一种用于估计时空脑电/脑磁图数据信号子空间的重采样方法。

Nijmegen Institute of Cognition and Information, section of Mathematical Psychology, University of Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, The Netherlands.

IEEE Trans Biomed Eng. 2003 Aug;50(8):935-49. doi: 10.1109/TBME.2003.814293.

Source localization using spatio-temporal electroencephalography (EEG) and magnetoencephalography (MEG) data is usually performed by means of signal subspace methods. The first step of these methods is the estimation of a set of vectors that spans a subspace containing as well as possible the signal of interest. This estimation is usually performed by means of a singular value decomposition (SVD) of the data matrix: The rank of the signal subspace (denoted by r) is estimated from a plot in which the singular values are plotted against their rank order, and the signal subspace itself is estimated by the first r singular vectors. The main problem with this method is that it is strongly affected by spatial covariance in the noise. Therefore, two methods are proposed that are much less affected by this spatial covariance, and old and a new method. The old method involves prewhitening of the data matrix, making use of an estimate of the spatial noise covariance matrix. The new method is based on the matrix product of two average data matrices, resulting from a random partition of a set of stochastically independent replications of the spatio-temporal data matrix. The estimated signal subspace is obtained by first filtering out the asymmetric and negative definite components of this matrix product and then retaining the eigenvectors that correspond to the r largest eigenvalues of this filtered data matrix. The main advantages of the partition-based eigen decomposition over prewhited SVD is that 1) it does not require an estimate of the spatial noise covariance matrix and 2b) that it allows one to make use of a resampling distribution (the so-called partitioning distribution) as a natural quantification of the uncertainty in the estimated rank. The performance of three methods (SVD with and without prewhitening, and the partition-based method) is compared in a simulation study. From this study, it could be concluded that prewhited SVD and the partition-based eigen decomposition perform equally well when the amplitude time series are constant, but that the partition-based method performs better when the amplitude time series are variable.

使用时空脑电图（EEG）和脑磁图（MEG）数据进行源定位通常借助信号子空间方法来完成。这些方法的第一步是估计一组向量，该向量组所跨越的子空间要尽可能包含感兴趣的信号。这种估计通常通过对数据矩阵进行奇异值分解（SVD）来实现：信号子空间的秩（用r表示）是根据奇异值与其秩次的关系图来估计的，而信号子空间本身则由前r个奇异向量来估计。该方法的主要问题在于它受噪声空间协方差的影响很大。因此，提出了两种受这种空间协方差影响小得多的方法，一种是旧方法，一种是新方法。旧方法涉及对数据矩阵进行预白化处理，利用空间噪声协方差矩阵的估计值。新方法基于两个平均数据矩阵的矩阵乘积，这两个平均数据矩阵来自对时空数据矩阵的一组随机独立复制进行的随机划分。估计的信号子空间是通过首先滤除该矩阵乘积的不对称和负定分量，然后保留与该滤波后数据矩阵的r个最大特征值相对应的特征向量而获得的。基于划分的特征分解相对于预白化SVD的主要优点在于：1）它不需要估计空间噪声协方差矩阵；2）它允许使用重采样分布（所谓的划分分布）作为对估计秩不确定性的自然量化。在一项模拟研究中比较了三种方法（有无预白化的SVD以及基于划分的方法）的性能。从这项研究可以得出结论，当幅度时间序列恒定时，预白化SVD和基于划分的特征分解表现相当，但当幅度时间序列可变时，基于划分的方法表现更好。