A Log-Gaussian Cox Process with Sequential Monte Carlo for Line Narrowing in Spectroscopy

TL;DR

This paper introduces a Bayesian statistical model using a log-Gaussian Cox process and sequential Monte Carlo methods to accurately identify and quantify narrow spectral lines in spectroscopy, with uncertainty estimates.

Contribution

It presents a novel Bayesian approach combining Cox processes and SMC for spectral line narrowing, including uncertainty quantification and prior incorporation.

Findings

Effective in simulated spectral data

Successfully applied to mineralogical Raman spectrum

Provides uncertainty estimates for peak locations

Abstract

We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum.