A Semi-parametric Approach for Decomposition of Absorption Spectra in the Presence of Unknown Components

Decomposition of absorption spectra using linear regression has been proposed for calculating concentrations of mixture compounds. The method is based on projecting the observed mixture spectrum onto the linear space generated by the reference spectra that correspond to the individual components comprising the mixture. The computed coefficients are then used as estimates for concentration of the components that comprise the mixture. Existence of unknown components in the mixture, however, introduces bias on the obtained concentration estimates. We extend the usual linear regression model to an additive semi-parametric model to take the unknown component into account, estimate the absorption profile of the unknown component, and obtain concentration estimates of the known compounds. A standard back-fitting method as well as a mean weighted least squares criterion are applied. The techniques are illustrated on simulated absorption spectra.