Preprocessing of spectral data in the extended multiplicative signal correction framework using multiple reference spectra

Extended multiplicative signal correction (EMSC) is a widely used framework for preprocessing spectral data. In the EMSC framework, spectra are scaled according to a given reference spectrum. Spectra that are far from collinear with the selected reference spectrum may not be scaled appropriately. An extension of the EMSC framework that allows for the incorporation of multiple reference spectra in the EMSC model is proposed to remedy this issue. Useful candidate reference spectra can be obtained from the dominant right singular vectors associated with the matrix of spectra, but any desired reference spectra can be used. As a part of this extension, we propose to change the basis used in the EMSC preprocessing to an orthonormal basis. Using an orthonormal basis will remove confounding issues between the basis vectors and make the obtained EMSC model simpler to interpret. We discuss the proposed modification theoretically and demonstrate its use with two data sets of Raman spectra and modelling with partial least quares regression and Tikhonov regularization. The data sets used are Raman spectra of oil samples from salmon with iodine value as the response and Raman spectra of an emulsion of water, whey protein, and different oils with polyunsaturated fatty acids as response (both as percentage of total fat content and total weight). In the paper, we discuss an extension of the EMSC preprocessing framework that allows for the inclusion of multiple reference spectra. This extension is particularly useful when dealing with data sets containing outlier spectra. We apply the suggested modification to two data sets of Raman spectra and show that the suggested modification to EMSC preprocessing can improve prediction when modelling with partial least squares or Tikhonov regularization.