How Forgiving are M/EEG Inverse Solutions to Noise Level Misspecification? An Excursion into the BSI-Zoo

Brain source imaging (BSI), also known as source localization, from magneto- and electroencephalographic (M/EEG) data, is a challenging ill-posed inverse problem. Accurate source estimation is sensitive to multiple modeling and experimental parameters, such as regularization strength and noise level, where misconfigurations can lead to under- or overfitting. Different BSI methods, however, may vary in their robustness to suboptimal parameter choices.

Here we conducted extensive simulations of brain sources superimposed by varying degrees of sensor noise to study the ranges of noise misspecification within which different BSI approaches can still localize well. Using the Earth Mover's Distance (EMD) and other metrics, we compare the performance of smooth linear inverse solutions with that of sparse non-linear Bayesian learning solutions. Additionally, we assess the effectiveness of various noise estimation and crossvalidation techniques to select hyperparameters close to those achieving optimal localization.

Our results characterize the robustness of commonly used BSI methods to noise and regularization misspecification. Across methods, moderate underfitting to noise generally yielded better performance than overfitting. Spatial cross-validation was effective in identifying hyperparameters that achieved near-optimal localization performance. Methods and experiments are made available within the BSI-Zoo Python package.

The choice of BSI method and hyperparameter estimation strategy substantially influences localization accuracy and robustness under noise misspecification.

These findings provide practical guidance for selecting and tuning BSI methods, improving the reliability and reproducibility of M/EEG source localization.