Local polynomial estimate of surface Laplacian

This paper describes a method for estimating the surface Laplacian of brain potentials. The method consists of two steps: local surface approximation by its tangent plane and local polynomial fitting. Compared to previous met hods for estimating surface Laplacian, this method has some new features. F irst, it can estimate the surface Laplacian at any point of the scalp, incl uding the locations of the peripheral electrodes. Secondly, it estimates th e brain potential and the surface Laplacian at any point simultaneously. Th is reduces the risk of error propagation, which occurs when the brain poten tial is interpolated first and the surface Laplacian is then computed based on the interpolated brain potential. Finally, the method automatically ada pts to noisy data by using more or less measurements at neighboring electro des based on estimated noise level. Simulations suggest that this method is effective. Application to event-related potentials are also presented.