Space-Time Extension of the MEM Approach for Electromagnetic Neuroimaging

The wavelet Maximum Entropy on the Mean (wMEM) approach to the MEG inverse problem is revisited and extended to infer brain activity from full space-time data. The resulting dimensionality increase is tackled using a collection of techniques , that includes time and space dimension reduction (using respectively wavelet and spatial filter based reductions), Kronecker product modeling for covariance matrices, and numerical manipulation of the free energy directly in matrix form. This leads to a smooth numerical optimization problem of reasonable dimension, solved using standard approaches. The method is applied to the MEG inverse problem. Results of a simulation study in the context of slow wave localization from sleep MEG data are presented and discussed. Index Terms: MEG inverse problem, maximum entropy on the mean, wavelet decomposition, spatial filters, Kronecker covariance factorization, sleep slow waves.