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, convex curve $\mathcal S$. We obtain a precise, quantitative formula describing view aliasing artifacts 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拉东变换 $\mathcal R$。设 $f$ 为分片光滑函数，其在光滑凸曲线 $\mathcal S$ 上存在跳跃。我们得到了一个精确的定量公式，用于描述当从沿视角方向离散化的数据 $\mathcal R f$ 重建 $f$ 时所产生的视角混叠伪影。该公式是渐近的，在采样率 $\epsilon\to0$ 的极限下建立。所提出的方法不要求 $f$ 是带限函数。针对经典拉东变换和广义拉东变换（在圆上积分）进行的数值实验验证了该公式的准确性。