Title: Prior Variances and Depth Un-Biased Estimators in EEG Focal Source Imaging,
Abstract: In electroencephalography (EEG) source imaging, the inverse source estimates
are depth biased in such a way that their maxima are often close to the
sensors. This depth bias can be quantified by inspecting the statistics (mean
and co-variance) of these estimates. In this paper, we find weighting factors
within a Bayesian framework for the used L1/L2 sparsity prior that the
resulting maximum a posterior (MAP) estimates do not favor any particular
source location. Due to the lack of an analytical expression for the MAP
estimate when this sparsity prior is used, we solve the weights indirectly.
First, we calculate the Gaussian prior variances that lead to depth un-biased
maximum a posterior (MAP) estimates. Subsequently, we approximate the
corresponding weight factors in the sparsity prior based on the solved Gaussian
prior variances. Finally, we reconstruct focal source configurations using the
sparsity prior with the proposed weights and two other commonly used choices of
weights that can be found in literature.