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

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...

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Autores principales:	Eugene B. Postnikov, Elena A. Lebedeva, Andrey Yu. Zyubin, Anastasia I. Lavrova
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	multiresolution Hilbert transform peak resolution Raman spectra Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3766821aca7045bcbab181cd6c4bf9ae
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spelling	oai:doaj.org-article:3766821aca7045bcbab181cd6c4bf9ae2021-11-11T18:20:09ZThe Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra10.3390/math92128022227-7390https://doaj.org/article/3766821aca7045bcbab181cd6c4bf9ae2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2802https://doaj.org/toc/2227-7390Raman 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 <i>Mycobacterium tuberculosis</i>. However, the proposed method can be applied to signals of different origins formed by overlapped localized pulses too.Eugene B. PostnikovElena A. LebedevaAndrey Yu. ZyubinAnastasia I. LavrovaMDPI AGarticlemultiresolutionHilbert transformpeak resolutionRaman spectraMathematicsQA1-939ENMathematics, Vol 9, Iss 2802, p 2802 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multiresolution Hilbert transform peak resolution Raman spectra Mathematics QA1-939
spellingShingle	multiresolution Hilbert transform peak resolution Raman spectra Mathematics QA1-939 Eugene B. Postnikov Elena A. Lebedeva Andrey Yu. Zyubin Anastasia I. Lavrova The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
description	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 <i>Mycobacterium tuberculosis</i>. However, the proposed method can be applied to signals of different origins formed by overlapped localized pulses too.
format	article
author	Eugene B. Postnikov Elena A. Lebedeva Andrey Yu. Zyubin Anastasia I. Lavrova
author_facet	Eugene B. Postnikov Elena A. Lebedeva Andrey Yu. Zyubin Anastasia I. Lavrova
author_sort	Eugene B. Postnikov
title	The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
title_short	The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
title_full	The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
title_fullStr	The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
title_full_unstemmed	The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra
title_sort	cascade hilbert-zero decomposition: a novel method for peaks resolution and its application to raman spectra
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3766821aca7045bcbab181cd6c4bf9ae
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The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra

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