$\u211d^2$中广义Radon变换的视图混叠分析
Analysis of view aliasing for the generalized Radon transform in $\mathbb R^2$
AI总结：
本文针对平面广义Radon变换，推导了分段光滑函数从视图方向离散数据重建时的视图混叠伪影渐近公式，无需带限假设，数值实验验证了其准确性。
摘要：
本文研究平面上的广义Radon变换$\u2112$。设$f$为分段光滑函数，沿光滑曲线$\u212b$存在跳变。我们推导了一个公式，可精确描述当$f$从沿视图方向离散化的数据$\u2112 f$重建时，$\u212b$以外区域的视图混叠伪影。该公式为渐近形式，在采样率$\u21920$的极限下成立。所提方法不要求$f$是带限的。针对经典Radon变换和（沿圆周积分的）广义Radon变换的数值实验验证了该公式的准确性。
英文摘要：
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 $ε\to0$. 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.
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