  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.
