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An algorithm for reducing spatially colored noise in evoked response magneto- and electro-encephalography data is presented. The algorithm models the repeatable component of the data, or signal of interest, as the mean, while the noise is modeled as Gaussian with unknown covariance structure. The mean matrix has a low rank structure due to the temporal and spatial structure of the data. Maximum likelihood estimates of the components of the low-rank signal structure are derived in order to estimate the signal component. The effectiveness of this approach is demonstrated using simulated and real MEG data.