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.

翻译：本文研究平面上的广义Radon变换 $\mathcal R$。设 $f$ 为分片光滑函数，且沿光滑曲线 $\mathcal S$ 存在跳变。我们推导出一个公式，该公式能精确描述当从视角方向离散化的数据 $\mathcal R f$ 重建 $f$ 时，远离 $\mathcal S$ 区域出现的视角混叠伪影。该公式具有渐进性质，是在采样率 $\epsilon\to0$ 的极限条件下建立的。所提出的方法不要求 $f$ 为带限函数。基于经典Radon变换和广义Radon变换（以圆为积分路径）的数值实验验证了该公式的准确性。