The Multi-Reconstruction Entropy Minimization Method: Unsupervised Spectral Reconstruction of Pure Components from Mixture Spectra, without the Use of a Priori Information

The band-target entropy minimization method (BTEM) and its variant methods excel at reconstructing known/unknown pure spectra from mixtures without prior information. These mixtures may represent either non-reactive or even reactive systems. In this work, an unsupervised form of the entropy minimization curve resolution, namely, the multi-reconstruction entropy minimization method (MREM), is presented. MREM differs from BTEM by removing the need for band-targets and by introducing a multiple search routine to find multiple local entropy minima. This multiple search routine, which provides a rapid survey of spectral estimates, utilizes a localized form of Corona's simulated annealing method in the optimization. The objective functions and penalty functions of the BTEM type methods are essentially retained. Compared to BTEM type methods, MREM (1) searches for multiple local minima instead of a single global minimum and hence reconstructs many pure component spectra at once instead of one pure spectrum; and (2) utilizes a user-defined broad spectral range [ν1, ν2] for all searches instead of multiple user-defined narrow “targets” as in BTEM. The new MREM has been tested on four sets of real spectra using Fourier transform infrared spectroscopy (FT-IR), mass spectroscopy (MS), and ultraviolet–visible (UV-Vis) spectroscopy. The results show that MREM is computationally much faster than BTEM for finding the major components present. Also, because MREM does not rely on band targeting, it is very useful for spectra that have no localized features and are highly overlapping, such as UV-Vis.