An information-theoretic methodology for the resolution of pure component spectra without prior information using spectroscopic measurements

The resolution of pure component spectra based on spectroscopic measurements from a reaction system is a challenging task for chemometric systems in the absence of a priori knowledge about the reaction components involved. A popular approach in the literature is based on constrained entropy minimization of the second-order derivative of the resolved pure component spectra. Using an analytical information theoretic framework, it can however be shown that minimization of this cost function is not sufficient to completely separate the underlying components from a set of mixture spectra. Instead, an augmented objective function derived from this analysis is proposed for complete minimization of the mutual information between separated components. The final optimization approach is further shown to be analog to independent component analysis (ICA), a signal processing technique successfully applied to biomedical and speech data to separate linear source mixtures in the absence of a priori information. The developed theoretical insights and proposed methodologies in this paper are illustrated in a simulation study on the separation of three component spectra based on absorbance data acquired from a first-order kinetic reaction system.