Improved Multiscale Entropy Technique with Nearest-Neighbor Moving-Average Kernel for Nonlinear and Nonstationary Short-Time Biomedical Signal Analysis

Figures

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  Figure 1. Schematic illustration to produce nearest neighbor moving-average time series with scale factor τ = 1 for the MSE algorithm. Blue squares represent raw time series data, and red dots represent the nearest-neighbor moving-averaged time series from which MSE is obtained. Brown squares represent the moving-window-averaging kernel for the raw second time point (X2) that averages one neighbor on both sides with τ = 1 to produce the first new time series point Z1(1). Similarly, green square produces Z2(1) and so on (orange square) with the blue square producing the last time series point Zi+1(1).

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  Figure 2. (a) Top panel shows white noise with 500 sample points; Middle panel shows the MSE for various time series (TS) lengths; bottom panel shows normalized MSE (for scale factors τ = 1,2,3, and 5) and SE; (b) top panel shows pink noise with 500 sample points; middle panel shows the MSE for various time series (TS) lengths; bottom panel shows normalized MSE (for scale factors τ = 1,2,3, and 5) and SE; (c) top panel shows brown noise with 500 sample points; middle panel shows the MSE for various time series (TS) lengths; bottom panel shows normalized MSE (for scale factors τ = 1,2,3, and 5) and SE.

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  Figure 3. (a) Left panel shows single-frequency (10 Hz) sinusoidal wave with 500 sample points; middle panel shows the MSE for various length time series across several scaling factors; right panel shows normalized MSE (for scale factors τ = 1–10) and SE; (b) top row shows sinusoidal wave with white noise, (c) pink noise, and (d) brown noise; (b) bottom row shows normalized MSE (for scale factors τ = 1–10) and SE for sine wave with white noise, (c) pink noise, and (d) brown noise, respectively.

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  Figure 4. (a) Left panel shows multifrequency sinusoidal wave with 500 sample points; middle panel shows the MSE for various length time series across several scaling factors; right panel shows normalized MSE (for scale factors τ = 1–10) and SE; (b) top row shows sinusoidal wave with white noise, (c) pink noise, and (d) brown noise; (b) bottom row shows normalized MSE (for scale factors τ = 1–10) and SE for sinusoidal wave with white noise, (c) pink noise, and (d) brown noise, respectively.

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  Figure 5. (a) Left panel shows sample ECG trace with 500 sample points; middle panel shows the MSE for various length time series across several scaling factors; right panel shows normalized MSE (for scale factors τ = 1–10) and SE; (b) top row shows sinusoidal wave with white noise, (c) pink noise, and (d) brown noise; (b) bottom row shows normalized MSE (for scale factors τ = 1–10) and SE for sinusoidal wave with white noise, (c) pink noise, and (d) brown noise, respectively.

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  Figure 6. (a) Representative example of an ECG trace with normal sinus rhythm; (b) representative example of an ECG trace with AF; (c) box plot showing MSE values for sinus rhythm and AF ECG datasets. The NSR and AF were significantly different (p < 0.01) on MSE.

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  Figure 7. (a) Top panel shows a representative example of a single rotor. Pixel locations “1” represent rotor core region and “2” represent rotor periphery; bottom panel shows corresponding voltage traces at those pixel locations. (b) Normalized 2D MSE maps; top panel with scale factor τ = 1; middle panel with τ = 2; bottom panel with τ = 3, correctly identifying rotor core regions; (c) normalized 2D SE map with lower SE values at the rotor core.

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  Figure 8. (a) Top panel shows a representative example of a figure-of-8 reentry. Pixel locations “1” and “2” represent rotor core region and “3” represent rotor periphery; bottom panel shows corresponding voltage traces at those pixel locations. (b) Normalized 2D MSE maps; top panel with scale factor τ = 1; middle panel with τ = 2; bottom panel with τ = 3, correctly identifying rotor core regions; (c) normalized 2D SE map with lower SE values at the rotor core.