  The study of functional connectivity from magnetoecenphalographic (MEG) data
consists in quantifying the statistical dependencies among time series
describing the activity of different neural sources from the magnetic field
recorded outside the scalp. This problem can be addressed by utilizing
connectivity measures whose computation in the frequency domain often relies on
the evaluation of the cross-power spectrum of the neural time-series estimated
by solving the MEG inverse problem. Recent studies have focused on the optimal
determination of the cross-power spectrum in the framework of regularization
theory for ill-posed inverse problems, providing indications that, rather
surprisingly, the regularization process that leads to the optimal estimate of
the neural activity does not lead to the optimal estimate of the corresponding
functional connectivity. Along these lines, the present paper utilizes
synthetic time series simulating the neural activity recorded by an MEG device
to show that the regularization of the cross-power spectrum is significantly
correlated with the signal-to-noise ratio of the measurements and that, as a
consequence, this regularization correspondingly depends on the spectral
complexity of the neural activity.
