诱发电位潜伏期变化估计方法的研究

【作者】 张金凤；

【导师】 邱天爽；

【作者基本信息】 大连理工大学 ， 信号与信息处理， 2004， 硕士

【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。更多还原

【Abstract】 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.更多还原