Hyperspectral Unmixing using Iterative, Sparse and Ensambling Approaches for Large Spectral Libraries Applied to Soils and Minerals

Unmixing is a fundamental process in hyperspectral image processing in which the materials present in a mixed pixel are determined based on the spectra of candidate materials and the pixel spectrum. Practical and general utility requires a large spectral library with sample measurements covering the full variation in each candidate material as well as a sufficiently varied collection of potential materials. However, any spectral library with more spectra than bands will lead to an ill-posed inversion problem when using classical least-squares regression-based unmixing methods. Moreover, for numerical and dimensionality reasons, libraries with over 10 or 20 spectra behave computationally as though they are ill-posed. In current practice, unmixing is often applied to imagery using manually-selected materials or image endmembers. General unmixing of a spectrum from an unknown material with a large spectral library requires some form of sparse regression; regression where only a small number of coefficients are nonzero. This requires a trade-off between goodness-of-fit and model size. In this study we compare variations of two sparse regression techniques, focusing on the relationship between structure and chemistry of materials and the accuracy of the various models for identifying the correct mixture of materials present. Specifically, we examine LASSO regression and ElasticNet in contrast with variations of iterative feature selection, Bayesian Model Averaging (BMA), and quadratic BMA (BMA-Q) -- incorporating LASSO regression and ElasticNet as their base model. To evaluate the the effectiveness of these methods, we consider the molecular composition similarities and differences of substances selected in the models compared to the ground truth.