Wavelet entropy

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.

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.

• 

  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]

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

1. Langley, Philip (2015). "Wavelet Entropy as a Measure of Ventricular Beat Suppression from the Electrocardiogram in Atrial Fibrillation". Entropy 17 (9): 6397–6411. doi:10.3390/e17096397.
2. Ibanez, Flor (2015). "Detection of damage in multiwire cables based on wavelet entropy evolution". SMART MATERIALS AND STRUCTURES 24 (8): 085036. doi:10.1088/0964-1726/24/8/085036.
3. Zarjam, Pega (2013). "Estimating cognitive workload using wavelet entropy-based features during an arithmetic task". COMPUTERS IN BIOLOGY AND MEDICINE 43 (12): 2186–2195. doi:10.1016/j.compbiomed.2013.08.021.
4. Xu, Peng; Hu, Xiao (2013). "Improved wavelet entropy calculation with window functions and its preliminary application to study intracranial pressure". COMPUTERS IN BIOLOGY AND MEDICINE 43 (5): 425–433. doi:10.1016/j.compbiomed.2013.01.022.
5. Zhang, Y. (2015). "Preclinical Diagnosis of Magnetic Resonance (MR) Brain Images via Discrete Wavelet Packet Transform with Tsallis Entropy and Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM)". Entropy 17: 1795–1813. doi:10.3390/e17041795.
6. Zhang, Xiaoli (2015). "Operational Safety Assessment of Turbo Generators with Wavelet Renyi Entropy from Sensor-Dependent Vibration Signals". Sensors 15 (4): 8898–8918. doi:10.3390/s150408898.
7. Gomez-Pilar, Javier (2015). "Neural Network Reorganization Analysis During an Auditory Oddball Task in Schizophrenia Using Wavelet Entropy". Entropy 17 (8): 5241–5256. doi:10.3390/e17085241.
8. Zhang, Y. (2015). "Pathological Brain Detection in Magnetic Resonance Imaging Scanning by Wavelet Entropy and Hybridization of Biogeography-based Optimization and Particle Swarm Optimization" (PDF). Progress in Electromagnetics Research – Pier 152: 41–58.