3D Compton scattering imaging (CSI) is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study. The so-called Compton scattering rules the collision of particles with electrons and describes their energy loss after scattering. Although physically relevant, multiple-order scattering was so far not considered and therefore, only first-order scattering is generally assumed in the literature. The purpose of this work is to argument why and how a contour reconstruction of the electron density map from scattered measurement composed of first- and second-order scattering is possible (scattering of higher orders are here neglected). After the development of integral representations for the first- and second-order scattering, we approximate these models by Fourier integral operators (FIO) and study their smoothness properties. The second-order scattered radiation reveals itself to be structurally smoother than the radiation of first-order indicating that the contours of the electron density are essentially encoded within the first-order part. This opens the way to contour-based reconstruction techniques when considering multiple scattered data. Our main results, modeling and reconstruction scheme, are successfully implemented on synthetic and Monte-Carlo data.

3D 康普顿散射成像 (CSI) 是一个即将到来的概念，它利用研究对象的电子结构引起的光子散射。所谓的康普顿散射统治着粒子与电子的碰撞，并描述了它们散射后的能量损失。尽管物理上相关，但到目前为止还没有考虑多阶散射，因此，文献中通常只假设一阶散射。这项工作的目的是论证为什么以及如何从由一阶和二阶散射组成的散射测量中重建电子密度图的轮廓是可能的（这里忽略高阶散射）。在开发了一阶和二阶散射的积分表示之后，我们通过傅立叶积分算子 (FIO) 来近似这些模型并研究它们的平滑特性。二阶散射辐射显示其自身在结构上比一阶辐射更平滑，这表明电子密度的轮廓基本上被编码在一阶部分内。在考虑多个分散数据时，这为基于轮廓的重建技术开辟了道路。我们的主要结果，建模和重建方案，在合成和蒙特卡洛数据上成功实现。在考虑多个分散数据时，这为基于轮廓的重建技术开辟了道路。我们的主要结果，建模和重建方案，在合成和蒙特卡洛数据上成功实现。在考虑多个分散数据时，这为基于轮廓的重建技术开辟了道路。我们的主要结果，建模和重建方案，在合成和蒙特卡洛数据上成功实现。