An expectation–maximization algorithm for spectral reconstruction under the spectral hard model

Abstract

Indirect Hard Modeling (IHM) is a physics-based evaluation method for the quantitative analysis of fluid compositions using spectroscopic techniques such as Raman spectroscopy. In this approach, mixture spectra are represented as a superposition of pure substance models, with each component described by a sum of parameterized peak functions. Nevertheless, the accuracy of the compositions prediction depends critically on user decisions regarding both the number of peak functions and the specific parameter adjustments employed. In this work, we apply an expectation–maximization (EM) based algorithm for generating spectral reconstructions of pure substance models that does not require the pre-specification of the number of peaks or any initial values. The efficient and fast performance of the used EM algorithm enables the fit of a given spectrum for an unknown number of peaks, based on a model selection criterion. In simulation studies, we demonstrate that this approach can recognize the true underlying function in settings of high noise, peak overlapping and background signals, yielding reliable results. In a validation study, the algorithm was tested using experimental data. It was integrated into an Indirect Hard Modeling framework and applied to three chemical test systems. The quality of the obtained results were in the range of other automated IHM model generating approaches while significantly reducing both time and computational effort.