Analysis of view aliasing for the generalized Radon transform in $\mathbb R^2$

TL;DR

This paper derives an asymptotic formula to describe view aliasing artifacts in the reconstruction of functions from generalized Radon transform data, applicable to non-band-limited functions, validated through numerical experiments.

Contribution

It provides a new asymptotic formula for view aliasing artifacts in generalized Radon transform reconstructions, independent of band-limitation assumptions.

Findings

The formula accurately predicts aliasing artifacts away from discontinuities.

Numerical experiments confirm the formula's accuracy for classical and generalized Radon transforms.

The approach works without requiring the function to be band-limited.

Abstract

In this paper we consider the generalized Radon transform $\mathcal R$ in the plane. Let $f$ be a piecewise smooth function, which has a jump across a smooth curve $\mathcal S$. We obtain a formula, which accurately describes view aliasing artifacts away from $\mathcal S$ when $f$ is reconstructed from the data $\mathcal R f$ discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate $\epsilon\to0$. The proposed approach does not require that $f$ be band-limited. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula.