TRLFS: Analysing spectra with an expectation-maximization (EM) algorithm

A new approach for fitting statistical models to time-resolved laser-induced fluorescence spectroscopy (TRLFS) spectra is presented. Such spectra result from counting emitted photons in defined intervals. Any photon can be described by emission time and wavelength as observable attributes and by component and peak affiliation as hidden ones. Understanding the attribute values of the emitted photons as drawn from a probability density distribution, the model estimation problem can be described as a statistical problem with incomplete data. To solve the maximum likelihood task, an expectation-maximization (EM) algorithm is derived and tested. In contrast to the well known least squares method, the advantage of the new approach is its ability to decompose the spectrum into its components and peaks using the revealed hidden attributes of the photons as well as the ability to decompose a background-superimposed spectrum into the exploitable signal of the fluorescent chemical species and the background. This facilitates new possibilities for evaluation of the resulting model parameters. The simultaneous detection of temporal and spectral model parameters provides a mutually consistent description of TRLFS spectra.