A High-Performance Entropy Estimator for Quantitative Analysis of Neurophysiological Signals

Abstract

In quantifying the complexity characteristics of neurophysiological signals, the most advanced entropy methods still have some inevitable limitations, such as poor accuracy, robustness, and reliability. This study proposed a novel entropy estimator, termed 'cumulative residual symbolic dispersion entropy (CRSDE),' to address these limits and improve entropy analysis performance. Meanwhile, a corresponding time-shift multiscale version, TCRSDE, is also introduced to describe the irregularity of time series on multiple time scales. The CRSDE starts with an improved symbolic dynamics filter (ISDF) based on the equal probability dividing criterion to map the raw time series to symbolic series. After that, embedding theory is used to derive the dispersion patterns. Finally, the cumulative residual probabilities of all dispersion patterns are counted, and corresponding CRSDE results are calculated. A series of performance validations are performed using synthetic signals and realistic EEG signals. The simulation results confirmed the CRSDE's optimal estimation accuracy and robustness to noise and data length. The EEG dataset's results proved our CRSDE could realize the best reliability with the lowest root mean square deviation (RMSD, <0.05). In the multiscale version, TCRSDE, a time-shift coarse-graining was introduced. The verification results further confirmed that the TCRSDE avoided false estimation and achieved the best-estimated stability on all scales with the lowest coefficient of variation (CV, <0.01) and running time. The suggested CRSDE method was ultimately applied to neonatal sleep EEG. As a pilot study, it revealed some impressive quantitative findings concerning the neurodynamics of neonatal sleep activity.

Note:
Funding Information: This work was supported in part by the Shanghai Municipal Science and Technology Major Project (Grant No. 2017SHZDZX01) and by the Shanghai Committee of Science and Technology under Grant No. 20S31903900.

Declaration of Interests: The authors declare that there are no conflicts of interest related to this paper.

Ethics Approval Statement: The research ethics committee of the children's hospital of Fudan University approved this study (approval No. (2017) 89).

Keywords: cumulative residual symbolic dispersion entropy, improved symbolic dynamics filter, robustness, reliability