等概率符号化样本熵应用于脑电分析

Application of equiprobable symbolization sample entropy to electroencephalography analysis

样本熵(或近似熵)以信息增长率刻画时间序列的复杂性,能应用于短时序列,因而在生理信号分析中被广泛采用.然而,一方面由于传统样本熵采用与标准差线性相关的容限,使得熵值易受非平稳突变干扰的影响,另一方面传统样本熵还受序列概率分布的影响,从而导致其并非单纯反映序列的信息增长率.针对上述两个问题,将符号动力学与样本熵结合,提出等概率符号化样本熵方法,并对其物理意义、数学推导及参数选取都做了详细阐述.通过对噪声数据的仿真计算,验证了该方法的正确性及其区分不同强度时间相关的有效性.此方法应用于脑电信号分析的结果表明,在不对信号做人工伪迹去除的前提下,只需要1.25 s的脑电信号即可有效地区分出注意力集中和注意力发散两种状态.这进一步证明了该方法可很好地抵御非平稳突变干扰,能快速获得短时序列的潜在动力学特性,对脑电生物反馈技术具有很大的应用价值.

Sample entropy or approximate entropy, a complexity measure that quantifies the new information generation rate and is applicable to short time series, has been widely applied to physiological signal analysis since it was proposed. However, on one hand, sample entropy is easily affected by non-stationary sudden noise, because the tolerance during calculation is set to be proportional to standard deviation; on the other hand, it is not independent of the probability distribution, so that it does not purely characterize the new information generation rate. To solve these two problems, a new improved method named equiprobable symbolization sample entropy is proposed in this paper. Through equiprobable symbolization, the effects of both non-stationary sudden noises and probability distribution are eliminated. Besides, since equiprobable symbolization is usually non-uniform, it further breaks through the linear constrains in classic sample entropy. The method is proved to be rational by simulating three typical noises that have different time correlations and new information generation rates. Then the method is applied to electroencephalography （EEG） analysis. Results show that the method can successfully discriminate two different attention levels based on EEG with duration as short as 1.25 s and without removing any artificial artifacts. Therefore, the method is of great significance for EEG biofeedback, in which strong real-time abilities are usually required.