诱发电位潜伏期变化估计方法的研究
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摘要
诱发电位(EP)中包含了丰富的有关神经系统传导通路上各个部位的信息，特别是潜伏期及其变化(延迟)表示了神经系统的传导及延迟，从而反映了神经系统的状态和变化。因此，检测这种潜伏期及其变化，对于诊断神经系统的损伤和病变具有十分重要的意义。
本课题属于时间延迟估计的范畴。传统的EP信号潜伏期变化检测算法主要包括基于相关的方法和基于自适应的方法。在这些算法中，带噪EP信号及EP信号中存在的EEG等加性噪声被假定为服从高斯分布。然而，分析和实验表明，采用分数低阶α稳定分布模型描述带噪EP信号及其EEG等加性噪声比常规的高斯分布模型具有更好的适应性。由于分数低阶α稳定分布信号不存在有限的二阶矩，因此这些传统的基于二阶矩有限的潜伏期变化检测算法都出现了很大程度的性能退化。
本文详细阐述了α稳定分布模型和时间延迟估计的基本理论知识，并着重分析了基于不同噪声分布模型假定下的EP信号潜伏期变化检测算法。在此基础上，通过对误差函数取绝对值后进行对数的变换，将原本不存在二阶矩的分数低阶α稳定分布噪声变换到二阶矩有限的范围，并借鉴DLMP(直接最小p均值)算法的思想，本文提出了一种新的低阶α稳定分布噪声下EP信号潜伏期变化检测算法—LOG算法。新算法相对已有算法具有
(1)无需预知噪声信号的α值；
(2)扩展现有算法的适用范围，适用于伴随噪声为0＜α≤2稳定分布的场合。两个显著优点。模拟实验数据结果表明，新算法无论在收敛速度上或是在估计结果上均具有相对现有算法更好的韧性。本文还从理论上初步给出了算法的收敛性证明。
DLMP算法作为一种在高斯噪声环境和分数低阶α稳定分布噪声环境下均具有良好韧性的EP信号潜伏期变化检测算法。本文基于分数低阶统计量的原理，根据确定性平均方法，结合文中给出并证明的两个引理，对DLMP算法的估计结果的无偏性进行了理论分析和证明。结果表明，若EP潜伏期变化为EP信号采样间隔的整数倍，则DLMP算法对这种变化的估计是无偏估计。若整数倍的条件不满足，则DLMP算法的估计偏差不大于半个采样间隔。
Evoked potentials (EPs) carry abundant information about neural conduction pathways. Especially, the EP latency and the latency changes (delays) indicate the actual conduction and delay of the neurological system. Since changes in EP latency reflect the state and variations of the neurological system, the detection and quantification of latency changes contribute to the detection and identification of neurological system injuries.
Previous studies show that adopting fractional lower order a stable distribution model to describe noise contaminated EP signals and underlying EEG noises has a more appropriate adaptation property than the traditional Gaussian distribution model. Through implementing a log transform to the absolute value of the error function, the fractional lower order a stable distribution noise signal with infinite second order moments are transformed to the situation with finite variances. Using DLMP(direct least mean p-norm) algorithm for reference, this thesis proposed a new EP latency change estimation algorithm under fractional lower order a stable noise conditions. Comparing with the existing estimating methods, the new algorithm have the two following remarkable advantages:
(1) The new algorithm needs not estimate the characteristic exponent (α) of the underlying noises in advance.
(2) The new algorithm spans the adaptation range of the existing algorithms. It can be applied to the case of 0 < α 2.
Simulation results demonstrate that the new algorithm has an improved performance and robustness over the existing algorithms not only in convergence speed but also in estimation accuracy. This thesis also proves the convergence property of the new algorithm.
The DLMP algorithm is a robust algorithm for estimating the latency changes of EP signals under both Guassian and fractional lower order a stable noise conditions. Based on the fractional lower order statistics theory, the deterministic averaging method and two lemmas introduced and proved, this thesis gives an analysis of the convergence property of the DLMP algorithm in theory. The results of the analysis indicate that, if the EP latency change is an integer multiple of the sampling interval, the DLMP algorithm gives an unbiased estimate of the latency change; otherwise, the algorithm yields an estimate which differs from the true latency change by at most half of a sampling interval.
