A spline framework for estimating the EEG surface laplacian using the Euclidean metric

This letter develops a framework for EEG analysis and similar applications based on polyharmonic splines. This development overcomes a basic problem with the method of splines in the Euclidean setting: that it does not work on low-degree algebraic surfaces such as spherical and ellipsoidal scalp models. The method's capability is illustrated through simulations on the three-sphere model and using empirical data.