PSIICOS projection optimality for EEG and MEG based functional coupling detection.

Functional connectivity is crucial for cognitive processes in the healthy brain and serves as a marker for a range of neuropathological conditions. Non-invasive exploration of functional coupling using temporally resolved techniques such as MEG allows for a unique opportunity of exploring this fundamental brain mechanism. The indirect nature of MEG measurements complicates the estimation of functional coupling due to the volume conduction and spatial leakage effects. In the previous work (Ossadtchi et al., 2018), we introduced PSIICOS, a method that for the first time allowed us to suppress the volume conduction effect and yet retain information about functional networks whose nodes are coupled with close to zero or zero mutual phase lag. In this paper, we demonstrate analytically that the PSIICOS projection is optimal in achieving a controllable trade-off between suppressing mutual spatial leakage and retaining information about zero- or close to zero-phase coupled networks. We also derive an alternative solution using the regularization-based inverse of the mutual spatial leakage matrix and show its equivalence to the original PSIICOS. We then discuss how PSIICOS solution to the functional connectivity estimation problem can be incorporated into the conventional source estimation framework. Instead of sources, the unknowns are the elementary dyadic networks and their activation time series are formalized by the corresponding source-space cross-spectral coefficients. This view on connectivity estimation as a regression problem opens up new opportunities for formulating a set of principled estimators based on the rich intuition accumulated in the neuroimaging community.