Digital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods

Digital total variation (DTV) filtering techniques, that originated in the field of image processing, are adapted to postprocess Radial Basis Function approximations of piecewise continuous functions. Through numerical examples, we show that DTV filtering is a fast, robust, postprocessing method that can be used to remove Gibbs oscillations while sharply resolving discontinuities. The method is applicable for arbitrarily located data points. A postprocessing method for scattered data had not been given previously. keywords: Gibbs phenomena, Radial Basis Functions, meshfree, Digital Total Variation filtering, postprocessing.