基于卡尔曼滤波的脑电信号去噪方法研究
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摘要
脑机接口BCI是一种新的实现人与外部环境进行通讯的人机交互系统，它不依赖于人体固有的神经和肌肉，只需要利用大脑意识就可以实现与外界的信息交流。脑电信号的特征提取、模式分类是脑机接口研究中的热点问题，但是对脑电信号的去噪预处理也是研究中必不可少的部分。本文运用卡尔曼滤波方法对脑电信号进行去噪处理。
首先，针对脑电信号中存在工频干扰的情况，研究了使用卡尔曼滤波方法来消除工频干扰。在文中将工频干扰当成正弦信号来处理，通过正弦信号的和差化积等变化关系建立了卡尔曼滤波模型，从而得到了其运算过程中所需的参数。针对正弦信号变频、变相、变幅值的情况进行了实验，估计了正弦叠加信号的每个分频率的值。然后又针对标准的脑电信号和实际脑电信号进行了实验，实验结果表明，此方法很好的去除了工频干扰。
其次，针对脑电信号中受到多种干扰如眨眼、心电、肌电等的问题，实现了一种卡尔曼滤波模型和模型参数估计的方法，仿真实验所用的数据是公开的脑机接口竞赛实验数据(BCI Competition III dataset I)。实验结果表明通过本方法去噪预处理后，分类正确率有了很大的提高，且优于小波去噪与谱减法等预处理方法。
最后，对扩展卡尔曼滤波方法进行了研究，以正弦信号为例来进行仿真实验。通过非线性计算得到正弦信号与其观测值，对观测值进行扩展卡尔曼滤波。实验结果表明，该方法很好的还原了原信号。
A brain computer interface (BCI) is a new man-machine interactive communicationsystem which can realize communication between people and external environment. Itdoes not pass through the human body inherent nerves and muscles, only need to usebrain consciousness to achieve information exchange with the outside world. Featureextraction, pattern classification of EEG is a hot issue in the study of brain-computerinterface, but EEG de-noising preprocessing is an essential part of the research. In thispaper, we use the kalman filtering method for EEG de-noising.
First of all, a method of using kalman filter to eliminate power line interference isresearched to solve the problems of power line interference which is included in the EEG.Power line interference in the text will be dealt with as a sinusoidal signal. Kalman filtermodel is established through variation relationship of the sinusoidal signal, and get therequired parameters which is need in the course of its operation process. We deal with theconversion of frequency、phase and amplitude sinusoidal signal on the experiment, andestimate value of each sub-frequency in sine superimposed signal. And then experimentsabout standard EEG and actual EEG were carried out. Experimental results show that thismethod is good to wipe off power line interference.
Secondly, for the issues that EEG is affected by a variety of interference such aseyeblink、cardiac electric activity and myoelectric activity etc, we achieved a method ofkalman filter modeling and model parameter estimation. The open brain ComputerInterface Competition experimental data (BCI Competition III dataset I) is used in theexperiment. The experimental results show that after the de-noising pretreatment of thismethod, Classification accuracy has been greatly improved and is better than thepretreatment method of wavelet de-noising and spectral subtraction etc.
Finally, the extended kalman filtering method is discussed. We use a sine signal inthe simulation experiment. We get sine signal and its observation through the nonlinearcalculated, and carry through extended kalman filter to the observations. Experimentalresults show that this method is good to restore the original signal.
首先，针对脑电信号中存在工频干扰的情况，研究了使用卡尔曼滤波方法来消除工频干扰。在文中将工频干扰当成正弦信号来处理，通过正弦信号的和差化积等变化关系建立了卡尔曼滤波模型，从而得到了其运算过程中所需的参数。针对正弦信号变频、变相、变幅值的情况进行了实验，估计了正弦叠加信号的每个分频率的值。然后又针对标准的脑电信号和实际脑电信号进行了实验，实验结果表明，此方法很好的去除了工频干扰。
其次，针对脑电信号中受到多种干扰如眨眼、心电、肌电等的问题，实现了一种卡尔曼滤波模型和模型参数估计的方法，仿真实验所用的数据是公开的脑机接口竞赛实验数据(BCI Competition III dataset I)。实验结果表明通过本方法去噪预处理后，分类正确率有了很大的提高，且优于小波去噪与谱减法等预处理方法。
最后，对扩展卡尔曼滤波方法进行了研究，以正弦信号为例来进行仿真实验。通过非线性计算得到正弦信号与其观测值，对观测值进行扩展卡尔曼滤波。实验结果表明，该方法很好的还原了原信号。
A brain computer interface (BCI) is a new man-machine interactive communicationsystem which can realize communication between people and external environment. Itdoes not pass through the human body inherent nerves and muscles, only need to usebrain consciousness to achieve information exchange with the outside world. Featureextraction, pattern classification of EEG is a hot issue in the study of brain-computerinterface, but EEG de-noising preprocessing is an essential part of the research. In thispaper, we use the kalman filtering method for EEG de-noising.
