  Source imaging based on magnetoencephalography (MEG) and
electroencephalography (EEG) allows for the non-invasive analysis of brain
activity with high temporal and good spatial resolution. As the
bioelectromagnetic inverse problem is ill-posed, constraints are required. For
the analysis of evoked brain activity, spatial sparsity of the neuronal
activation is a common assumption. It is often taken into account using convex
constraints based on the l1-norm. The resulting source estimates are however
biased in amplitude and often suboptimal in terms of source selection due to
high correlations in the forward model. In this work, we demonstrate that an
inverse solver based on a block-separable penalty with a Frobenius norm per
block and a l0.5-quasinorm over blocks addresses both of these issues. For
solving the resulting non-convex optimization problem, we propose the iterative
reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on
iterative reweighted convex surrogate optimization problems, which are solved
efficiently using a block coordinate descent scheme and an active set strategy.
We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC
approach based on two MEG data sets. We provide empirical evidence based on
simulations and analysis of MEG data that the proposed method improves on the
standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support
recovery, and stability.
