Evaluation of Spectral Mixing Techniques for Geological Mixture in a Laboratory Setup: Insights on the nature of mixing

Geological mixtures having endmembers mixed at a fine scale pose a challenge to estimating their fractional abundances. Light incident on these mixtures interacts both at multilayered and surface levels, resulting in volumetric and albedo scattering, respectively. Accounting for these effects necessitates a nonlinear spectral mixing model approach rather than conventional linear mixing. In this study, we evaluate the performances of linear and various nonlinear spectral mixing models for an intimately mixed geological mixture, i.e., a banded hematite quartzite (BHQ) sample. The BHQ sample with distinct endmembers of hematite and quartzite facilitated our study of the behavior of light on two-component nonlinear mixtures. In a laboratory-based experimental setup, we used a spectroradiometer of full spectral range in the visible and near-infrared regions (350 to 2500nm) to acquire a hyperspectral image of the BHQ sample. It was followed by the identification of nonlinearly mixed regions and inferring changes in their spectral features. The nonlinearity induced in these regions was attributed to two significant causes- (1) the fine scale of spectral mixing and (2) the spectroradiometer sensor’s limited ability to spatially distinguish between focused and neighboring points, thereby producing a point spread effect. We observed the effects of nonlinear spectral mixing for our sample by changing the sensor’s height from 1mm to 5mm, to simulate fine and coarse-resolution images, respectively. The spectral mixing was modeled using the existing mapped ground truth fractional abundances and library endmembers’ spectra by linear mixing and established nonlinear techniques of the generalized bilinear model (GBM), polynomial post-nonlinear model (PPNM), kernel-based support vector machines (k-SVMs). The evaluated performance metric of reconstruction error revealed the nonlinearity effect in image pixels through statistical tests and nonlinearity parameters used in these models. It was further observed that the associated nonlinearity increases from fine to coarse-resolution images. The minimum error of image reconstruction was observed for the polynomial post-nonlinear model, with a single nonlinearity parameter and an average reconstruction error (ARE) of 0.05. Our study provided insights into the nature of nonlinear mixing with endmember composition and particle sizes.