本课题属于时间延迟估计的范畴。传统的EP信号潜伏期变化检测算法主要包括基于相关的方法和基于自适应的方法。在这些算法中，带噪EP信号及EP信号中存在的EEG等加性噪声被假定为服从高斯分布。然而，分析和实验表明，采用分数低阶α稳定分布模型描述带噪EP信号及其EEG等加性噪声比常规的高斯分布模型具有更好的适应性。由于分数低阶α稳定分布信号不存在有限的二阶矩，因此这些传统的基于二阶矩有限的潜伏期变化检测算法都出现了很大程度的性能退化。
本文详细阐述了α稳定分布模型和时间延迟估计的基本理论知识，并着重分析了基于不同噪声分布模型假定下的EP信号潜伏期变化检测算法。在此基础上，通过对误差函数取绝对值后进行对数的变换，将原本不存在二阶矩的分数低阶α稳定分布噪声变换到二阶矩有限的范围，并借鉴DLMP(直接最小p均值)算法的思想，本文提出了一种新的低阶α稳定分布噪声下EP信号潜伏期变化检测算法—LOG算法。新算法相对已有算法具有
(1)无需预知噪声信号的α值；
(2)扩展现有算法的适用范围，适用于伴随噪声为0＜α≤2稳定分布的场合。两个显著优点。模拟实验数据结果表明，新算法无论在收敛速度上或是在估计结果上均具有相对现有算法更好的韧性。本文还从理论上初步给出了算法的收敛性证明。
DLMP算法作为一种在高斯噪声环境和分数低阶α稳定分布噪声环境下均具有良好韧性的EP信号潜伏期变化检测算法。本文基于分数低阶统计量的原理，根据确定性平均方法，结合文中给出并证明的两个引理，对DLMP算法的估计结果的无偏性进行了理论分析和证明。结果表明，若EP潜伏期变化为EP信号采样间隔的整数倍，则DLMP算法对这种变化的估计是无偏估计。若整数倍的条件不满足，则DLMP算法的估计偏差不大于半个采样间隔。
Evoked potentials (EPs) carry abundant information about neural conduction pathways. Especially, the EP latency and the latency changes (delays) indicate the actual conduction and delay of the neurological system. Since changes in EP latency reflect the state and variations of the neurological system, the detection and quantification of latency changes contribute to the detection and identification of neurological system injuries.
Previous studies show that adopting fractional lower order a stable distribution model to describe noise contaminated EP signals and underlying EEG noises has a more appropriate adaptation property than the traditional Gaussian distribution model. Through implementing a log transform to the absolute value of the error function, the fractional lower order a stable distribution noise signal with infinite second order moments are transformed to the situation with finite variances. Using DLMP(direct least mean p-norm) algorithm for reference, this thesis proposed a new EP latency change estimation algorithm under fractional lower order a stable noise conditions. Comparing with the existing estimating methods, the new algorithm have the two following remarkable advantages:
(1) The new algorithm needs not estimate the characteristic exponent (α) of the underlying noises in advance.
(2) The new algorithm spans the adaptation range of the existing algorithms. It can be applied to the case of 0 < α 2.
Simulation results demonstrate that the new algorithm has an improved performance and robustness over the existing algorithms not only in convergence speed but also in estimation accuracy. This thesis also proves the convergence property of the new algorithm.
The DLMP algorithm is a robust algorithm for estimating the latency changes of EP signals under both Guassian and fractional lower order a stable noise conditions. Based on the fractional lower order statistics theory, the deterministic averaging method and two lemmas introduced and proved, this thesis gives an analysis of the convergence property of the DLMP algorithm in theory. The results of the analysis indicate that, if the EP latency change is an integer multiple of the sampling interval, the DLMP algorithm gives an unbiased estimate of the latency change; otherwise, the algorithm yields an estimate which differs from the true latency change by at most half of a sampling interval.
