Abundance Estimation of Spectrally Similar Minerals by Using Derivative Spectra in Simulated Annealing

This paper presents a 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. The error is minimized by means of simulated annealing. Experiments were made on several different mixtures of selected endmember, which could plausibly occur in real situations. The variance of the differences between the first derivatives of the observed spectrum and the first derivatives of the endmember spectra gives the most precise estimates for the partial abundance of each endmember. We conclude that the use of first-order derivatives provides a valuable contribution to unmixing procedures provided that the signal-to-noise ratio is at least 50 : 1