Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning - Paz-Linares, Deirel; Gonzalez-Moreira, Eduardo; Areces-Gonzalez, Ariosky; Wang, Ying; Li, Min; Vega-Hernandez, Mayrim; Wang, Qing; Bosch-Bayard, Jorge; Bringas-Vega, Maria L.; Martinez-Montes, Eduardo; Valdes-Sosa, Mitchel J.; Valdes-Sosa, Pedro A. (Frontiers in Neuroscience, 2023)
Oscillatory processes at all spatial scales and frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This paper aims at an ESI of the source cross-spectrum, controlling common distortions of the estimates. As with all ESI problems under realistic settings, the main obstacle is that we are facing a severely ill-conditioned and high-dimensional inverse problem. We opt for Bayesian inverse solutions that posit a priori probabilities upon the source process. Indeed, rigorously specifying both the likelihoods and a priori probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires a priori of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem are NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a joint a priori probability upon the source cross-spectrum to avoid these problems. Thus, cESI inverse solutions are low-dimensional for the set of random vector instances and not random matrices. We achieve cESI inverse solutions through the variational approximations via our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning. We compared low-density EEG (10-20 system) ssSBL inverse solutions with reference cESIs for two experiments a) high-density MEG used to generate simulate EEG; b) high-density macaque ECoG recorded simultaneously with EEG. SSBL resulted in two orders of magnitude less distortion than state-of-the-art methods for the standad ESI. Our cESI toolbox including the ssSBL method is available at https://github.com/CCC-members/BC-VARETA_Toolbox.