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

Abstract State-space models are used in many research fields where dynamics are unobserved. Popular methods such as Kalman filtering and expectation maximization enable the estimation of these models but have a high computational cost in large-scale analysis. In such approaches, sparse inverse covariance estimators can reduce the cost; however, a trade-off between enforced sparsity and increased estimation bias occurs, which demands careful consideration in low signal-to-noise ratio scenarios. We overcome these limitations by 1) Introducing multiple penalised state-space (MPSS) models based on data-driven regularisation; 2) Solving MPSS models with novel algorithms extended from backpropagation, state-space gradient descent, or alternating least squares; 3) Proposing an extension of K-fold cross-validation to evaluate the regularisation parameters. Finally, we use MPSS models to solve the simultaneous brain source localisation and functional connectivity problems for simulated and real MEG/EEG data for thousands of sources on the cortical surface, thereby demonstrating a substantial improvement over state-of-the-art methods.