A mathematical approach to the temporal stationarity of background noise in MEG/EEG measurements
A mathematical approach to the temporal stationarity of background noise in MEG/EEG measurements
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DOI：
10.1016/s1053-8119(03)00215-5
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发表时间：
2003-09-01
期刊：
影响因子：
5.7
通讯作者：
Heethaar, RM
中科院分区：
文献类型：
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作者：
Bijma, F;de Munck, JC;Heethaar, RM
MEG/EEG信号中背景噪声的一般时空协方差矩阵是巨大的。为了降低这个矩阵的维数，它被建模为空间和时间协方差矩阵的克罗内克积。当时间样本的数量大于例如J = 500时，这两个矩阵的迭代最大似然估计仍然太耗时而不能在常规基础上使用。在这项研究中，我们寻找方法来规避这个计算昂贵的过程中使用的参数模型与受试者相关的参数。这样的模型还有助于解释MEG/EEG信号。对于空间协方差，已经推导出模型，并且已经表明，测量的MEG/EEG信号可以在空间上被理解为由随机偶极子产生的随机过程。然而，时间协方差还没有被建模，因此我们研究了几个主题的时间协方差矩阵。对于所有受试者的时间协方差，显示出α振荡和消失的大时滞。这就产生了一个由两个组成部分组成的时间噪声模型：α活动和额外的随机噪声。α活动被建模为具有随机相位的随机发生的波，并且附加噪声的协方差随滞后呈指数下降。该模型只需要六个参数，而不是1/2 J（J + 1）。理论上，该模型是平稳的，但在实践中，矩阵的平稳性受到基线校正的高度影响。当适当考虑基线校正窗口时，数据和参数模型之间的一致性似乎非常好。这一发现意味着，背景噪声在原则上是一个平稳的过程和非平稳性主要是由预处理方法的性质。当在刺激之后以固定样本分析事件时（例如，SEF N20响应），可以通过优化基线窗口来利用这种非平稳性，以在该特定样本处获得低噪声方差。(C)2003 Elsevier Science（美国）。All rights reserved.
The general spatiotemporal covariance matrix of the background noise in MEG/EEG signals is huge. To reduce the dimensionality of this matrix it is modeled as a Kronecker product of a spatial and a temporal covariance matrix. When the number of time samples is larger than, say, J = 500, the iterative Maximum Likelihood estimation of these two matrices is still too time-consuming to be useful on a routine basis. In this study we looked for methods to circumvent this computationally expensive procedure by using a parametric model with subject-dependent parameters. Such a model would additionally help with interpreting MEG/EEG signals. For the spatial covariance, models have been derived already and it has been shown that measured MEG/EEG signals can be understood spatially as random processes, generated by random dipoles. The temporal covariance, however, has not been modeled yet, therefore we studied the temporal covariance matrix in several subjects. For all subjects the temporal covariance, shows an alpha oscillation and vanishes for large time lag. This gives rise to a temporal noise model consisting of two components: alpha activity and additional random noise. The alpha activity is modeled as randomly occurring waves with random phase and the covariance of the additional noise decreases exponentially with lag. This model requires only six parameters instead of 1/2J(J + 1). Theoretically, this model is stationary but in practice the stationarity of the matrix is highly influenced by the baseline correction. It appears that very good agreement between the data and the parametric model can be obtained when the baseline correction window is taken into account properly. This finding implies that the background noise is in principle a stationary process and that nonstationarities are mainly caused by the nature of the preprocessing method. When analyzing events at a fixed sample after the stimulus (e.g., the SEF N20 response) one can take advantage of this nonstationarity by optimizing the baseline window to obtain a low noise variance at this particular sample. (C) 2003 Elsevier Science (USA). All rights reserved.