Drawbacks of using linear mixture modeling on hyperspectral images

Hyperspectral spectroscopy can be used remotely to measure emitted radiation from minerals and rocks at a series of narrow and continuous wavelength bands resulting in a continuous spectrum for each pixel, thereby providing ample spectral information to identify and distinguish spectrally unique materials. Linear mixture modeling ("spectral unmixing"), a commonly used method, is based on the theory that the radiance in the thermal infrared region (8-12 μm) from a multi-mineral surface can be modeled as a linear combination of the endmembers. A linear mixture model can thus potentially model the minerals present on planetary surfaces. It works by scaling the endmember spectra so that the sum of the scaled endmember spectra matches the measured spectrum with the smallest "error" (difference). But one of the drawbacks of this established method is that mathematically, a fit with an inverted spectrum is valid, which effectively returns a negative abundance of a material. Current models usually address the problem by elimination of endmembers that have negative scale factors. Eliminating the negative abundance problem is not a major issue when the endmembers are known. However, identifying unknown target composition (like on Mars) can be a problem. The goal of this study is to improve the understanding and find a subsequent solution of the negative abundance problem for Mars analog field data obtained from airborne and ground spectrometers. We are using a well-defined library of spectra to test the accuracy of hyperspectral analysis for the identification of minerals on planetary surfaces.