引文
[1] B Grundy, R Heros, A Tung, et al. Intraoperative hypoxia detected by evoked potential monitoring. Anasth. Analg. 1981, Vol 60, pp:437-439
[2] S Xu, H Wagner, F Joo, et al. Reduced latency of the visual evoked cortical response following cryogenic injury to cerebral cortex-A neuroexcitatory phenomenon. Neurological Res. 1992, Vol 14, pp:233-235
[3] 王士雷，庄心良。麻醉深度检测技术—AEPindex。2003年上海市医学会麻醉学学术年会，中国，上海
[4] 洪波，唐庆玉，杨福生等，ICA在视觉诱发电位的少次提取与波性分析中的应用。中国生物医学工程学报，2000，Vol 19(3)
[5] CA Vaz, NV Thakor. Adaptive fourier estimation of time varying potentials. IEEE Tram, Biomed, Eng, 1989, Vol, 36, pp:448-455
[6] Karjalainen, A Pasi. Regularization and Bayesian methods for evoked potential estimation. Kuopio university publications C. Natural and environmental sciences 1997
[7] 李汀滢，姚凯，宋策。关于视觉诱发电位提取方法的探讨。佳木斯工学院学报，1997，Vol 9，pp：254-257
[8] A Bezedanos, N Laskaris, S Fotopoulos, et al. Data dependent weighted averages for recording of evoked potential signals. Electroencephalography and clinical Neurophysiology, 1995, Vol 96, pp:468-471
[9] XH Yu, ZY He, YS Zhang. Time-Varying adaptive filters for evoked potential estimation. IEEE transactions on biomedical engineering, 1994, Vol 41 (11), pp: 1062-1071
[10] DS Ruchkin, J Villegas, ER John. An analysis of average evoked potentials making use of least mean square techniques. Annals of new york academy of science, 1964, Vol 115, pp:799-821
[11] KB Yu, CD McGillem. Optimum filters for estimating evoked potential waveforms. IEEE Transactions on biomedical engineering, 1983, Vol 30(11), pp:730-737
[12] PA Karjalaimen, JP Kaipio, AS Koistinen. PCA based Bayesian estimation of single trial evoked potentials, in Proc 1st int conf bielectormagn, 1996, pp:195-196
[13] NV Thakor, CA Vaz, RW McPherson, et al. Adaptive fourier series modeling of time-varying evoked potentials: study of human somatosensory evoked response to etomidate anesthetic. Electroencephalography and clinical neurophysiology, 1991, Vol 80, pp: 108-118
[14] JA Sgro, RG. Emerson, TA Pedley. Real-time reconstruction of evoked potentials using a new two-dimensional filter method. Electroencephalography and clinical neurophysiology. 1985, Vol 62, pp:372-380
[15] X Kong, TS Qiu. Adaptive estimation of latency change in evoked potentials by direct least mean p-norm time-delay estimation. IEEE transactions on biomedical engineering, 1999, Vol 46(8), pp:994-1003
[16] CL Nikias, M Shao. Signal processing with alpha-stable distributions. 1995, New York:Wiley
[17] X Kong, NV Thakor. Adaptive estimation of latency changed in evoked potentials. IEEE transactions
on biomedical engineering. 1996, Vol 43(2)
[18] X Kong, T Qiu. Latency change estimation for evoked potentials: a comparison of algorithms. Medical & Biological Engineering & Computing. 2001, Vol 39, pp:208-223
[19] T Qiu, H. Wang, Y. Zhang, et al. Non-linear transform-based robust adaptive latency change estimation of evoked potentials, 2002, Methods infMed, Vol 4
[20] M Bouvet, SC Schwartz. Comparison of adaptive and robust receivers for signal detection in ambient underwater noise. IEEE trans. Acoust. Speech. Signal processing, 1989, Vol 37, pp:621-626
[21] P Levy. Calul des probabilities. 1925, Paris: Gauthier-Villars
