Optimum Multielectrode A Posteriori Estimates of Single-Response Evoked Potentials

This paper discusses the design and performance of an optimum linear multielectrode filter for estimating the evoked potential contained in a single scalp-recorded brain response to a visual stimulus. The filter is derived under the criterion of minimum mean-square error and is time varying to allow for the nonstationarity of the brain response. Single-and two-channel filters are designed for simulated and human visual evoked potential data. Cross-correlation matrices required to design the filters are estimated "a posteriori" from multielectrode recordings of the prestimulus electroencephalogram and are derived from a multielectrode model of the evoked potential. Filter performance is evaluated using the criteria of mean-square error, signal bias, noise reduction, and output signal-to-noise ratio. The filter is shown to be very effective at suppressing the ongoing electroencephalogram and emphasizing the underlying evoked potential.