Abstract: A method and system for the localization and characterization of the generators of human brain electromagnetic physiological activity includes a set of bioelectromagnetic amplifiers, sensorial stimulators, and a computer based system for signal analog to digital conversion and recording. Sufficient statistics, including higher order statistical moments, for event related components are computed from the recorded signals, either in the time, frequency, or time-frequency domain, retaining stationary, non-stationary, linear, and non-linear information. The localizations, orientations, activities, and connectivities of the generators are obtained by solving the inverse problem using sufficient statistics under anatomical and functional constraints. Realistic head geometry and conductivity profiles are used to transform the measurements into infinite homogeneous medium measurements, through use of ananatomical deconvolution operator, thus simplifying optimally inverse solution computations.