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 the ability to decompose the spectrum into its components and peaks using the revealed hidden attributes of the photons. The simultaneous detection of temporal and spectral model parameters provides a mutually consistent description of TRLFS spectra. Theoretical aspects were investigated using simulated spectra and the applicability in practice is illustrated by spectra originating from uranyl species.