[22] BW Stuck. Minimum error dispersion linear filtering of scalar symmetric stable processes. IEEE trans. Automat. Contr, 1978, Vol 23(3), pp:507-509
[23] L Breiman. Probability. 1968, Reading, MA:Addison-Wesley
[24] WH DuMouchel. Stable distributions in statistical inference. 1971, ph.D dissertation, Department of Statistics, Yale University
[25] JH McCulloch. Simple consistent estimators of stable distribution parameters. Commun. Statist. Simula, 1986, Vol 15(4), pp:1109-1136
[26] EF Fama, R Roll. Parameter estimates for symmetric stable distributions. J. Amer. Statist. Assoc, 1971, Vol 66, pp:331-338
[27] IA Koutrouvelis. Regression-Type estimation of the parameters of stable laws. J. Amer. Statist. Assoc, 1980, Vol 75, pp:915-928
[28] CH Knapp, GC Carter. The generalized correlation forestimation of time delay. IEEE Trans on ASSP, 1976, Vol 24(3), pp:320-327
[29] 王宏禹，邱天爽。自适应噪声抵消与时间延迟估计，大连理工大学出版社，1998
[30] DH Youn, N Ahmed, GC Carter. On using the LMS algorithm for time delay estimation. IEEE Trans on ASSP, 1982, Vol 30(5), pp:795-801
[31] B Widrow, et al. Adaptive noise canceling: principles and applications. Proc IEEE, 1975, Vol 63(12), pp:1692-1716
[32] DM Etter, SD Steam. Adaptive estimation of time delay in sampled system. IEEE trans on acoustics, speech, signal processing. 1981, Vol 29, pp:582-587
[33] M Xinyu, CL Nikas. Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE transactions on signal processing. 1996, Vol 44(11), pp:2669-2687
[34] 邱天爽，王宏禹等．α稳定分布噪声下诱发电位潜伏期变化的自适应检测．国外医学生物医学工程分册，2001，Vol 24(4)，pp：174-178
[35] 邱天爽，X Kong，鲍海平等。一种基于脑电信号分析的中枢神经系统损伤检测的韧性自适应方法。中国生物医学工程学报，2003，Vol．22，pp：23-30
[36] 邱天爽，孔轩等。非高斯分布噪声下诱发电位潜伏期变化自适应检测。大连理工大学学报，2002，Vol 42(3)，pp：371-375
[2] S Xu, H Wagner, F Joo, et al. Reduced latency of the visual evoked cortical response following cryogenic injury to cerebral cortex-A neuroexcitatory phenomenon. Neurological Res. 1992, Vol 14, pp:233-235
[3] 王士雷，庄心良。麻醉深度检测技术—AEPindex。2003年上海市医学会麻醉学学术年会，中国，上海
[4] 洪波，唐庆玉，杨福生等，ICA在视觉诱发电位的少次提取与波性分析中的应用。中国生物医学工程学报，2000，Vol 19(3)
[5] CA Vaz, NV Thakor. Adaptive fourier estimation of time varying potentials. IEEE Tram, Biomed, Eng, 1989, Vol, 36, pp:448-455
[6] Karjalainen, A Pasi. Regularization and Bayesian methods for evoked potential estimation. Kuopio university publications C. Natural and environmental sciences 1997
[7] 李汀滢，姚凯，宋策。关于视觉诱发电位提取方法的探讨。佳木斯工学院学报，1997，Vol 9，pp：254-257
[8] A Bezedanos, N Laskaris, S Fotopoulos, et al. Data dependent weighted averages for recording of evoked potential signals. Electroencephalography and clinical Neurophysiology, 1995, Vol 96, pp:468-471
[9] XH Yu, ZY He, YS Zhang. Time-Varying adaptive filters for evoked potential estimation. IEEE transactions on biomedical engineering, 1994, Vol 41 (11), pp: 1062-1071
[10] DS Ruchkin, J Villegas, ER John. An analysis of average evoked potentials making use of least mean square techniques. Annals of new york academy of science, 1964, Vol 115, pp:799-821
[11] KB Yu, CD McGillem. Optimum filters for estimating evoked potential waveforms. IEEE Transactions on biomedical engineering, 1983, Vol 30(11), pp:730-737
[12] PA Karjalaimen, JP Kaipio, AS Koistinen. PCA based Bayesian estimation of single trial evoked potentials, in Proc 1st int conf bielectormagn, 1996, pp:195-196
