Because the surface Laplacian is inherently computed from signal differences (i.e., second spatial derivative), and differences are typically more variable than the original data, it may be reasoned that one of the costs of the surface Laplacian transform is a greater sensitivity to the level of noise in the data (e.g., Bradshaw and Wikswo, 2001; Murray et al., 2008). Systematic manipulations have shown that the surface Laplacian estimation error increased proportionally with magnitude and spatial frequency of simulated noise levels (Babiloni et al., 1995). The particular concern is that because the surface Laplacian will amplify higher over lower spatial frequencies, signal distortions will be caused by high frequency noise, including recording artifacts (Bradshaw and Wikswo, 2001). While these negative effects can be counteracted by heavier regularization and use of more rigid splines, this comes with a loss in spatial resolution, as one of the declared goals of using a surface Laplacian is to enhance the spatial resolution of the EEG signal. Obviously, this concern constitutes a paradox of sorts with the lamented signal loss of low spatial frequencies discussed above.
