Reproducing kernel Hilbert space method for optimal interpolation of potential field data

The RKHS-based optimal image interpolation method, presented by Chen and de Figueiredo (1993), is applied to scattered potential field measurements. The RKHS which admits only interpolants consistent with Laplace's equation is defined and its kernel, derived. The algorithm is compared to bicubic spline interpolation, and is found to yield vastly superior results.