This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem linking the Laplacian of the Radon transform (RT) of a function to its MRT in combination with the classical filtered back projection formula for inverting the RT. Discretizing the inversion formula using Fourier techniques leads to our novel Laplacian Modulo Unfolding - Filtered Back Projection algorithm, in short LMU-FBP, to recover a function from fully discrete MRT data. Our theoretical findings are finally supported by numerical experiments.

翻译：本文证明了一种针对所谓模Radon变换（MRT）的新型解析反演公式，该变换建模了近期提出的一种单次高动态范围断层成像方法。该公式基于求解一个泊松问题，该问题将函数Radon变换（RT）的拉普拉斯算子与其MRT相关联，并结合了反演RT的经典滤波反投影公式。利用傅里叶技术对该反演公式进行离散化，导出了我们新颖的拉普拉斯模展开-滤波反投影算法（简称LMU-FBP），用于从完全离散的MRT数据中恢复函数。我们的理论结果最终得到了数值实验的支持。