Computational implementation of the Cascade Hilbert-Zero Decomposition and perspectives of its applications for biophysical signal processing

Eugene B. Postnikov; Elena A. Lebedeva; Andrey Yu. Zyubin; Anastasia I. Lavrova

doi:10.1117/12.2625864

29 April 2022 Computational implementation of the Cascade Hilbert-Zero Decomposition and perspectives of its applications for biophysical signal processing

Eugene B. Postnikov, Elena A. Lebedeva, Andrey Yu. Zyubin, Anastasia I. Lavrova

Author Affiliations +

Proceedings Volume 12194, Computational Biophysics and Nanobiophotonics; 1219404 (2022) https://doi.org/10.1117/12.2625864
Event: XXV Annual Conference Saratov Fall Meeting 2021; and IX Symposium on Optics and Biophotonics, 2021, Saratov, Russian Federation

Abstract

We present a detailed description of the numerical implementation (for either MATLAB or GNU Octave) of a novel method for processing data with serial localized peaks intended to distinguish between individual components even when they form a mono-modal but complicatedly shaped structure [E.B. Postnikov et al. Mathematics 9 (2021) 2802]. The essence of the method consists of a cascade of local non-linear approximations by the Gaussian function at the vicinity of the zero-crossings for the signal’s Hilbert transform. At the first level, this procedure is applied to the processed signal directly; at the next level, it is applied to residuals between the signal and approximations on the previous levels. As a practical example, we consider the decomposition of Raman spectra recorded from different strains of Mycobacterium tuberculosis. Finally, we discuss other areas of applicability for the proposed method of signal processing.

Citation Download Citation

Eugene B. Postnikov, Elena A. Lebedeva, Andrey Yu. Zyubin, and Anastasia I. Lavrova "Computational implementation of the Cascade Hilbert-Zero Decomposition and perspectives of its applications for biophysical signal processing", Proc. SPIE 12194, Computational Biophysics and Nanobiophotonics, 1219404 (29 April 2022); https://doi.org/10.1117/12.2625864

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