Improved realistic Laplacian estimate of highly-sampled EEG potentials by regularization techniques

In this study we investigated the effects of λ correction, generalized cross-validation (GCV), and Tikhonov regularization techniques on the realistic Laplacian (RL) estimate of highly-sampled (128 channels) simulated and actual EEG potential distributions. The simulated EEG potential distributions were mathematically generated over a 3-shell spherical head model (analytic potential distributions). Noise was added to the analytic potential distributions to mimic EEG noise. The magnitude of the noise was 20, 40 and 80% that of the analytic potential distributions. Performance of the regularization techniques was evaluated by computing the root mean square error (RMSE) between regularized RL estimates and analytic surface Laplacian solutions. The actual EEG data were human movement-related and short-latency somatosensory-evoked potentials. The RL of these potentials was estimated over a realistically-shaped, magnetic resonance-constructed model of the subject's scalp surface. The RL estimate of the simulated potential distributions was improved with all the regularization techniques. However, the λ correction and Tikhonov regularization techniques provided more precise Laplacian solutions than the GCV computation (P < 0.05); they also improved better than the GCV computation the spatial detail of the movement- related and short-latency somatosensory-evoked potential distributions. For both simulated and actual EEG potential distributions the Tikhonov and λ correction techniques provided nearly equal Laplacian solutions, but the former offered the advantage that no preliminary simulation was required to regularize the RL estimate of the actual EEG data.