Measuring the complexity of time series: An application to neurophysiological signals
Measuring the complexity of time series: An application to neurophysiological signals
复制标题
测量时间序列的复杂性：神经生理学信号的应用
作者：
S. G. González Andino;R. Grave de Peralta Menéndez;G. Thut;L. Spinelli;O. Blanke;C. Michel;T. Landis
信号复杂性的测量可用于在那些神经成像技术中区分神经生理学激活与噪声，在这些神经成像技术中，我们记录大脑活动随时间的变化，例如，功能磁共振脑电图ERP在本文中，我们探讨了最近开发的方法来计算确定性信号的复杂性和信息含量的定量测量：Renyi数。Renyi数定义为熵，即，一个经典使用的措施，在物理系统中的混乱，并计算在本文的基础上的时频表示（TFR）的测量信号。当以这种形式计算时，Renyi熵（RE）通过提供对构成时间频率平面中的时间序列的分离的基本原子的数量的近似计数来间接表征信号的复杂性。从这个意义上说，这个措施符合我们的视觉概念的复杂性，因为低复杂性的值是由少量的“组件”形成的信号。这种测量的最显著的特性是双重的：1）它不依赖于关于时间序列的假设，例如平稳性或高斯性，以及2）不需要所研究的神经过程的模型，例如，功能磁共振成像没有血流动力学反应模型。本文使用fMRI，颅内ERPs和颅内电位估计头皮记录ERPs通过逆解（ELECTRA）的方法来说明。这种措施的主要理论和实践的缺点，特别是它的依赖选定的总生育率，进行了讨论。此外，这种方法产生的能力，较少的限制性假设，结果与那些获得更标准的方法，但强调。Hum.脑图谱11：46-57，2000年。© 2000 Wiley利斯公司
Measures of signal complexity can be used to distinguish neurophysiological activation from noise in those neuroimaging techniques where we record variations of brain activity with time, e.g., fMRI, EEG, ERP. In this paper we explore a recently developed approach to calculate a quantitative measure of deterministic signal complexity and information content: The Renyi number. The Renyi number is by definition an entropy, i.e., a classically used measure of disorder in physical systems, and is calculated in this paper over the basis of the time frequency representation (TFRs) of the measured signals. When calculated in this form, the Renyi entropy (RE) indirectly characterizes the complexity of a signal by providing an approximate counting of the number of separated elementary atoms that compose the time series in the time frequency plane. In this sense, this measure conforms closely to our visual notion of complexity since low complexity values are obtained for signals formed by a small number of “components”. The most remarkable properties of this measure are twofold: 1) It does not rely on assumptions about the time series such as stationarity or gaussianity and 2) No model of the neural process under study is required, e.g., no hemodynamic response model for fMRI. The method is illustrated in this paper using fMRI, intracranial ERPs and intracranial potentials estimated from scalp recorded ERPs through an inverse solution (ELECTRA). The main theoretical and practical drawbacks of this measure, especially its dependence of the selected TFR, are discussed. Also the capability of this approach to produce, with less restrictive hypothesis, results comparable to those obtained with more standard methods but is emphasized. Hum. Brain Mapping 11:46–57, 2000. © 2000 Wiley‐Liss, Inc.