Solving large-scale MEG/EEG source localization and functional connectivity problems simultaneously using state-space models

TL;DR

This paper introduces a novel regularisation framework using penalised state-space models and advanced algorithms to efficiently solve large-scale MEG/EEG source localization and connectivity problems simultaneously, overcoming computational and bias limitations of existing methods.

Contribution

The paper presents multiple penalised state-space models with data-driven regularisation, new algorithms for their solution, and a cross-validation method for parameter tuning, enabling large-scale brain analysis.

Findings

Validated on complex simulations with varying SNRs

Successfully applied to real MEG/EEG data with thousands of sources

Outperforms existing methods in large-scale source localization and connectivity analysis

Abstract

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high computational costs in large-scale analyses. Sparse inverse covariance estimators can mitigate these costs, but at the expense of a trade-off between enforced sparsity and increased estimation bias, necessitating careful assessment in low signal-to-noise ratio (SNR) situations. To address these challenges, we propose a three-fold solution: 1) Introducing multiple penalised state-space (MPSS) models that leverage data-driven regularisation; 2) Developing novel algorithms derived from backpropagation, gradient descent, and alternating least squares to solve MPSS models; 3) Presenting a K-fold cross-validation extension for evaluating regularisation parameters. We validate this MPSS regularisation framework through lower and more complex simulations under varying SNR conditions, including a large-scale synthetic magneto- and electro-encephalography (MEG/EEG) data analysis. In addition, we apply MPSS models to concurrently solve brain source localisation and functional connectivity problems for real event-related MEG/EEG data, encompassing thousands of sources on the cortical surface. The proposed methodology overcomes the limitations of existing approaches, such as constraints to small-scale and region-of-interest analyses. Thus, it may enable a more accurate and detailed exploration of cognitive brain functions.