Wavelet entropy
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Wavelet entropy (WE) is a new approach with the ability to analyze transient features of non-stationary signals or images.[1] Generally speaking, WE perform entropy operation over the coefficients of discrete wavelet transform.
Contents
Introduction
Wavelet Entropy (WE) is a novel tool with the ability to analyze transient features of non-stationary signals. This metric combines wavelet decomposition and entropy to estimate the degree of order/disorder of a signal with a high time-frequency resolution.[2]
Initially, Shannon entropy was proposed to quantify the energy distribution in wavelet sub-bands, the metric defined in this way being applied to a wide variety of different scenarios. Special interest has shown WE’s application to physiological signals, such as electrocardiogram, electroencephalography,[3] intracranial pressure recordings [4] or evoked related potentials, in which it is able to reveal clinically useful information, e.g., in the prevention of cardiac diseases or the detection of sleep-deprived driving.
A similar attention has also initiated WE’s use in forecasting faults and dangers in modern power systems and detecting machinery vibration . Moreover, several studies have also shown the superiority of WE in analyzing the variability and complexity of climate processes compared with traditional methods. Finally, it is worth noting that WE-based analysis of electromechanical noise has recently gained an increasing interest regarding remote corrosion monitoring in industrial applications.
Implementation
It calculates the entropy value of the Probability density function of the energy distribution of wavelet subband coefficients in the wavelet domain. Suppose we have a brain image with size of 256x256, and take a 2-level WE as an example.
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Wavelet entropy.jpg
Diagram of WE
Extensions
Wavelet packet entropy
The wavelet packet entropy combines "wavelet packet transform" with Shannon entropy.[5]
Wavelet Renyi entropy
The wavelet Renyi entropy combines "wavelet transform" with "Renyi entropy".[6]
Relative wavelet entropy
Wavelet singular entropy
Application
Gomez-Pilar, Javier et al. applied wavelet entropy to analyze Neural Network Reorganization.[7] Zhang, Y et al. used wavelet entropy to detect pathological brains.[8]
References
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