3D image reconstruction from a set of X-ray projections is an important image reconstruction problem, with applications in medical imaging, industrial inspection and airport security. The innovation of X-ray emitter arrays allows for a novel type of X-ray scanners with multiple simultaneously emitting sources. However, two or more sources emitting at the same time can yield measurements from overlapping rays, imposing a new type of image reconstruction problem based on nonlinear constraints. Using traditional linear reconstruction methods, respective scanner geometries have to be implemented such that no rays overlap, which severely restricts the scanner design. We derive a new type of 3D image reconstruction model with nonlinear constraints, based on measurements with overlapping X-rays. Further, we show that the arising optimization problem is partially convex, and present an algorithm to solve it. Experiments show highly improved image reconstruction results from both simulated and real-world measurements.

使用发射器阵列的X射线扫描仪可同时产生多个发射源，但可能存在测量值重叠的非线性约束。本文提出了一种新的基于测量值重叠的非线性约束的3D图像重建模型，并提出了一种可解决该问题的算法。实验结果表明，模型在模拟和真实测量中均具有高度优异的图像重建效果。

带重叠区域的X射线测量下的3D图像重建