First of all, a method of using kalman filter to eliminate power line interference isresearched to solve the problems of power line interference which is included in the EEG.Power line interference in the text will be dealt with as a sinusoidal signal. Kalman filtermodel is established through variation relationship of the sinusoidal signal, and get therequired parameters which is need in the course of its operation process. We deal with theconversion of frequency、phase and amplitude sinusoidal signal on the experiment, andestimate value of each sub-frequency in sine superimposed signal. And then experimentsabout standard EEG and actual EEG were carried out. Experimental results show that thismethod is good to wipe off power line interference.
Secondly, for the issues that EEG is affected by a variety of interference such aseyeblink、cardiac electric activity and myoelectric activity etc, we achieved a method ofkalman filter modeling and model parameter estimation. The open brain ComputerInterface Competition experimental data (BCI Competition III dataset I) is used in theexperiment. The experimental results show that after the de-noising pretreatment of thismethod, Classification accuracy has been greatly improved and is better than thepretreatment method of wavelet de-noising and spectral subtraction etc.
Finally, the extended kalman filtering method is discussed. We use a sine signal inthe simulation experiment. We get sine signal and its observation through the nonlinearcalculated, and carry through extended kalman filter to the observations. Experimentalresults show that this method is good to restore the original signal.
引文
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[2]侯建华,田金文,柳建.一种迭代小波域维纳滤波算法[J].华中科技大学学报(自然科学版).2006, 34(4): 24-26
[3] Simon Doclo, Ann Spriet, Jan Wouters, et al. Frequency-Domain Criterion for the SpeechDistortion Weighted Multichannel Wiener Filter for Robust Noise Reduction[J]. SpeechCommunication, 2007, 49(7): 636-640.
[4] Kalman R E. A New Approach to Linear Filtering and Prediction Problems[J]. Transactions ofthe ASME Journal of Basic Engineering, 1960, 82(D): 35-45.
[5]权太范.目标跟踪新理论与技术[M].北京:国防工业出版社, 2009: 17-26.
[6]柴霖,袁建平,罗建军,等.非线性估计理论的最新进展[J].宇航学报. 2005, 26(3):380-384.
[7]丁美玉,阔永红,高新波.数字信号处理[M].第二版.西安:西安电子西科技大学出版社,2001: 10-12.
[8] Karl Spingarn, Brendan H.Robinson. Attitude Determination with UD Implementation ofDecoupled Bias Estimation[J]. IEEE Transactions on Aerospace and Electronic Systems. 2007,43(4): 1294-1304.
[9]张丽艳,殷福亮.一种改进的奇异值分解语音增强方法[J].电子与信息学报, 2008, 30(2):357-361.
[10] Lerro D, Bar-Shalom Y. Tracking with Debiased Consistent Converted Measurements VersusEKF [J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 1015-1022.
[11] Song Weon-Keun, Kim Seung-Eock. Analysis of the Overall Collapse Mechanism ofCable-Stayed Bridges with Different Cable Layouts[J]. Engineering Structures, 2007, 29(9):2133-2142.
[12] Cristian Perea, Julian Alcala, Victor Yepes, et al. Design of Reinforced Concrete Bridge Framesby Heuristic Optimization[J]. Advances in Engineering Software, 2008, 39(8): 676-688.
[13] Julier S J, Uhlmann J K, Durrant-Whyte H F. A New Method for the Nonlinear Transformation ofMeans and Covariances in Filters and Estimators[J]. IEEE Transactions on Automatic Control,2000, 45(3): 477-482.
[14] Julier S J, Uhlmann J K. The Scaled Unscented Transformation[C]. In Proc. Amer. Control Conf,2002: 4555-4559.
