北京生物医学工程

熵理论发展史及其在生物医学信号分析中的作用

History of entropy theory and its role in biomedical signal analysis

作者：刘澄玉赵莉娜

单位：山东大学控制科学与工程学院（济南250061）

分类号：

出版年·卷·期（页码）：2012·31·5（539-543）

摘要：

自1948年信息论之父C. E. Shannon提出“信息熵”的概念后，熵测度用于生理信号复杂度分析得到众多研究者的支持和青睐。其后在“信息熵”理论的指导下，出现了Kolmogorov熵、近似熵、动态近似熵、样本熵、模式熵、多尺度熵、基本尺度熵、联合熵、模糊近似熵、模糊测度熵等多种熵测度算法，极大提升了生物医学信号分析水平。本文系统综述了熵理论的发展历史及在生物医学信号分析中的作用，归纳出熵理论的4个历史阶段：起源、发展、繁荣和现状，并详细分析了每一阶段各种熵测度算法产生的原因、结果及存在的问题。

Since C.E. Shannon proposed the “information entropy” in 1948, the entropy measures have achieved encouraging progresses in the complexity analysis for biomedical signals. Later with the guidance of “information entropy”, many measures, such as Kolmogorov entropy, approximate entropy, dynamic approximate entropy, sample entropy, mode entropy, multiscale entropy, base scale entropy, joint entropy, fuzzy entropy, fuzzy measure entropy, were proposed and they greatly promoted the level of biomedical signal analysis. In this paper, the history of entropy theory and its role in biomedical signal analysis were reviewed. This paper systematically summarized the four development phases of entropy theory: origin, development, prosperity and status quo. Meanwhile, there was also a detailed analysis for the reasons and defects of each entropy algorithm.

参考文献：

［1］Clausius R. ber die Wrmeleitung gasfrmiger Krper ［J］. Annalen der Physik, 1865, 125: 353-400.
［2］Boltzmann L. Vorlesungen über Gastheorie ［M］. Leipzig：J A Barth, 1896.
［3］Shannon CE. A mathematical theory of communication ［J］. ACM SIGMOBILE Mobile Computing and Communication Review, 1948, 5(1): 3-55.
［4］Kolmogorov AH. A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces ［J］. Dokl Akad Nauk SSSR, 1958, 119: 861-864.
［5］Benettin G, Galganil, Strelcyn JM. Kolmogorov entropy and numerical experiments ［J］. Phys Rev A, 1976, 14: 2338-2345.
［6］Pincus SM. Approximation entropy as a measure of system complexity ［J］. Proc Natl Acad Sci USA, 1991, 88(7): 2297-2313.
［7］Pincus SM. Approximate entropy (ApEn) as a complexity measure ［J］. Chaos, 1995, 5: 110-117.
［8］Pincus SM, Singer B. Randomness and degrees of irregularity ［J］. Proc Nat Acad Sci USA, 1996, 93: 2083-2088.
［9］徐安, 刘军, 彭旗宇, 等. 动态近似熵快速算法在心率变异研究中的应用［J］. 同济大学学报：自然科学版, 2005, 33(4): 520-524.
［10］Richman JS, Moorman JR. Physiological time-series analysis using approximate entropy and sample entropy ［J］. Am J Physiol Heart Circ Physiol, 2000, 278(6): 2039-2049.
［11］李玲，王瑞平. 睡眠脑电信号的非线性动力学分析［J］.北京生物医学工程， 2010， 29（3）：304-307.
Li Ling, Wang Ruiping. Nonlinear dynamics analysis for sleep EEG［J］. Beijing Biomedical. Engineering, 2010, 29(3)：304-307.
［12］Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of complex physiologic time series ［J］. Physical Review Letters, 2002, 89(6): 68-81.
［13］Ning XB, Xu YL, Wang J, et al. Approximate entropy analysis of short-term HFECG based on wave mode ［J］. Physica A, 2005, 346(3): 475-483.
［14］李锦,宁新宝. 短时心率变异性信号的基本尺度熵分析［J］. 科学通报, 2005, 50(14): 1438-1441.
［15］李锦, 宁新宝, 马千里. 用联合熵分析短时心率变异信号的非线性动力学复杂性［J］. 生物医学工程学杂志, 2007, 24(2): 285-289.
Li Jin, Ning Xinbao, Ma qianli. Nonlinear dynamical complexity analysis of short-term heartbeat series using joint entropy［J］. Journal of Biomedical Engineering, 2007, 24(2): 285-289.
［16］Lu S, Chen X, Kanters JK, et al. Automatic selection of the threshold value R for approximate entropy ［J］. IEEE Trans Biomed Eng, 2008, 55: 1966-1972.
［17］Chon KH, Scully CG, Lu S. Approximate entropy for all signals ［J］. IEEE Engineering in Medicine and Biology Magazine, 2009,28: 18-23.
［18］Castiglioni P, Rienzo MD. How the threshold "R" influences approximate entropy analysis of heart-rate variability ［J］. Computers in Cardiology, 2008, 35: 561-564.
［19］Liu Chengyu ,Liu Changchun,Shao Peng, et al. Comparison of different threshold values r for approximate entropy: application to investigate the heart rate variability between heart failure and healthy control groups ［J］. Physiol Meas, 2011, 32(2): 167-180.
［20］Zadeh LA. Fuzzy sets［J］. Information and Contro1, 1965, 8: 338-353.
［21］Chen WT, Wang ZZ,Xie H, et al. Characterization of surface EMG signal based on fuzzy entropy ［J］. IEEE Trans Neural Syst Rehabil Eng, 2007, 15(2): 266-272.
［22］Liu Chengyu, Zhao Lina. Using fuzzy measure entropy to improve the stability of traditional entropy measures for HRV analysis ［C］. Computing in Cardiology, 2011, in process.

服务与反馈：

【文章下载】【加入收藏】

提示：您还未登录，请登录！点此登录