  The problem of interest here is the study of brain functional and effective
connectivity based on non-invasive EEG-MEG inverse solution time series. These
signals generally have low spatial resolution, such that an estimated signal at
any one site is an instantaneous linear mixture of the true, actual, unobserved
signals across all cortical sites. False connectivity can result from analysis
of these low-resolution signals. Recent efforts toward "unmixing" have been
developed, under the name of "leakage correction". One recent noteworthy
approach is that by Colclough et al (2015 NeuroImage, 117:439-448), which
forces the inverse solution signals to have zero cross-correlation at lag zero.
One goal is to show that Colclough's method produces false human connectomes
under very broad conditions. The second major goal is to develop a new
solution, that appropriately "unmixes" the inverse solution signals, based on
innovations orthogonalization. The new method first fits a multivariate
autoregression to the inverse solution signals, giving the mixed innovations.
Second, the mixed innovations are orthogonalized. Third, the mixed and
orthogonalized innovations allow the estimation of the "unmixing" matrix, which
is then finally used to "unmix" the inverse solution signals. It is shown that
under very broad conditions, the new method produces proper human connectomes,
even when the signals are not generated by an autoregressive model.
