# Prior Variances and Depth Un-Biased Estimators in EEG Focal Source Imaging

## TL;DR

This paper introduces a Bayesian method to determine weighting factors in EEG source imaging that eliminate depth bias, leading to more accurate focal source reconstructions.

## Contribution

It develops a novel approach to compute weights in sparsity priors for EEG source imaging, ensuring depth-unbiased MAP estimates.

## Key findings

- Proposes Gaussian prior variances for depth-unbiased estimates
- Derives approximate weights for sparsity priors based on these variances
- Demonstrates improved focal source reconstruction with proposed weights

## 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.