ArticleBioelectronic medicine2022
Coarse-graining and the Haar wavelet transform for multiscale analysis.
Article in Bioelectronic medicine, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Cognitive Processing and EEG Complexity.Entropy (Basel, Switzerland) · 2026Review
- Age-Related Changes in EEG Signal Complexity and Behavioral Variability from Childhood to Adulthood: A Multiscale Entropy Approach.Entropy (Basel, Switzerland) · 2026Article
- A dynamical systems framework for precision psychiatry.NPJ digital medicine · 2025Review
- Brain Complexity and Parametrization of Power Spectral Density in Children with Specific Language Impairment.Entropy (Basel, Switzerland) · 2025Article
- Cortical changes associated with an anterior cruciate ligament injury may retrograde skilled kicking in football: preliminary EEG findings.Scientific reports · 2025Article
- Multiscale entropy of ADHD children during resting state condition.Cognitive neurodynamics · 2023Article
- A biomarker discovery framework for childhood anxiety.Frontiers in psychiatry · 2023Article
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Authors and funding
3 authors.
Funding
Abstract
backgroundMultiscale 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.
methodsThe 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.
resultsCoarse-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.
conclusionCoarse-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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