分尺度复杂性及希尔伯特-黄变换在脑电分析中的应用
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摘要
人脑是一个高度复杂的非线性非平稳系统,所以脑电图和皮层脑电图也是非线性非平稳信号,基于线性和平稳假设的分析方法尽管取得了一些重要的研究成果,但是无法对神经系统进行更加深入的解释。复杂性分析方法和时频分析方法为分析脑电分析提供了新的手段,本文第一部分对复杂性方法的粗粒化问题进行了研究,第二部分将希尔伯特—黄变换方法用于分析运动表象。
Lempel-Ziv复杂性是一种实用的脑电分析方法,但现有的二值化方法会丢失部分原始信息。另外,在不同尺度下复杂性一般是不同的,计算小尺度下序列的复杂性,可以得到更多的信息,所以需要在不同尺度下计算信号的复杂性。增加符号数目可以减少信息损失但会增加符号序列长度和计算时间。本文提出了一种新的二值化方法,将原始信号分为多个区间,用“0”“1”表示序列在一定尺度范围内的下降和上升。这种方法在不增加符号数目的情况下减小信息损失并且可以计算不同尺度下的复杂性。以下工作证明了此方法的有效性:
用叠加了正弦曲线的Logistic映射对这种方法进行了分析,分析结果显示此方法可以刻画在小尺度下序列的复杂性;将这一方法应用于区分文字和照片,实验发现随着复杂性计算尺度的减小,照片复杂性的增加大于文字复杂性的增加,这一结果表明不同尺度下的复杂性可以作为文字和照片分类的一个特征;对精神分裂症病人和正常人的脑电分析显示,在计算复杂性过程中选用小尺度下二值化方法同传统的二值化方法相比,可以降低误判率。
运动表象分析是脑机接口(BCI)的一个分支,因为脑电是非平稳非线性信号,所以本文采用了一种全新的非平稳、非线性分析方法:希尔伯特—黄变换(HHT)分析运动表象。和其它分解方法不同,HHT的基函数来自数据本身,具有局部性、自适应性并且是数据驱动的。分析结果如下:
在对BCI2005数据Ⅲb的分析过程中,在不同频率下观察到了事件相关去同步化(ERD)和事件相关同步化(ERS)现象。利用时频窗口内的振幅标准差和能量对想象的左手和右手进行分类,一名被试的分类误判率低于10%。发现了一名被试左右脑的不对称现象,在单独利用两个对称电极中的一个进行运动表象分类
Brain is a very complex non-linear system, and electroencephalograph (EEG) and electrocorticogram (ECoG) are also non-stationary and nonlinear in nature, signal processing methods based on linear and stationary assumptions, although has obtained important result, can not grasp the entire picture of neuroscience. Complexity and time-frequency analysis give us chances to analyze EEG by these entirely new methods, in the first part of this paper coarse graining of Lempel-Ziv complexity was analyzed and in the second part Hilbert-Huang transform was used to analyze motor imagery.Lempel-Ziv complexity is a useful method to analyze EEG, but current binary processing might lose some useful information of the original signal. In addition, complexity is different at different scales, and we can derive some useful information by calculating complexity at small scale, so sometimes we need to calculate Lempel-Ziv complexity at different scale. Increasing the number of symbol can decrease the information loss but need more data and time for calculation. In this paper we divide the original signal into more than two parts, "0" and "1" denote decrease and increase respectively. This new binary method can reduce the information loss and calculate Lempel-Ziv complexity at multi-scale but do not increase the number of symbol. The following works testify the validity of this new binary method:We test this method with Logistic map added by sine wave and have a good result when the added sine wave has low frequency; This new approach was also presented for distinguishing textual images from pictorial images and we found that the pictorial images' complexity had more significant increase than the textual images' complexity did when the calculating scale became small. The test shows that multi-scale Lempel-Ziv complexity can be used as an image classification method or as a feature of image classifier; Schizophrenia and normal EEG was classified by
large-scale compleiity and small-seale complexity, the error rate of small-scale complexity is low than large-scale complexity.Motor imagery is a branch of brain computer interface (BCI). As EEG is non-stationary. Hilbert-Huang Transform (HHT), a novel approach for analyzing nonlinear and non-stationary signals, was presented to motor imagery analysis. The basis function of HHT comes from signal itself, the decomposition is local, self-adaptive and data driven. The results are as follows:When BCI2005 data Illb (EEG) was analyzed we observed event-related desynchronization (ERD) and event-related synchronization (ERS) at different frequency. Using standard deviation of amplitude and energy in time-frequency window as a feature to classify imagined left and right hand movement, the error of one subject is lower than 10%.One subject of data Illb has asymmetry phenomena, that is, only one of the two symmetry leads was used to classify two imagined movements, one can get error rate as low as 27.43% while the other get error as high as 37.69%.We use the same feature as used in data Illb to classify imagined tongue and left small finger movement (ECoG BCI2005 data I), the lowest error rate is 16.19% by featuring from one time-frequency window. Using standard deviation of time-frequency window from 7 electrodes, single frequency band and 11 continuous time windows as feature, the error rate can be as low as 11.87%. Compared with energy, the standard deviation of time-frequency window performs better. Surface Laplacian Filter is a good EEG preprocessing method, we use this method to preprocess ECoG but can not reduce error rate, this prompt us that not all method used in EEG can be used to analyze ECoG.
