Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning

Abstract

Oscillatory processes at all spatial scales and on all 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 study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited a priori probabilities on 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 were 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. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved 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 that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox.

Multimodal pipeline for HCP-compatible processing and registration of legacy datasets (MRI, MEG, and EEG)

“…Precisely, conventional algorithms such as, Extract low-resolution brain electromagnetic tomography eLORETA (Pascual-Marqui et al, 2006) and Linear constrainer minimum variance LCMV (Lin et al, 2008) achieve robust inverse imaging at the expense of imposing overly smooth distributions in the source space. Novel inverse solution methods, like Spectral-Structured-Sparse-Bayesian-Learning ssSBL (Paz-Linares et al, 2023) and Hidden Gaussian Graphical Spectral model HiGGS aim at an ESI of the source cross-spectrum controlling common distortions of the estimates and facing a severely ill-conditioned and highdimensional inverse problem.…”

“…Structured Sparse Bayesian Learning (sSSBL) method(Gonzalez-Moreira et al, 2020;Paz-Linares et al, 2023) and 4 (connectivity level analysis) the Hidden Gaussian Graphical State-Model (HIGGS) with connectivity regularization of the Hermitian Graphical LASSO (hgLASSO) method(Paz-Linares et al, 2018).…”