An obvious limitation of the local Hjorth is that the second spatial derivative is derived from a discrete differentiation grid, impeding estimates not only at the edge of the EEG montage but at any given site, as estimates depend on the number and location of nearest neighbors. These adverse effects are compounded by the characteristics of the EEG montage, namely electrode density and spacing uniformity. However, signal interpolation can be used to overcome these deficiencies. Several algorithms have been proposed for smooth EEG surface reconstruction and surface Laplacian estimation (Carvalhaes and Suppes, 2011; Nunez and Srinivasan, 2006), ranging from local polynomial estimates (e.g., Wang and Begleiter, 1999) to global spline interpolations using a simple spherical (e.g., Carvalhaes and Suppes, 2011; Gevins, 1996; Nunez and Westdorp, 1994; Nunez et al., 1994; Perrin et al., 1987, 1989; Pascual-Marqui et al., 1988; Srinivasan et al., 1996, 1998a) or increasingly realistic scalp surface head models (e.g., Babiloni et al., 1995, 1996, 1997; Bortel and Sovka, 2007, 2013; Gevins et al., 1999; He et al., 2001; Law et al., 1993a; Yao, 2000, 2002a). A popular choice among these surface Laplacian techniques is interpolation via spherical splines, as proposed by Perrin et al. (1989).
