[Paper Review] EEG reconstruction and skull conductivity estimation using a Bayesian model promoting structured sparsity

Facundo Costa, Hadj Batatia+2 more|arXiv (Cornell University)|Sep 22, 2016

Sparse and Compressive Sensing Techniques21 references3 citations

TL;DR

This paper proposes a hierarchical Bayesian framework that jointly estimates EEG source activity and skull conductivity using structured sparsity priors, enabling unsupervised, high-fidelity M/EEG source reconstruction. By employing a partially collapsed Gibbs sampler and a polynomial approximation of the leadfield operator, the method improves localization accuracy—particularly in multi-dipole scenarios and when skull conductivity is misestimated—achieving a posterior mean conductivity estimate of 10.6 mS/m, closer to recent empirical findings than standard defaults.

ABSTRACT

M/EEG source localization is an open research issue. To solve it, it is important to have good knowledge of several physical parameters to build a reliable head operator. Amongst them, the value of the conductivity of the human skull has remained controversial. This report introduces a novel hierarchical Bayesian framework to estimate the skull conductivity jointly with the brain activity from the M/EEG measurements to improve the reconstruction quality. A partially collapsed Gibbs sampler is used to draw samples asymptotically distributed according to the associated posterior. The generated samples are then used to estimate the brain activity and the model hyperparameters jointly in a completely unsupervised framework. We use synthetic and real data to illustrate the improvement of the reconstruction. The performance of our method is also compared with two optimization algorithms introduced by Vallaghé extit{et al.} and Gutierrez extit{et al.} respectively, showing that our method is able to provide results of similar or better quality while remaining applicable in a wider array of situations.

Motivation & Objective

• To address the persistent challenge of uncertain skull conductivity in M/EEG source localization, which significantly degrades reconstruction quality.
• To develop a fully unsupervised method that jointly estimates brain activity and skull conductivity without requiring prior knowledge of active dipole locations.
• To improve reconstruction accuracy in scenarios with multiple dipoles or incorrect conductivity assumptions, where standard methods fail.
• To provide a robust, generalizable framework applicable across diverse subject anatomies and conductivity values.
• To validate the method against state-of-the-art optimization techniques and standard fixed-conductivity models.

Proposed method

• A hierarchical Bayesian model is formulated with a multivariate Bernoulli-Laplacian prior to promote structured sparsity in brain activity, approximating an ℓ20 mixed norm.
• A partially collapsed Gibbs sampler is used to generate asymptotically correct samples from the joint posterior distribution of brain activity and skull conductivity.
• The leadfield operator is approximated using a polynomial expansion to reduce computational cost during MCMC sampling.
• Model hyperparameters and skull conductivity are estimated jointly from data using the posterior samples, enabling a fully unsupervised inference process.
• The method is applied to both synthetic and real auditory evoked response data to evaluate performance.
• Convergence is assessed using Potential Scale Reduction Factors (PSRFs), confirming stable sampling behavior.

Experimental results

Research questions

• RQ1 Can a Bayesian framework jointly estimate brain activity and skull conductivity with improved reconstruction accuracy compared to fixed-conductivity models?
• RQ2 Does structured sparsity promotion enhance localization precision, especially in multi-dipole scenarios?
• RQ3 How does the method perform when skull conductivity is far from the true value or when prior knowledge of active dipoles is absent?
• RQ4 Can the proposed method outperform or match optimization-based approaches like those of Vallaghé et al. and Gutierrez et al. without requiring restrictive assumptions?
• RQ5 What is the estimated skull conductivity from real M/EEG data, and how does it compare to recent empirical values?

Key findings

• The proposed method achieved superior localization accuracy compared to a fixed-conductivity model with ρ = 6 mS/m, particularly in multi-dipole scenarios where the fixed model spread activity across multiple dipoles.
• The method estimated a skull conductivity of 10.6 mS/m, corresponding to a scalp-to-skull conductivity ratio of 31, which is more consistent with recent empirical studies than the commonly used value of 80.
• In real auditory evoked response data, the method concentrated activity on the auditory cortices with strong, clinically expected peaks at ~90 ms post-stimulus, unlike other methods that spread activity.
• The MMSE estimate of brain activity showed higher spatial concentration and better agreement with expected neurophysiological patterns than ℓ21 regularization or default MNE settings.
• PSRF convergence diagnostics confirmed reliable sampling, with all statistics approaching 1.0, indicating effective Markov chain convergence.
• The method outperformed both Vallaghé et al.'s and Gutierrez et al.'s optimization techniques in reconstruction quality without requiring knowledge of active dipole locations or assuming a single active dipole.