The inverse problem for scalp EEG or MEG data is normally viewed as a problem in mathematical physics, since if the impedance model is known (or assumed) the biophysical forward problem is simply formulated. However, the general inverse problem of solving from a 2-D scalp map to the 3-D brain volume is underdetermined. Most current efforts seek to reduce the solution space to 2+ dimensions - i.e., to multiple neurophysiologically plausible domains of synchronous electromagnetic activity that are near-radially oriented with respect to the folded cortical sheet. I outline a radically different approach that ignores biophysical modeling altogether, focusing instead on another neurophysiologically plausible assumption - that over sufficient time, the time courses of synchronous activity in cortical source domains approach temporal indpendence. In fact, I show that applying infomax independent component analysis (ICA) to dense-array EEG data can separate 20 or more near-independent EEG processes whose scalp projections strongly resemble single current dipoles, compatible with their accounting for partially synchronous activity within compact cortical source domains. Next, I will introduce a new statistical measure of spatial complexity that can be used to reasonably characterize the complexity and quality of EEG or MEG data sets, as well as the relative success of any linear decomposition method in separating the recorded data into physiologically plausible processes. I will compare results of applying over 20 linear decomposition algorithms to actual EEG data and, finally, will outline the further prospect of noninvasive modeling of cortical current flow patterns using complex ICA (Anemueller, Sejnowki and Makeig, 2003).
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