Lempel-Ziv复杂性是一种实用的脑电分析方法,但现有的二值化方法会丢失部分原始信息。另外,在不同尺度下复杂性一般是不同的,计算小尺度下序列的复杂性,可以得到更多的信息,所以需要在不同尺度下计算信号的复杂性。增加符号数目可以减少信息损失但会增加符号序列长度和计算时间。本文提出了一种新的二值化方法,将原始信号分为多个区间,用“0”“1”表示序列在一定尺度范围内的下降和上升。这种方法在不增加符号数目的情况下减小信息损失并且可以计算不同尺度下的复杂性。以下工作证明了此方法的有效性:
用叠加了正弦曲线的Logistic映射对这种方法进行了分析,分析结果显示此方法可以刻画在小尺度下序列的复杂性;将这一方法应用于区分文字和照片,实验发现随着复杂性计算尺度的减小,照片复杂性的增加大于文字复杂性的增加,这一结果表明不同尺度下的复杂性可以作为文字和照片分类的一个特征;对精神分裂症病人和正常人的脑电分析显示,在计算复杂性过程中选用小尺度下二值化方法同传统的二值化方法相比,可以降低误判率。
运动表象分析是脑机接口(BCI)的一个分支,因为脑电是非平稳非线性信号,所以本文采用了一种全新的非平稳、非线性分析方法:希尔伯特—黄变换(HHT)分析运动表象。和其它分解方法不同,HHT的基函数来自数据本身,具有局部性、自适应性并且是数据驱动的。分析结果如下:
在对BCI2005数据Ⅲb的分析过程中,在不同频率下观察到了事件相关去同步化(ERD)和事件相关同步化(ERS)现象。利用时频窗口内的振幅标准差和能量对想象的左手和右手进行分类,一名被试的分类误判率低于10%。发现了一名被试左右脑的不对称现象,在单独利用两个对称电极中的一个进行运动表象分类
Brain is a very complex non-linear system, and electroencephalograph (EEG) and electrocorticogram (ECoG) are also non-stationary and nonlinear in nature, signal processing methods based on linear and stationary assumptions, although has obtained important result, can not grasp the entire picture of neuroscience. Complexity and time-frequency analysis give us chances to analyze EEG by these entirely new methods, in the first part of this paper coarse graining of Lempel-Ziv complexity was analyzed and in the second part Hilbert-Huang transform was used to analyze motor imagery.Lempel-Ziv complexity is a useful method to analyze EEG, but current binary processing might lose some useful information of the original signal. In addition, complexity is different at different scales, and we can derive some useful information by calculating complexity at small scale, so sometimes we need to calculate Lempel-Ziv complexity at different scale. Increasing the number of symbol can decrease the information loss but need more data and time for calculation. In this paper we divide the original signal into more than two parts, "0" and "1" denote decrease and increase respectively. This new binary method can reduce the information loss and calculate Lempel-Ziv complexity at multi-scale but do not increase the number of symbol. The following works testify the validity of this new binary method:We test this method with Logistic map added by sine wave and have a good result when the added sine wave has low frequency; This new approach was also presented for distinguishing textual images from pictorial images and we found that the pictorial images' complexity had more significant increase than the textual images' complexity did when the calculating scale became small. The test shows that multi-scale Lempel-Ziv complexity can be used as an image classification method or as a feature of image classifier; Schizophrenia and normal EEG was classified by
large-scale compleiity and small-seale complexity, the error rate of small-scale complexity is low than large-scale complexity.Motor imagery is a branch of brain computer interface (BCI). As EEG is non-stationary. Hilbert-Huang Transform (HHT), a novel approach for analyzing nonlinear and non-stationary signals, was presented to motor imagery analysis. The basis function of HHT comes from signal itself, the decomposition is local, self-adaptive and data driven. The results are as follows:When BCI2005 data Illb (EEG) was analyzed we observed event-related desynchronization (ERD) and event-related synchronization (ERS) at different frequency. Using standard deviation of amplitude and energy in time-frequency window as a feature to classify imagined left and right hand movement, the error of one subject is lower than 10%.One subject of data Illb has asymmetry phenomena, that is, only one of the two symmetry leads was used to classify two imagined movements, one can get error rate as low as 27.43% while the other get error as high as 37.69%.We use the same feature as used in data Illb to classify imagined tongue and left small finger movement (ECoG BCI2005 data I), the lowest error rate is 16.19% by featuring from one time-frequency window. Using standard deviation of time-frequency window from 7 electrodes, single frequency band and 11 continuous time windows as feature, the error rate can be as low as 11.87%. Compared with energy, the standard deviation of time-frequency window performs better. Surface Laplacian Filter is a good EEG preprocessing method, we use this method to preprocess ECoG but can not reduce error rate, this prompt us that not all method used in EEG can be used to analyze ECoG.
引文
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