Reconstruction of EEG from limited channel acquisition using estimated signal correlation

Nearby scalp channels in multi-channel EEG data exhibit high correlation. A question that naturally arises is whether it is required to record signals from all the electrodes in a group of closely spaced electrodes in a typical measurement setup. One could save on the number of channels that are recorded, if it were possible to reconstruct the omitted channels to the accuracy needed for identifying the relevant information (say, spectral content in the signal), required to carry out a preliminary diagnosis. We address this problem from a compressed sensing perspective and propose a measurement and reconstruction scheme. Working with publicly available EEG database, we have demonstrated that up to 12 channels in the 10-10 system of electrode placement can be estimated within an average error of 2% from recordings of the remaining channels. As a limiting case, all the channels of the 10-10 system can be estimated using recordings on the sparser 10-20 system within an error of less than 20% in each of the significant bands: delta, theta, beta and alpha.