Advancement of Hyperspectral Image Unmixing and Analysis: An Application in Mineral Detection and Identification

This dissertation contributes to data science by addressing theoretical and practical challenges to advance hyperspectral image analysis. Hyperspectral imaging captures high dimensional spectral information at the pixel level, enabling enhanced material detection and identification. A common process in hyperspectral image analysis is spectral unmixing --- the task of identifying pure materials, from an observed pixel spectrum and estimating their relative abundances.

Spectral unmixing is often framed as a regression problem, with Ordinary Least Squares (OLS) regression serving as a foundational approach. Despite its widespread use, the assumptions underlying OLS and its extensions are seldom articulated, particularly in the context of spectral unmixing. This body of work compares a variety of unmixing techniques, but also incorporates an explanation of the algorithmic assumptions and relationships between OLS and its extensions contributing to their unmixing success and failure. Through outlining the OLS assumptions, we identify alignments and misalignments with the practical demands of spectral unmixing and develop a novel technique addressing these discrepancies.

Through this exploration, the research also addresses foundational questions in data science: To what extent do algorithmic assumptions reflect real-world phenomena, and how can models balance algorithmic complexity with practical generalizability? Much of the research contributing to hyperspectral imaging involves developing or enhancing unmixing algorithms rather than evaluating them. These research questions guided the development of a comprehensive benchmarking framework. The framework evaluates techniques using metrics such as root mean squared error (RMSE), computation time, model size, percent detection, and average precision of the top-K results. To date, no study has integrated this breadth of unmixing techniques and evaluation metrics into a single framework.

Beyond evaluation metrics, we contribute to the theoretical foundation of unmixing by examining the physical-chemical phenomena contributing to material identification. We develop a spectral taxonomy classifying minerals based on their molecular design structure, providing insights into spectral material patterns and detection strengths of various techniques. Our analysis reveals two core findings: 1) technique success depends on the primary objective of the study and 2) the minerals included in the mixture model were either the target mineral (successful detection), a substitution from the same mineral category as the target, or a mineral with similar spectral pattern features (failed detection).