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

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 $\epsilon \to 0$. 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.