Abstract
The choice of reference for the electroencephalogram (EEG) is a long-lasting unsolved issue resulting in inconsistent usages and endless debates. Currently, both the average reference (AR) and the reference electrode standardization technique (REST) are two primary, apparently irreconcilable contenders. We propose a theoretical framework to resolve this reference issue by formulating both (a) estimation of potentials at infinity, and (b) determination of the reference, as a unified Bayesian linear inverse problem, which can be solved by maximum a posterior estimation. We find that AR and REST are very particular cases of this unified framework: AR results from biophysically non-informative prior; while REST utilizes the prior based on the EEG generative model. To allow for simultaneous denoising and reference estimation, we develop the regularized versions of AR and REST, named rAR and rREST, respectively. Both depend on a regularization parameter that is the noise to signal variance ratio. Traditional and new estimators are evaluated with this framework, by both simulations and analysis of real resting EEGs. Toward this end, we leverage the MRI and EEG data from 89 subjects which participated in the Cuban Human Brain Mapping Project. Generated artificial EEGs—with a known ground truth, show that relative error in estimating the EEG potentials at infinity is lowest for rREST. It also reveals that realistic volume conductor models improve the performances of REST and rREST. Importantly, for practical applications, it is shown that an average lead field gives the results comparable to the individual lead field. Finally, it is shown that the selection of the regularization parameter with Generalized Cross-Validation (GCV) is close to the “oracle” choice based on the ground truth. When evaluated with the real 89 resting state EEGs, rREST consistently yields the lowest GCV. This study provides a novel perspective to the EEG reference problem by means of a unified inverse solution framework. It may allow additional principled theoretical formulations and numerical evaluation of performance.
Highlights
The human electroencephalogram (EEG) has been an indispensable technology for both cognitive and clinical neuroscience for almost 90 years
Injecting higher sensor noise with SNR being from 20 to 2 dB, the relative error (RE) of regularized average reference (rAR) increase from less than 15% to higher than 60% while the REs of reference electrode standardization technique (rREST) with spherical lead field (SLF) excluded rise from 4.1 to 40%. These results indicate that: (1) except for the case of average reference (AR) and rAR with SNR = 20 dB, AR, rAR, reference electrode standardization technique (REST), and rREST by using SLF that roughly approximated the actual volume conduction model may be not able to reconstruct the EEG signal at infinity due to the quite large REs; (2) the effects of REST and rREST are volume conduction model dependent; (3) stronger regularization applied, better effect of rREST obtained; (4) for REST and rREST, the REs by using average lead field (ALF) seems to be almost same with the REs by individual lead field (ILF); (5) rAR may not have the effect of denoising
Since Generalized Cross-Validation (GCV) was found to be the best criteria to choose the proper regularization parameter λ in the simulation shown in Figure 6, we suggest adopting GCV to select the value of λ for each EEG recording in practice when the ground truth is unknown
Summary
The human electroencephalogram (EEG) has been an indispensable technology for both cognitive and clinical neuroscience for almost 90 years. We will rather concentrate on the vexing and still incompletely resolved “EEG reference problem.”. One might think that such a reference electrode could be placed at infinity, yielding the ideal potentials φ∞. This would not work in practice, since this configuration would serve as an antenna, picking unwanted activity from the environment. Some researchers experimented with reference electrode placed on the body so that EEG differential amplimers could eliminate environmental noise with high common mode rejection ratio
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