SEPARATION OF OVERLAPPING SPECTRA FROM EVOLVING SYSTEMS USING FACTOR-ANALYSIS .1. THEORY TO OBTAIN REAL SPECTRA

A method based on factor analysis is developed that permits us to retrieve the real spectra and multiplication factors (or concentrations) of individual species in spectra of evolving complex systems with no a priori information. The application of constraints of non-negative intensities and non-negative concentrations to the matrices of abstract factors gives the unoptimized real spectra. Then searching for the most likelihood spectra by using the maximum entropy criterion gives the real spectra. Mixtures of experimental spectra are used to illustrate the method.