Restoration of an entire epicortical electrocorticogram from a spatially sampled electroencephalogram

Abstract

The restoration of an entire epicortical ECoG-potential pattern from spatially sampled EEG-potentials can be performed according to the general principle of inverse spatial filtering: if a forward spatial filter is an averaging one, then a mutually inverse spatial filter can form a sharpened pattern from a slurred sampled pattern thus restoring more or less a spatial contrast of a primary source pattern. Brain coverings are the averaging forward spatial time-lag free filter in the transformation “eECoG $\longrightarrow$ EEG”; several models have been already developed for calculating the weight coefficients of this filter. Proposed here method to obtain weight coefficients of the mutually inverse spatial time-lag free filter of EEG is based on the generalized inversion of forward filter's weight coefficients matrix. The developed algorithm is verified using 3-dimensional depiction of numerically simulated patterns: the “real” eECoGs are visually compared with the restored eECoGs, that were obtained from the corresponding spatial samples of the “real” EEGs.