Non-linear Covariance Estimation for Reconstructing Neural Activity with MEG/EEG Data

MEG/EEG brain imaging approaches are commonly based on linear covariance matrices that contain the prior information needed to solve the inverse problem. We expect that non-linear covariance matrices (or kernel matrices) provide more information than the widely used smoothers (Loreta, MSP) or data-based matrices (beamformers). Data-based covariance matrices have shortcomings such as being prone to be singular, having limited capability in modeling, complicated relationships in the data, and having a fixed form of representation. The multiple sparse priors (MSP) algorithm provides flexibility but in its original form it only contains smoothers. In this work, we propose to modify both MSP and beamformers by introducing a Gaussian kernel matrix with the objective of enhancing the reconstruction of neural activity. The proposed approach was tested with two well-known simulation benchmarks: Haufe’s and SPM. Simulation results showed improvements in the ROIs recognition with Haufe’s benchmark, and smaller localization error with SPM benchmark. A real data validation (MEG and EEG) was performed with the faces-scrambled dataset. The expected active sources were obtained, but their strength presented slight variations.