Bosl WJ, Loddenkemper T, Vieluf S. Coarse-graining and the Haar wavelet transform for multiscale analysis.
Bioelectron Med 2022;
8:3. [PMID:
35105373 PMCID:
PMC8809023 DOI:
10.1186/s42234-022-00085-z]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 01/18/2022] [Indexed: 11/10/2022] Open
Abstract
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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