Standardized hierarchical adaptive Lp regression for noise robust focal epilepsy source reconstructions

Objective
To investigate the ability of standardization to reduce source localization errors and measurement noise uncertainties for hierarchical Bayesian algorithms with
L1- and L2-norms as priors in electroencephalography and magnetoencephalography of focal epilepsy.

Methods
Description of the standardization methodology relying on the Hierarchical Bayesian framework, referred to as the Standardized Hierarchical Adaptive Lp-norm Regularization (SHALpR).
The performance was tested using real data from two focal epilepsy patients. Simulated data that resembled the available real data was constructed for further localization and noise robustness investigation.

Results
The proposed algorithms were compared to their non-standardized counterparts, Standardized low-resolution brain electromagnetic tomography, Standardized Shrinking LORETA-FOCUSS, and Dynamic statistical parametric maps. Based on the simulations, the standardized Hierarchical adaptive algorithm using
L2-norm was noise robust for 10 dB signal-to-noise ratio (SNR), whereas the L1-norm prior worked robustly also with 5 dB SNR. The accuracy of the standardized
L1-normed methodology to localize focal activity was under 1 cm for both patients.

Conclusions
Numerical results of the proposed methodology display improved localization and noise robustness. The proposed methodology also outperformed the compared methods when dealing with real data.

Significance
The proposed standardized methodology, especially when employing the L1-norm, could serve as a valuable assessment tool in surgical decision-making.