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Coarse-graining and the Haar wavelet transform for multiscale analysis

BACKGROUND: Multiscale entropy (MSE) has become increasingly common as a quantitative tool for analysis of physiological signals. The MSE computation involves first decomposing a signal into multiple sub-signal ‘scales’ using a coarse-graining algorithm. METHODS: The coarse-graining algorithm averag...

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Autores principales: Bosl, William J., Loddenkemper, Tobias, Vieluf, Solveig
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BioMed Central 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8809023/
https://www.ncbi.nlm.nih.gov/pubmed/35105373
http://dx.doi.org/10.1186/s42234-022-00085-z
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author Bosl, William J.
Loddenkemper, Tobias
Vieluf, Solveig
author_facet Bosl, William J.
Loddenkemper, Tobias
Vieluf, Solveig
author_sort Bosl, William J.
collection PubMed
description BACKGROUND: Multiscale entropy (MSE) has become increasingly common as a quantitative tool for analysis of physiological signals. The MSE computation involves first decomposing a signal into multiple sub-signal ‘scales’ using a coarse-graining algorithm. METHODS: The coarse-graining algorithm averages adjacent values in a time series to produce a coarser scale time series. The Haar wavelet transform convolutes a time series with a scaled square wave function to produce an approximation which is equivalent to averaging points. RESULTS: Coarse-graining is mathematically identical to the Haar wavelet transform approximations. Thus, multiscale entropy is entropy computed on sub-signals derived from approximations of the Haar wavelet transform. By describing coarse-graining algorithms properly as Haar wavelet transforms, the meaning of ‘scales’ as wavelet approximations becomes transparent. The computed value of entropy is different with different wavelet basis functions, suggesting further research is needed to determine optimal methods for computing multiscale entropy. CONCLUSION: Coarse-graining is mathematically identical to Haar wavelet approximations at power-of-two scales. Referring to coarse-graining as a Haar wavelet transform motivates research into the optimal approach to signal decomposition for entropy analysis.
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spelling pubmed-88090232022-02-03 Coarse-graining and the Haar wavelet transform for multiscale analysis Bosl, William J. Loddenkemper, Tobias Vieluf, Solveig Bioelectron Med Short Report BACKGROUND: Multiscale entropy (MSE) has become increasingly common as a quantitative tool for analysis of physiological signals. The MSE computation involves first decomposing a signal into multiple sub-signal ‘scales’ using a coarse-graining algorithm. METHODS: The coarse-graining algorithm averages adjacent values in a time series to produce a coarser scale time series. The Haar wavelet transform convolutes a time series with a scaled square wave function to produce an approximation which is equivalent to averaging points. RESULTS: Coarse-graining is mathematically identical to the Haar wavelet transform approximations. Thus, multiscale entropy is entropy computed on sub-signals derived from approximations of the Haar wavelet transform. By describing coarse-graining algorithms properly as Haar wavelet transforms, the meaning of ‘scales’ as wavelet approximations becomes transparent. The computed value of entropy is different with different wavelet basis functions, suggesting further research is needed to determine optimal methods for computing multiscale entropy. CONCLUSION: Coarse-graining is mathematically identical to Haar wavelet approximations at power-of-two scales. Referring to coarse-graining as a Haar wavelet transform motivates research into the optimal approach to signal decomposition for entropy analysis. BioMed Central 2022-02-02 /pmc/articles/PMC8809023/ /pubmed/35105373 http://dx.doi.org/10.1186/s42234-022-00085-z Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Short Report
Bosl, William J.
Loddenkemper, Tobias
Vieluf, Solveig
Coarse-graining and the Haar wavelet transform for multiscale analysis
title Coarse-graining and the Haar wavelet transform for multiscale analysis
title_full Coarse-graining and the Haar wavelet transform for multiscale analysis
title_fullStr Coarse-graining and the Haar wavelet transform for multiscale analysis
title_full_unstemmed Coarse-graining and the Haar wavelet transform for multiscale analysis
title_short Coarse-graining and the Haar wavelet transform for multiscale analysis
title_sort coarse-graining and the haar wavelet transform for multiscale analysis
topic Short Report
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8809023/
https://www.ncbi.nlm.nih.gov/pubmed/35105373
http://dx.doi.org/10.1186/s42234-022-00085-z
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