Novel RBF Approximation Method Based on Geometrical Properties for Signal Processing with a New RBF Function: Experimental Comparison

Abstract

Interpolation and approximation methods are widely used in many areas. They can be divided to methods based on meshing (tessellation) of the data domain and to meshless (meshfree) methods, which do not require the domain tessellation of scattered data. Scattered n-dimensional data radial basis function (RBF) interpolation and approximation leads to a solution of linear system of equations.This contribution presents a new approach to the RBF approximation based on analysis of geometrical properties of signals, i.e. sampled curves. Also a newly developed radial basis function was used and proved better precision of approximation.Experimental comparison of several RBF functions (Gauss, Thin-Plate Spline, CS-RBF and a new proposed RBF) is described with analysis of their properties. Special attention was taken to the precision of approximation and conditionality issues. The proposed approach can be extended to a higher dimensional case and for vector data, e.q. fluid flow, too.