Estimating cross-modal transfer functions without source ground truth

Develop methods to estimate the cross-modal transfer-function matrices required for temporal geometric eigenmode source localisation from experimental scalp EEG without direct knowledge of the underlying neural source activity.

Background

The empirical and oracle temporal geometric eigenmode source-localisation methods substantially improve reconstruction when cross-eigenmode interactions are available. In the simulations, these interactions can be estimated because the ground-truth source dynamics are known and can be projected into the geometric eigenmode basis.

For experimental scalp EEG, however, the source activity is precisely the unknown quantity that source imaging seeks to infer. This creates a recursive estimation problem: an accurate source estimate is needed to estimate the transfer functions, while accurate transfer functions are needed to obtain the source estimate. The paper discusses complementary measurements, including intracranial recordings and fMRI, as possible sources of prior information, but does not resolve the general estimation problem.

References

The strong performance of the empirical and oracle approaches raises an important practical question: how could the required transfer function matrices be estimated without knowledge of the true underlying source activity? In the present simulation study, the source dynamics were known and could therefore be projected directly into the eigenmode basis to estimate the corresponding cross-modal relationships. However, with experimental scalp EEG, the underlying source activity is itself unknown. We thus have a seemingly recursive problem in that an accurate source estimate is required to estimate the transfer functions to produce an accurate source estimate.

— Temporally constraining source imaging estimates in an underdetermined neural system with eigenmodes of cortical geometry  (2609.00809 - Siu et al., 1 Sep 2026) in Section 4.2, “Estimating the Cross-Modal Coupling Terms in Practice”