By comparison, spatial noise and montage density had only moderate impact for determining optimal values for λ. Importantly, λ correction significantly improved spherical spline surface Laplacian estimates when compared with the ‘analytic’ surface Laplacian distribution, which was directly computed from the (mathematically) simulated surface potentials (Babiloni et al., 1995). Finding an optimal regularization constant is of critical relevance for realistic Laplacian computation, and various regularization techniques have been proposed for this purpose (e.g., Bortel and Sovka, 2007, 2013). An optimal value for λ may be derived from the actual data by computing a cross-validation (CV) criterion that minimizes the prediction error for estimated potentials (i.e., using spherical spline interpolation to predict the data at any given site from the data of all other sites; e.g., Pascual-Marqui et al., 1988; Stone, 1974). Figure 9 compares λ-optimized CSD topographies for an auditory N1, revealing that the spatial low-pass filter properties associated with less flexible splines (i.e., greater m constant) and more regularization or smoothing (i.e., greater λ value) can - to a certain degree - mutually compensate to achieve optimal potential estimates. As a consequence, λ-optimized CSDs obtained with different spline orders yield more similar surface Laplacian estimates (between-topography correlations were 0.6872
