximation of multiple scattering was derived by the Chandrasekhar H-function. Finally, LUT was established using H81 model. The root-mean-square error (RMSE) was calculated to find the best match between the reflectance of mixtures and LUT. We used the laboratory mineral mixtures to verify the accuracy of abundance estimation. The results show that RMSEs are less than 1% and the absolute errors of abundance retrieval are within 5%. The presented method can retrieve mineral abundance effectively and rapidly. It can be a potential method applying for hyperspectral images of the earth and planetary.