Robust and sparse estimator for EEG source localization

EEG source localization involves reconstructing brain activity from observed EEG measurements, a critical task for diagnosing various neurological disorders. The distributed approach to this problem is inherently ill-posed, posing significant challenges. In this study, we present a sparsity-controlled Lorentzian norm-based method for EEG source localization. This approach effectively balances robustness to measurement noise and sparsity in the solution.

The proposed method employs a non-linear conjugate gradient descent algorithm to minimize the loss function, where the Lorentzian norm replaces the conventional ${\ell }_2$ norm. The Lorentzian norm’s unique ability to handle impulsive noise ensures precise estimation of active sources, even under challenging conditions. Comparative analyses with ${\ell }_2$, ${\ell }_1$ and ${\ell }_p,p<1$ norm-based methods highlight the Lorentzian norm’s superior robustness and sparsity control. The results demonstrate that this novel approach improves the accuracy and reliability of EEG source localization, making it a valuable tool for medical applications.