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

Area of Science:

• Analytical Chemistry
• Spectroscopy
• Statistical Modeling

Background:

• Time-resolved laser-induced fluorescence spectroscopy (TRLFS) generates complex spectral data.
• Traditional methods like least squares struggle with decomposing superimposed signals and background noise.
• Photon emission attributes (time, wavelength) contain hidden information crucial for accurate analysis.

Purpose of the Study:

• To introduce a novel statistical approach for fitting models to TRLFS spectra.
• To address the challenge of incomplete data by treating photon attributes as probabilistic.
• To enable the decomposition of TRLFS spectra into constituent components and background.

Main Methods:

• Developed a statistical model treating photon emission as a probability density distribution.
• Implemented an expectation-maximization (EM) algorithm to solve the maximum likelihood estimation problem.
• Utilized hidden attributes of photons (component and peak affiliation) for spectral decomposition.

Main Results:

• The EM algorithm successfully decomposes TRLFS spectra into individual components and peaks.
• The method effectively distinguishes fluorescent signals from background noise in superimposed spectra.
• Simultaneous estimation of temporal and spectral parameters provides a consistent spectral description.

Conclusions:

• The new statistical approach offers significant advantages over traditional methods for TRLFS analysis.
• It enables enhanced evaluation of model parameters by revealing hidden photon attributes.
• This method provides new possibilities for accurate characterization of fluorescent chemical species.