Automatic spectral reconstruction via expectation-maximization

Communications in Statistics - Simulation and Computation, pp. 1–13

Abstract

In this paper, we propose an automatic, user-independent algorithm based on an expectation-maximization (EM) approach to recover the structure of spectral data emerging from Raman spectroscopy - a well-established method used, among others, for the identification of substances in materials. More precisely, the goal of this work is to represent a given Raman signal through a suitable statistical model to identify the unknown substance from which this signal emerges from. Commonly used techniques in the field of Raman spectroscopy are based on least-squares estimation and they highly depend on the initial values specified by the user, leading to inconsistent and non-reproducible results. In contrast, the presented EM algorithm does not require any user-specified initial values, as a peak birth strategy is used, which effectively resolves these issues. Furthermore, the presented approach enables the fit of a given spectrum for an unknown number of underlying peaks by employing the BIC model selection criterion. The accuracy and robustness of the proposed algorithm is demonstrated in simulation studies considering different settings, such as high noise, strong baselines and low data availability.

Authors 3

1. Lea Kaufmann corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Pontdriesch 14-16, 52062 Aachen, Germany

2. Jan Meißner Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Pontdriesch 14-16, 52062 Aachen, Germany

3. Maria Kateri Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Pontdriesch 14-16, 52062 Aachen, Germany