Improved MEG/EEG source localization with reweighted mixed-norms

Abstract

MEG/EEG source imaging allows for the noninvasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, a priori information is required to find a unique source estimate. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation can be assumed. Due to the convexity, ℓ-norm based constraints are often used for this, which however lead to source estimates biased in amplitude and often suboptimal in terms of source selection. As an alternative, non-convex regularization functionals such as ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> -quasinorms with 0 < p < 1 can be used. In this work, we present a MEG/EEG inverse solver based on a ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,0.5</inf> -quasinorm penalty promoting spatial sparsity as well as temporal stationarity of the brain activity. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate, which is based on reweighted convex optimization and combines a block coordinate descent scheme and an active set strategy to solve each surrogate problem efficiently. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method outperforms the standard Mixed Norm Estimate in terms of active source identification and amplitude bias.