This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyhar...

An adaptive decision based inverse distance weighted interpolation (DBIDWI) algorithm for the elimination of highdensity salt and pepper noise in images is proposed. The pixel is initially checked for salt and pepper noise. If classified as noisy pixel, replace it with an inverse distance weighted interpolation value. This interpolation estimates the values of corrupted pixels using the distanc...

This paper presents an adaptive regularized image interpolation algorithm from blurred and noisy low resolution image sequence, which is developed by a general framework based on data fusion. This framework can preserve edge information and suppress noise, effectively. To obtain a higher resolution image, both discontinuities across the edge orientation and smoothness along the edge orientation...

We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...

A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially non-oscillatory (ENO) interpolation is a classic example schemes. In the aforementioned application areas, property preservation often manifests itself requirement fo...