[15] Julier S J, Uhlmann J K. Unscented Filtering and Nonlinear Estimation[J]. Proceedings of theIEEE, 2004, 92(3): 401-422.
[16]程水英.无味变换与无味卡尔曼滤波[J].计算机工程与应用, 2008, 44(24): 25-35.
[17] Ienkaran Arasaratnam, Simon Haykin. Cubature Kalman Filters[J]. IEEE Transactions onAutomatic Control, 2009, 54(6): 1254-1269.
[18]穆静,蔡远利.迭代容积卡尔曼滤波算法及其应用[J].系统工程与电子技术, 2011, 33(7):1454-1457.
[19] Gustafsson F, Gunnarsson F, Bergman N, et al. Particle Filters for Positioning, Navigation andTracking [J]. IEEE Transactions on Signal Processing, 2002, 50(2): 425-437.
[20] De-Freitas J F G, Niranjan M, Gee A H, et al. Sequential Monte Carlo Methods to Train NeuralNetwork Models[J]. Neural Computation, 2000, 12(4): 955-993.
[21] Cappe O, Godsill S J, Moulines E. An Overview Existing Methods and Recent Advances inSequential Monte Carlo[J]. Proceedings of the IEEE, 2007, 95(5): 899-924.
[22]付梦印,邓忠红,张继伟. Kalman滤波理论及其在导航系统中的应用[M].北京:科学出版社, 2003: 5-11.
[23]张仁龙,马文丽,姚文娟,等.基于小波包变换对脑电信号的分析和处理[J].电子测量技术,2007, 30(3): 22-24.
[24]金盟涛,邹俊忠,王行愚,等.一种新的基于小波变换的EEG视觉伪信号修正方法[J].华东理工大学学报(自然科学版), 2007, 32(11): 1331-1336.
[25]万柏坤,朱欣,杨春梅,等. ICA去除EEG中眼动伪差和工频干扰方法研究[J].电子技术,2003, 31(10): 1571-1574.
[26] Li Zheng, Joseph E.O Doherty, Timothy L Hanson, et al. Unscented Kalman Filter forBrain-Machine Interfaces[J]. Public Library of Science One, 2009, 4(7): 6243-6261.
[27]西蒙赫金.自适应滤波器原理[M].北京:电子工业出版社, 2010: 367~368.
[28]蒋恩松,李孟超,孙刘杰.一种基于神经网络的卡尔曼滤波改进方法[J].电子与信息学报,2007, 29(9): 2073~2076.
[29] R Kazemi, Farsi A, Ghaed M H, et al. Detection and Extraction of Periodic Noises in Audio andBiomedical Signals Using Kalman Filter[J]. Signal Processing, 2008, 88(1): 2114-2121.
[30] Teixeira O S, Chandrasekar J, et al. State Estimation for Linearand Nonlinear EqualityConstrained Systems [J]. International Journal of Control, 2009, 82(5): 918- 936.
[31]文传博,王致杰,焦斌.一类带有等式约束的动态系统的滤波方法[J].电子学报, 2011,39(3A): 110-114
[32]胡晓,魏薇,刘长红,等.基于正弦参数估计的工频干扰消除算法[J].生物医学工程学杂志,2010, 27(6): 1243-1246.
[33]胡瑜,陈涛.抑制心电中工频干扰的数字滤波方法[J].电子测量技术, 2011, 34(8): 22-26.
[34] Oikonomou V P, Tzallas A T, Fotiadis D I. A Kalman Filter Based Methodology for EEG SpikeEnhancement [J]. Computer Methods and Programs in Biomedicine, 2007, 8(5): 101-108.
[35] Yubo Wang, Jung Eun Lim, Bo Hyeok Seo, et al. Estimation of EEG during Voluntary Movementby Using Kalman Smoother Based BMFLC[C]. (iCBBE) 2011 5th International Conference onBioinformatics and Biomedical Engineering, 2011: 1-4.
[36] Ienkaran Arasaratnam, Simon Haykin. Cubature Kalman Filters[J]. IEEE Transactions onAutomatic Control, 2009, 54(6): 1254-1269.
[37] Tarvainen M, Hiltunen J, Ranta-aho P, et al. Estimation of Nonstationary EEG with KalmanSmoother Approach: An Application to Event-Related Synchronization (ERS)[J]. IEEETransactions on Biomedical Engineering, 2004, 51(3): 516–524.
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