An Application of Abel's Method to the Inverse Radon Transform

TL;DR

This paper explores a new approximation method for the inverse Radon transform using smooth kernels, providing convergence proofs and addressing Gibbs phenomena, with implications for computational applications.

Contribution

It introduces an Abel's method-based approach for the inverse Radon transform, including convergence theorems and practical implementation insights.

Findings

Proven convergence for piecewise smooth functions

Gibbs phenomena are eliminated in the method

Discussion on kernel properties for computer implementation

Abstract

A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out. Geometric properties of the kernel and their implications for computer implementation are discussed. Suggestions are made for applications and an example is presented.