Chen Mingli, Van Veen Barry D, Wakai Ronald T
Department of Medical Physics, University of Wisconsin-Madison, Madison, WI 53706, USA.
IEEE Trans Biomed Eng. 2006 May;53(5):959-63. doi: 10.1109/TBME.2006.872822.
This paper describes a linear minimum mean-squared error (LMMSE) approach for designing spatial filters that improve the signal-to-noise ratio (SNR) of multiepoch evoked response data. This approach does not rely on availability of a forward solution and thus is applicable to problems in which a forward solution is not readily available, such as fetal magnetoencephalography (fMEG). The LMMSE criterion leads to a spatial filter that is a function of the autocorrelation matrix of the data and the autocorrelation matrix of the signal. The signal statistics are unknown, so we approximate the signal autocorrelation matrix using the average of the data across epochs. This approximation is reasonable provided the mean of the noise is zero across epochs and the signal mean is significant. An analysis of the error incurred using this approximation is presented. Calculations of SNR for the exact and approximate LMMSE filters and simple averaging for the rank-1 signal case are shown. The effectiveness of the method is demonstrated with simulated evoked response data and fetal MEG data.
本文描述了一种用于设计空间滤波器的线性最小均方误差（LMMSE）方法，该方法可提高多段诱发反应数据的信噪比（SNR）。此方法不依赖于正向解的可用性，因此适用于正向解不易获得的问题，如胎儿脑磁图（fMEG）。LMMSE准则产生的空间滤波器是数据自相关矩阵和信号自相关矩阵的函数。由于信号统计量未知，我们使用各段数据的平均值来近似信号自相关矩阵。只要各段噪声的均值为零且信号均值显著，这种近似就是合理的。本文给出了使用这种近似所产生误差的分析。展示了精确和近似LMMSE滤波器的SNR计算以及秩为1信号情况下的简单平均。该方法的有效性通过模拟诱发反应数据和胎儿MEG数据得到了验证。
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