Error Reduction in Spectrum Estimation by Means of Concentration-Spectrum Correlation

A new technique is introduced for reducing the estimation errors accompanying component spectra estimated by means of the concentration-spectrum correlation method. Many estimates of the component spectra, given to different errors, are obtained by the nonparametric statistical method called the bootstrap. Among them, there exists a spectrum that has a very small error. This spectrum can be found by searching for the spectrum that has the least entropy, since a parameter of the entropy is correlated positively with the estimation error. Computer-simulation experiments are performed to demonstrate the effectiveness of the present technique for cases involving both unconstrained concentrations and constrained concentrations whose sum for all the components in a sample is unity.