[13] NV Thakor, CA Vaz, RW McPherson, et al. Adaptive fourier series modeling of time-varying evoked potentials: study of human somatosensory evoked response to etomidate anesthetic. Electroencephalography and clinical neurophysiology, 1991, Vol 80, pp: 108-118
[14] JA Sgro, RG. Emerson, TA Pedley. Real-time reconstruction of evoked potentials using a new two-dimensional filter method. Electroencephalography and clinical neurophysiology. 1985, Vol 62, pp:372-380
[15] X Kong, TS Qiu. Adaptive estimation of latency change in evoked potentials by direct least mean p-norm time-delay estimation. IEEE transactions on biomedical engineering, 1999, Vol 46(8), pp:994-1003
[16] CL Nikias, M Shao. Signal processing with alpha-stable distributions. 1995, New York:Wiley
[17] X Kong, NV Thakor. Adaptive estimation of latency changed in evoked potentials. IEEE transactions
on biomedical engineering. 1996, Vol 43(2)
[18] X Kong, T Qiu. Latency change estimation for evoked potentials: a comparison of algorithms. Medical & Biological Engineering & Computing. 2001, Vol 39, pp:208-223
[19] T Qiu, H. Wang, Y. Zhang, et al. Non-linear transform-based robust adaptive latency change estimation of evoked potentials, 2002, Methods infMed, Vol 4
[20] M Bouvet, SC Schwartz. Comparison of adaptive and robust receivers for signal detection in ambient underwater noise. IEEE trans. Acoust. Speech. Signal processing, 1989, Vol 37, pp:621-626
[21] P Levy. Calul des probabilities. 1925, Paris: Gauthier-Villars
[22] BW Stuck. Minimum error dispersion linear filtering of scalar symmetric stable processes. IEEE trans. Automat. Contr, 1978, Vol 23(3), pp:507-509
[23] L Breiman. Probability. 1968, Reading, MA:Addison-Wesley
[24] WH DuMouchel. Stable distributions in statistical inference. 1971, ph.D dissertation, Department of Statistics, Yale University
[25] JH McCulloch. Simple consistent estimators of stable distribution parameters. Commun. Statist. Simula, 1986, Vol 15(4), pp:1109-1136
[26] EF Fama, R Roll. Parameter estimates for symmetric stable distributions. J. Amer. Statist. Assoc, 1971, Vol 66, pp:331-338
[27] IA Koutrouvelis. Regression-Type estimation of the parameters of stable laws. J. Amer. Statist. Assoc, 1980, Vol 75, pp:915-928
[28] CH Knapp, GC Carter. The generalized correlation forestimation of time delay. IEEE Trans on ASSP, 1976, Vol 24(3), pp:320-327
[29] 王宏禹，邱天爽。自适应噪声抵消与时间延迟估计，大连理工大学出版社，1998
[30] DH Youn, N Ahmed, GC Carter. On using the LMS algorithm for time delay estimation. IEEE Trans on ASSP, 1982, Vol 30(5), pp:795-801
[31] B Widrow, et al. Adaptive noise canceling: principles and applications. Proc IEEE, 1975, Vol 63(12), pp:1692-1716
[32] DM Etter, SD Steam. Adaptive estimation of time delay in sampled system. IEEE trans on acoustics, speech, signal processing. 1981, Vol 29, pp:582-587
[33] M Xinyu, CL Nikas. Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE transactions on signal processing. 1996, Vol 44(11), pp:2669-2687
[34] 邱天爽，王宏禹等．α稳定分布噪声下诱发电位潜伏期变化的自适应检测．国外医学生物医学工程分册，2001，Vol 24(4)，pp：174-178
[35] 邱天爽，X Kong，鲍海平等。一种基于脑电信号分析的中枢神经系统损伤检测的韧性自适应方法。中国生物医学工程学报，2003，Vol．22，pp：23-30
[36] 邱天爽，孔轩等。非高斯分布噪声下诱发电位潜伏期变化自适应检测。大连理工大学学报，2002，Vol 42(3)，pp：371-375
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