Extended Multiplicative Signal Correction of Noisy Raman Spectra

Abstract

Extended multiplicative signal correction (EMSC) is a common toolkit for preprocessing of vibrational spectra in chemometrics. The core of the EMSC is the ordinary least squares procedure, which is known to be affected by regression dilution bias in the presence of random noise in independent variables, i.e., reference spectra. For the simplest EMSC instance containing a single noisy reference spectrum with several baseline components, we introduce the proper statistical model for the EMSC procedure, which shows that the array of processed spectra is divided into two sets with different bias properties. An experimentally assessable parameter α, which defines the magnitude of bias for both sets, was suggested. The validity of several existing estimators together with two newly introduced ones was theoretically evaluated for bias correction. Next, selected estimators were tested using a specially designed experimental data set of sucrose Raman spectra. We believe that our study will serve as a proper introduction to the broad scientific field of regression dilution bias management for EMSC procedures.