Cortical potential imaging using L-curve and GCV method to choose the regularisation parameter

Regularization and a general linear model for event-related potential estimation

The usual event-related potential (ERP) estimation is the average across epochs time-locked on stimuli of interest. These stimuli are repeated several times to improve the signal-to-noise ratio (SNR) and only one evoked potential is estimated inside the temporal window of interest. Consequently, the average estimation does not take into account other neural responses within the same epoch that are due to short inter stimuli intervals. These adjacent neural responses may overlap and distort the evoked potential of interest. This overlapping process is a significant issue for the eye fixation-related potential (EFRP) technique in which the epochs are time-locked on the ocular fixations. The inter fixation intervals are not experimentally controlled and can be shorter than the neural response's latency. To begin, the Tikhonov regularization, applied to the classical average estimation, was introduced to improve the SNR for a given number of trials. The generalized cross validation was chosen to obtain the optimal value of the ridge parameter. Then, to deal with the issue of overlapping, the general linear model (GLM), was used to extract all neural responses inside an epoch. Finally, the regularization was also applied to it. The models (the classical average and the GLM with and without regularization) were compared on both simulated data and real datasets from a visual scene exploration in co-registration with an eye-tracker, and from a P300 Speller experiment. The regularization was found to improve the estimation by average for a given number of trials. The GLM was more robust and efficient, its efficiency actually reinforced by the regularization.

High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.