Linear minimum mean-square error filtering for evoked responses: Application to fetal MEG

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.