Reconstruction of Smooth Signals from Irregular Samples by Using Radial Basis Function Approximation

Based on constrained least squares approximation and techniques from computational geometry, this paper shall provide a new approximation scheme which achieves to combine well-known features from radial basis function interpolation with recent developments concerning scattered data filtering. The suggested method is shown to be well-posed, and moreover by using local error estimates from radial basis function interpolation, approximation orders for the least squares error are proven. An efficient adaptive algorithm for the purpose of automatically selecting a suitable basis of the approximation space is provided.