Section: New Results

M/EEG source reconstruction based on Gabor thresholding in the source space

Thanks to their high temporal resolution, source reconstruction based on Magnetoencephalography (MEG) and/or Electroencephalography (EEG) is an important tool for noninvasive functional brain imaging. Since the MEG/EEG inverse problem is ill-posed, inverse solvers employ priors on the sources. While priors are generally applied in the time domain, the time-frequency (TF) characteristics of brain signals are rarely employed as a spatio-temporal prior. In this work, we present an inverse solver which employs a structured sparse prior formed by the sum of ${\ell }_{21}$ and ${\ell }_1$ norms on the coefficients of the Gabor TF decomposition of the source activations. The resulting convex optimization problem is solved using a first-order scheme based on proximal operators. We provide empirical evidence based on EEG simulations that the proposed method is able to recover neural activations that are spatially sparse, temporally smooth and non-stationary. We compare our approach to alternative solvers based also on convex sparse priors, and demonstrate the benefit of promoting sparse Gabor decompositions via a mathematically principled iterative thresholding procedure. See also [24] .