The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra

Abstract

Raman spectra of biological objects are sufficiently complex since they are comprised of wide diffusive spectral peaks over a noisy background. This makes the resolution of individual closely positioned components a complicated task. Here we propose a method for constructing an approximation of such systems by a series, respectively, to shifts of the Gaussian functions with different adjustable dispersions. It is based on the coordination of the Gaussian peaks’ location with the zeros of the signal’s Hilbert transform. The resolution of overlapping peaks is achieved by applying this procedure in a hierarchical cascade way, subsequently excluding peaks of each level of decomposition. Both the mathematical rationale for the localization of intervals, where the zero crossing of the Hilbert-transformed uni- and multimodal mixtures of Gaussians occurs, and the step-by-step outline of the numerical algorithm are provided and discussed. As a practical case study, we analyze results of the processing of a complicated Raman spectrum obtained from a strain of Mycobacterium tuberculosis. However, the proposed method can be applied to signals of different origins formed by overlapped localized pulses too.

Oil content analysis of corn seeds using a hand-held Raman spectrometer and spectral peak decomposition algorithm

“…Although Raman spectroscopy can be used simultaneous measurement of various compositions of seeds, the Raman characteristic peaks of oil in corn seeds suffer from interference from starch, protein, lignin, and other compositions ( Yang et al., 2018 ). To overcome this issue, Raman spectroscopy could be combined with a spectral peak decomposition algorithm to realize the identification, classification, and quantification of composition ( Postnikov et al., 2021 ). Sadat and Joye (2020) uaed a peak decomposition method based on the second derivative of the original spectrum and the curve fitting of the Voigt function to identify, separate and quantify hidden peaks of the amide I band in the infrared and Raman spectra of globular proteins, hydrated zein and gluten proteins.…”