Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models

Figure 1

Theoretical profiles of the multiscale entropy (MSE) computed applying the proposed approach to the true parameters of simulated AR processes. Plots depict the exact values of MSE () computed as a function of the cutoff frequency of the low-pass filter used to eliminate the fast temporal scales of the process for different values of the modulus (a) and of the frequency (b) of the pole set in Type 1 simulations, and for different values of the modulus (c) and frequency (d) of the second pole set in Type 2 simulations. The multiscale complexity of AR processes increases with decreasing the amplitude (a) or moving the frequency of a single stochastic oscillation closer to half the Nyquist frequency (b), as well as adding a second stochastic oscillation with increasing amplitude (c) or with increasing frequency mismatch compared to the first one (d).

(a) Theoretical MSE

(b) Theoretical MSE

(c) Theoretical MSE

(d) Theoretical MSE