X-ray and gamma-ray photons are widely used for imaging but require a mathematical reconstruction step, known as tomography, to produce cross-sectional images from the measured data. Theoretically, the back-to-back annihilation photons produced by positron–electron annihilation can be directly localized in three-dimensional space using time-of-flight information without tomographic reconstruction; however, this has not yet been demonstrated due to the insufficient timing performance of available radiation detectors. Here we develop techniques based on detecting prompt Cherenkov photons, which, when combined with a convolutional neural network for timing estimation, resulted in an average timing precision of 32 ps, corresponding to a spatial precision of 4.8 mm. We show this is sufficient to produce cross-sectional images of a positron-emitting radionuclide directly from the detected coincident annihilation photons, without using any tomographic reconstruction algorithm. The reconstruction-free imaging demonstrated here directly localizes positron emission and frees the design of an imaging system from the geometric and sampling constraints that are normally present for tomographic reconstruction.

X 射线和伽马射线光子广泛用于成像，但需要数学重建步骤（称为断层扫描）从测量数据生成横截面图像。理论上，正电子-电子湮灭产生的背靠背湮没光子可以利用飞行时间信息直接定位在三维空间中，无需进行断层扫描重建；然而，由于现有辐射探测器的定时性能不足，这一点尚未得到证实。在这里，我们开发了基于检测瞬发切伦科夫光子的技术，当与卷积神经网络相结合进行定时估计时，平均定时精度为 32 ps，对应于 4.8 mm 的空间精度。我们证明这足以直接从检测到的重合湮没光子生成正电子发射放射性核素的横截面图像，而无需使用任何断层扫描重建算法。这里演示的免重建成像直接定位正电子发射，并将成像系统的设计从断层扫描重建通常存在的几何和采样约束中解放出来。