A Two-Level Iterative Method for Image Reconstruction with Radial Basis Functions

Abstract

Radial basis functions are popular basis for interpolating scattered data during the image reconstruction process in graphic analysis. In this context, the solution of a linear system of equations is required for each color (blue, red, green) and represents the most time-consuming operation. In this paper a two-level iterative algorithm is proposed to solve efficiently these linear systems of equations. This two-level algorithm consists of a preconditioned iterative method which enforces at each iteration a projection of the residual onto a suitable coarse space. This constraint is ensured by solving an auxiliary second-level problem at each iteration. Numerical results illustrate the convergence properties of the proposed method on a wide range of interpolation problems for image reconstruction.