分布式光源静态 CT 系统利用在物体周围分布的 X 射线源的高速切换来实现 CT 扫描， 其等效转速远高于传统螺旋 CT 的滑环机械转动，能满足诸多应用场景对快速 CT 成像的迫切需求。取消滑环结构还带来了设备体积减小、运动摩擦损耗减小、维护成本降低等诸多优势。故静态 CT 被公认为新一代 CT 系统的最佳选择。本文围绕该系统 CT 重建方法进行研究，针对该系统独特的成像几何带来的稀疏视角重建、有限角重建和非标准轨迹重建三个核心问题进行深入探索。 首先，本文针对静态 CT 的稀疏重建需求，提出了基于反投影卷积神经网络的 CT 重建方法。本章首先证明了 BPF 重建算法可以由反投影运算和 CNN 网络进行拟合，且字典学习的图像优化方法可以被视为神经网络的一种特例。在此两者的基础上，本章设计了多分辨率非局部网络结构。据作者所知，本文是第一个把基于二维解卷积和基于 PI 线的两种 BPF 类重建算法思路融合在一起的卷积神经网络，该算法能够同时完成重建与图像优化，从而能实现较高精度的稀疏投影重建。 其次，针对静态 CT 缺失投影数据修复的需求，本文设计了跨域联合优化的 CT 重建方法。首先基于解析延拓理论证明了有限角问题解的唯一性，而其缺失投影恢复函数可以通过人工神经网络进行拟合。在此基础上，本文提出了一种可实现不完备投影数据修补的自监督重建网络结构，该算法将解析重建整合进神经网络，具有速度快、具备自我纠正能力、对数据需求少等特点。不同于以前深度学习模型训练和推断分离的部署模式，该网络具有自监督闭环反馈网络结构，能够在线挖掘难点样本并于休眠时间自行复习，以增强自身的泛化能力。 最后，静态 CT 扫描几何不同于传统螺旋 CT ，直线排布光源与探测器几何对称。参考逆 CT 的思路，可增加光源长度以减少探测器面积，节省设备占用空间。针对非标准轨迹重建问题，本文构建了基于偏微分方程的自监督 CT 重建框架。首先基于粒子输运方程定义了通量分布一致性指标，为 CT 重建问题提供了一种新的优化目标，相比于传统迭代算法关注的投影残差，该指标的权重在图像域分布均匀。随后利用多粒子动力学方程的数值求解工具，构建了一致性感知并行子集的卷积神经网络。利用该算法反向传播能力，可经由数据驱动学习模型参数，灵活适应各种扫描几何。该方法具备自监督学习能力，可在无配对数据的情况下，完成迁移学习，因此在医疗等数据收集成本高的领域中有广泛应用空间。

The stationary CT system based on distributed sources uses high-speed switching of X-ray sources distributed around the object to achieve CT scanning. Its equivalent rotation speed is much higher than the mechanical rotation of the slip ring of traditional spiral CT, so that it meets the urgent demand for rapid CT imaging in many application scenarios. The elimination of the slip ring brings many advantages such as reduced noise volume, reduced movement friction losses, and reduced maintenance costs. Therefore, stationary CT is recognized as the best choice for the next generation of CT systems. This article focuses on stationary CT reconstruction method, and conducts in-depth exploration on the following three core issues brought by the unique imaging geometry of the CT system: sparse view reconstruction, limited angle reconstruction and non-standard trajectory reconstruction.First of all, this article proposes a CT reconstruction method based on back-projection convolutional neural network for the sparse reconstruction requirements of stationary CT. This chapter first proves that the BPF reconstruction algorithm can be fitted by joining back-projection operation and CNN, and the image optimization method of dictionary learning is regarded as a special case of neural network. Based on these, this chapter designs a multi-resolution non-local network structure. As far as the author knows, this article is the first convolutional neural network that combines two BPF-type reconstruction algorithms, one based on two-dimensional deconvolution and the other based on PI line. This algorithm is capable to complete reconstruction and image optimization at the same time, thereby enabling high-precision reconstruction from sparse-view projection.Secondly, to address the need of recovering the missing projection data for stationary CT, this paper designs a cross-domain joint optimization CT reconstruction method. The solution of the limited-angle CT problem is proved unique based on the analytical continuation theory, and the missing projection data recovery function can be fitted by artificial neural network. On this basis, this paper proposes a self-supervised reconstruction network structure that inpaints incomplete projection data. The algorithm integrates analytical reconstruction into the neural network and has the advantages of higher speed, self-correction ability and less data demand. Different from the previous deployed deep learning model which separates training and inference phases ,the network has a self-supervised closed-loop feedback network structure, which mines difficult samples online and reviews them during sleep time to enhance the algorithm's generalization ability.Finally, the scanning geometry of stationary CT is different from traditional spiral CT. The linear arrangement of X-ray sources and detectors of stationary CT are geometrically symmetrical. With reference to the idea of ?​inverse CT, increasing the length of the distributed sources is capable to reduce the area of ?​the detector and therefore save equipment space. Aiming at the non-standard trajectory CT problem, this paper constructs a self-supervised CT reconstruction framework based on partial differential equations. First, the flux distribution consistency index is defined based on the particle transport equation, which provides a new optimization goal for CT reconstruction problems. Compared with the projection residuals that traditional iterative algorithms focus on, the weight of the flux distribution consistency index is evenly distributed in the image domain. Then, using the numerical solution tool of multi-particle dynamics equations, a convolutional neural network with consistent perception of parallel subsets is proposed. Because of the backpropagation capability of this algorithm, model parameters can be learned through data-driven method, and various scanning geometries can be flexibly adapted. This method has the ability of self-supervised learning, which enables it to complete transfer learning without paired data, and therefore has a wide range of applications in fields with high data collection costs such as medical care.