Greedy algorithms for image approximation from scattered Radon data

Abstract

Positive definite kernels are powerful tools for multivariate approximation from scattered data. This contribution discusses kernel-based image approximation from scattered Radon data. To this end, we use weighted kernels for the reconstruction. Moreover, we propose greedy algorithms, which are used to adaptively select suitable approximation spaces. This reduces the complexity of the resulting image reconstruction method and, moreover, it improves the numerical stability quite significantly.