Self-subtraction improves consistency in spectral curve fitting

Abstract

Common practice in curve fitting of overlapped spectral features often imparts overextending the number of optimized parameters, resulting in increased model complexity and exacerbated sensitivity to initial conditions, that ultimately leads to inflated uncertainty in values of optimized parameters. We introduce a lightweight operator that unifies two important steps of model initialization: (1) resolution of overlapped bands that exceeds the benefits of the widely used second derivative transform, and (2) bandwidth estimation for overlapped features, to achieve a reliable data-driven contraction of optimization complexity and outperform similar methods in terms of speed, flexibility and ease of interpretation. Since only the spectrum at hand is used, the curve fitting process is steamlined by avoiding multivariate models and/or assumptions about the profile line shape included in the choice of a digital filter or a basis function. All statements are reinforced with illustrative theoretical models and x-ray fluorescence spectra obtained from a publicly available database.