等概率符号化样本熵应用于脑电分析

黄晓林; 霍铖宇; 司峻峰; 刘红星

doi:10.7498/aps.63.100503

摘要

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
南京大学电子科学与工程学院, 生物医学电子工程研究所, 南京 210023;

2.
常熟理工学院物理与电子工程学院, 常熟 215500

基金项目: 江苏省自然科学基金（批准号：BK2011565）和国家自然科学基金（批准号：61271079）资助的课题.

Authors and contacts

1.
Institute of Biomedical Electronic Engineering, School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China;

2.
School of Physics and Electronic Engineering, Changshu Institute of Technology, Changshu 215500, China

Funds: Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2011565) and the National Natural Science Foundation of China (Grant No. 61271079).

参考文献

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施引文献

[1]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[2]	Richman J S, Moorman J R 2000 Am. J. Physiol. Heart Circ. Physiol. 278 2039
[3]	Bruhn J, Röpcke H, Hoeft A 2000 Anesthesiology 92 715
[4]	Lake D E, Richman J S, Griffin M P, Moorman J R 2002 Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 R789
[5]	Srinivasan V, Eswaran C, Sriraam N 2007 IEEE Trans. Inf. Technol. Biomed. 11 288
[6]	Sohn H, Kim I, Lee W, Peterson B S, Hong H, Chae J H, Hong S, Jeong J 2010 Clin. Neurophysiol. 121 1863
[7]	Acharya U R, Molinari F, Sree S V, Chattopadhyay S, Ng K H, Suri J S 2012 Biomed. Signal Proces. Control. 7 401
[8]	Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[9]	Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[10]	Hu M, Liang H 2012 IEEE Trans. Biomed. Eng. 59 12
[11]	Song A L, Huang X L, Si J F, Ning X B 2011 Acta Phys. Sin. 60 020509 (in Chinese) [宋爱玲, 黄晓林, 司峻峰, 宁新宝 2011 60 020509]
[12]	Zhang M, Wang J 2013 Acta Phys. Sin. 62 038701 (in Chinese) [张梅, 王俊 2013 62 038701]
[13]	Wu S, Li J, Zhang M L, Wang J 2013 Acta Phys. Sin. 62 238701 (in Chinese) [吴莎, 李锦, 张明丽, 王俊 2013 62 238701]
[14]	Chen G, Xie L, Chu J 2013 Chin. Phys. B 22 038902
[15]	Wang J, Yu Z F 2012 Chin. Phys. B 21 018702
[16]	Lin J, Keogh E, Wei L, Lonardi S 2007 Data Min. Knowl. Disc. 15 107
[17]	Hou F Z, Huang X L, Chen Y, Huo C Y, Liu H X, Ning X B 2013 Phys. Rev. E 87 012908
[18]	Kantz H, Schreiber T 2003 Nonlinear Time Series Analysis (2nd Ed.) (Cambridge: Cambridge University Press) pp39-40
[19]	Klimesch W 1999 Brain Res. Rev. 29 169
[20]	David J V 2005 Appl. Psychophysiol. Biofeedback 30 347
[21]	Egner T, Gruzelier J H 2004 Clin. Neurophysiol. 115 131

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