Reconstruction from Radon projections and orthogonal expansion on a ball

TL;DR

This paper explores the connection between Radon transforms and orthogonal expansions on a unit ball, providing formulas and algorithms for image reconstruction from Radon data, and analyzing the singular value decomposition of the Radon transform.

Contribution

It introduces a compact formula linking Radon projections with orthogonal expansions, enabling improved image reconstruction algorithms and insights into the Radon transform's singular value decomposition.

Findings

Derived a compact formula for partial sums of orthogonal expansions using Radon data

Developed algorithms for image reconstruction from Radon projections

Analyzed the singular value decomposition of the Radon transform

Abstract

The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.