Abstract: Evoked response data in electroencephalography (EEG) has typically very low signal-to-noise ratio, the presence and character of the response to a stimulus is often obscured by background noise. Detecting a weak signal of interest on a cluttered background is a problem that arises also e.g. in radar signal processing. We present a maximum-likelihood based algorithm for reducing the effects of spatially colored noise in evoked response EEG data. Similar signal and noise models have been used in radar detection problem.