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

Background

The electroencephalography (EEG) is an attractive and a simple technique to measure the brain activity. It is attractive due its excellent temporal resolution and simple due to its non-invasiveness and sensor design. However, the spatial resolution of EEG is reduced due to the low conducting skull. In this paper, we compute the potential distribution over the closed surface covering the brain (cortex) from the EEG scalp potential. We compare two methods – L-curve and generalised cross validation (GCV) used to obtain the regularisation parameter and also investigate the feasibility in applying such techniques to N170 component of the visually evoked potential (VEP) data.

Methods

Using the image data set of the visible human man (VHM), a finite difference method (FDM) model of the head was constructed. The EEG dataset (256-channel) used was the N170 component of the VEP. A forward transfer matrix relating the cortical potential to the scalp potential was obtained. Using Tikhonov regularisation, the potential distribution over the cortex was obtained.

Results

The cortical potential distribution for three subjects was solved using both L-curve and GCV method. A total of 18 cortical potential distributions were obtained (3 subjects with three stimuli each – fearful face, neutral face, control objects).

Conclusions

The GCV method is a more robust method compared to L-curve to find the optimal regularisation parameter. Cortical potential imaging is a reliable method to obtain the potential distribution over cortex for VEP data.