Abundance estimation of spectrally similar minerals

This paper evaluates a spectral unmixing method for estimating the partial abundance of spectrally similar minerals in complex mixtures. The method requires formulation of a linear function of individual spectra of individual minerals. The first and second derivatives of each of the different sets of mixed spectra and the individual spectra are determined, at signal-to-noise ratios of 50:1, 200:1 and 500:1. The error is minimized by means of simulated annealing. Experiments were made on several different mixtures of selected end-members, which could plausibly occur in real situations. We conclude that in the method proposed, the use of the original and first order derivatives provides a valuable contribution to unmixing procedures provided the signal-to-noise ratio is between 50:1 and 200:1. When the signal-to-noise ratio increases, the second derivative of the observed spectrum and the second derivatives of the end-member spectra give most precise estimates for the partial abundance of each end-member. This can often be seen when the signal-to-noise ratio is of the order 500:1.