Multiscale entropy (MSE) analysis was introduced in the 2002 to evaluate the complexity of a time series by quantifying its entropy over a range of temporal scales. 一些改进的算法在熵的估计精度上下功夫，另外一些探索了另外的粗粒化过程（粗粒化过程是为了fast temporal scales，由于无法阻止失真，是个次优化的过程 ）。这个review评述了各种改进的算法。
The multiscale entropy (MSE) method is aimed at evaluating the complexity of time series. It is based on the analysis of the entropy values assigned not only to the original time series but also to coarse-grained time series, each of which represents the system’s dynamics on a different scale
Original MSE several drawbacks:
- 短时间序列和大的时间尺度，熵值误差大。For shorter time series, the variance of the entropy estimator grows very fast as the number of data points is reduced.....For synthetic signals for which the theoretical MSE values are known, the estimated MSE values (numerical solutions) may significantly differ from the analytic solutions. This is particularly annoying for practical applications where it is difficult to obtain long recordings (biomedical field for example).
- Equation (1) is similar to the use of a finite-impulse response (FIR) filter. As a result, the filter does not eliminate fast temporal scale above the filter’s cutoff frequency. The down sampling procedure that follows produces aliasing generating spurious oscillations in the frequency between 0 and the filter’s cutoff frequency [11]. The authors of [11] therefore conclude that the evaluation of the complexity of the downsampled time series is biased by these artifacts.
- The value of r is constant for all scale factors. Equation (1) can be seen as a low-pass filtering followed by a downsampling. As a result, when the scale factor increases, the standard deviation of the resulting filtered time series may become lower and lower. Therefore, the patterns may become closer and closer. If the parameter r is constant while the scale factor τ increases, more and more patterns will be considered indistinguishable. This will lead to a decrease of the entropy when the scale factor τ increases.
改进的多尺度熵：
- Refined Multiscale Entropy ： 2009年Valencia提出，"a way to remove the fast temporal scales and used a coarse-graining that prevents the influence of the reduced variance on the complexity evaluation." 通过低通Butterworth滤波代替FIR滤波，来提高消除fast temporal scales。
In order to analyze the performance of RMSE, Valencia et al. processed (among others) a fully unpredictable process (Gaussian white noise) and a signal with long-range correlation (1/f noise). They reported that RMSE is flat with scale factor τ for the Gaussian white noise and presents a slow but progressive increase with scale factor τ in the case of 1/f noise. By opposition, the original MSE presents a monotonic decrease with scale factor τ both for the Gaussian white noise and the 1/f noise [11]. Since aliasing is more significant at short time scales when the fast oscillations are dominant, the largest differences between RMSE and the original MSE algorithms are found in the presence of high frequency oscillations [11]. The RMSE algorithm has also been applied on experimental data (see, e.g., [11,14]).
- 广义多尺度熵：基于employing different moments to coarse-grain a time series. First, the original signal is divided into non-overlapping segments of length τ. Second, a selected moment is estimated for the data in each of these segments to derive the coarse-grained time series at scale τ.Third, a measure of entropy, sample entropy, is calculated for each coarse-grained time series. Fourth, a complexity index is derived by adding the entropy values for a selected range of scales. 原始的多尺度熵度量复杂度，广义熵度量volatility. Mathematical models purporting to capture the dynamics of healthy heartbeat variability should account for the observed multiscale volatility and for its degradation with aging and disease.