Investigation into Bayesian inversion techniques for estimating mineral particle size distribution and abundance utilizing hyperspectral data

Hyperspectral data serve as an important tool for interpreting mineral information. However, the issue of spectral variability poses challenges to its inversion. The physically based Hapke model takes into account the influences of factors such as observation geometry and grain size. Nevertheless, existing studies have not fully considered the variability of grain size characteristics. Typically, grain sizes are subjectively set as constants or modeled using discrete grid approaches. In this study, we propose a new method based on the inversion of a two-layer Bayesian framework, which models the particle size parameters as continuous random variables and sets the particle size distribution parameters as hyperparameters, and takes into account the influence of the variability of the particle size features on the interpretation of mineral abundance. This method directly inverts grain size characteristics from the spectra. The validity of the method is verified by RELAB laboratory data, and the simulated reflectance fitting residuals and the RMSE of the inversion results are in the order of 0.01 to 0.001, and the inversion abundance agrees well with the actual abundance. The method is also applied to the lunar surface to analyze the distribution characteristics of common minerals in the landing areas of Chang'e-3 and Chang'e-5. The inverted abundances of pyroxene, plagioclase, olivine and agglutinate are in high agreement with the correlation results, while the results of this study also provide continuous grain size distribution characterization, which provides reference recommendations and decision support for scientific and engineering analyses of the Moon.