Coarse Space Correction for Graphic Analysis

TL;DR

This paper introduces a coarse space correction method to accelerate solving linear systems from Radial Basis Function interpolation in graphic analysis, significantly reducing computation time in image reconstruction.

Contribution

It proposes a novel coarse space correction approach tailored for Radial Basis Function-based linear systems in image reconstruction, demonstrating improved efficiency.

Findings

Certain basis functions outperform others in speed

Numerical experiments confirm faster convergence

Method enhances image reconstruction efficiency

Abstract

In this paper we present an effective coarse space correction addressed to accelerate the solution of an algebraic linear system. The system arises from the formulation of the problem of interpolating scattered data by means of Radial Basis Functions. Radial Basis Functions are commonly used for interpolating scattered data during the image reconstruction process in graphic analysis. This requires to solve a linear system of equations for each color component and this process represents the most time-consuming operation. Several basis functions like trigonometric, exponential, Gaussian, polynomial are here investigated to construct a suitable coarse space correction to speed-up the solution of the linear system. Numerical experiments outline the superiority of some functions for the fast iterative solution of the image reconstruction problem.