An Improved Method Combining Fisher Transformation and Multiple Endmember Spectral Mixture Analysis for Lunar Mineral Abundance Quantification Using Spectral Data

Mineral abundance quantification of lunar surface materials using remotely acquired spectra can be achieved with spectral unmixing methods, but this has remained a challenging problem. The existing unmixing methods neglect the existence of widespread glass material and the spectral similarity of different minerals. To solve this problem, this study proposes a method to calculate the main mineral abundances in lunar regolith based on reflectance spectra by utilizing Fisher transformation combined with multiple endmember spectral mixture analysis (MESMA). A set of spectra of lunar main constituents, including plagioclase, pyroxene, ilmenite, olivine and glass material, were selected from the RELAB spectral database and used as endmembers. The endmember spectra were utilized to compute the projection vectors, with which the spectral characteristics can be trans-formed into low-dimensional Fisher space in which intraclass spectral variability can be minimized while the interclass variability of different mineral spectra can be maximized. The endmember spectra and the lunar soil spectra in the Lunar Soil Characterization Consortium (LSCC) dataset were both transformed into Fisher space, in which MESMA was executed to acquire the fraction of each endmember. MESMA allows for comprehensive endmember expressions by representing a type of mineral using multiple spectra rather than a single end-member. Compared with laboratory mineral measurements, this approach estimated the mineral abundances with determination coefficient R2 values equal to 0.88 and 0.65 in the lunar mare and highland regions, respectively. After validation with laboratory data, the method was further applied at the regional scale where Apollo 12 and Apollo 16 landed by using M3 images, and the estimated accuracy of different minerals was similar to that of the laboratory spectra.