Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these approaches inherit the limitations of multiple-exposure fusion strategy. To overcome these disadvantages, the modulo Radon transform (MRT) has been proposed. The MRT is based on a co-design of hardware and algorithms. In the hardware step, Radon transform projections are folded using modulo non-linearities. Thereon, recovery is performed by algorithmically inverting the folding, thus enabling a single-shot, HDR approach to tomography. The first steps in this topic established rigorous mathematical treatment to the problem of reconstruction from folded projections. This paper takes a step forward by proposing a new, Fourier domain recovery algorithm that is backed by mathematical guarantees. The advantages include recovery at lower sampling rates while being agnostic to modulo threshold, lower computational complexity and empirical robustness to system noise. Beyond numerical simulations, we use prototype modulo ADC based hardware experiments to validate our claims. In particular, we report image recovery based on hardware measurements up to 10 times larger than the sensor's dynamic range while benefiting with lower quantization noise ($\sim$12 dB).

翻译：受计算摄影中多曝光融合方法的启发，近年来一些研究者探索了高动态范围（HDR）X射线成像与断层扫描技术。尽管这些方法取得了令人鼓舞的结果，但它们继承了多曝光融合策略的局限性。为克服这些缺陷，研究者提出了模数Radon变换（MRT）。MRT基于硬件与算法的协同设计：在硬件环节中，Radon变换投影通过模数非线性进行折叠；随后，通过算法反演折叠过程实现重建，从而提供单次曝光的HDR断层扫描方案。该领域的前期工作已为折叠投影重建问题建立了严格的数学基础。本文进一步提出一种基于傅里叶域恢复的新算法，并给出数学保证。该算法的优势包括：在无需依赖模数阈值的前提下实现更低采样率的恢复、更低的计算复杂度以及对系统噪声的经验鲁棒性。除数值仿真外，我们通过基于模数ADC原型的硬件实验验证了所述结论。特别地，我们报道了基于硬件测量的图像恢复结果：在实现传感器动态范围10倍以上的恢复能力的同时，获得了更低的量化噪声（约12分贝）。