直线分布式光源CT是近年来快速发展起来的新型断层扫描成像方式，它通过多光源高速交替出束实现CT投影数据的采集，避免了CT机架的旋转，这种新型静态CT在提高CT扫描成像速度、简化系统设计等方面有着很大的优势，有望成为CT研究领域的重大突破。本文围绕基于直线分布式光源的新型静态CT，在成像理论、重建算法、以及成像优化策略等方面展开研究工作。 基于直线分布式光源的新型静态CT成像是一种重要的非标准扫描轨迹成像，其投影数据采样具有特殊性， 一直缺失高效的解析重建方法，亟需突破现有成像理论实现关键技术创新。在对该新型静态CT扫描模式进行数学建模以及深入分析的基础上，本文创新地引入了投影几何加权和物体变形，在国际上率先推导出了直线分布式光源静态CT的傅里叶切片定理，从而建立了该新型静态CT投影数据和被扫描物体在频域空间中的映射关系，并奠定了其图像重建的理论基础，对于投影数据采样形式的理解与分析、系统的设计与优化有着重要的指导意义。 在重建算法方面：本文提出了直接滤波反投影重建方法和冗余数据处理权重策略，实现了投影数据的最大化利用，与传统重排平行束方法相比，能保持更高的空间分辨率且对于截断投影的敏感性较低；进一步，利用几何加权投影是变形物体的Linogram采样这一重要性质，本文推导和发展了基于Linogram的直接傅立叶重建方法，它和滤波反投影重建方法相比，具有运行速度快的优势；为了将神经网络强大的学习能力迁移到图像重建任务中来，本文通过数学建模将Linogram解析重建理论作为先验知识引入到了神经网络的设计中来，建立了第一个端到端、数据驱动式、参数可学习的Linogram重建神经网络(Linogram-Net)，它可以通过网络的训练来减少有限角度重建伪影并提高重建图像的质量。 在成像优化策略方面：为了改善投影截断问题对于滤波反投影重建方法和Linogram解析重建方法的限制，提出了截断投影补全策略，可以抑制截断伪影并进一步扩大重建ROI的尺寸；为了实现三维扫描成像，提出了倾斜直线扫描模式，并进一步建立了对应的三维重建算法。以上的成像优化策略对于增加重建方法的灵活性并拓展其适用范围有着很大的意义。 本文的研究成果填补了直线分布式光源静态CT在解析重建理论和方法上的空白，为它的发展和应用提供了重要算法基础和关键技术支撑。数值仿真实验以及实际系统实验均验证了本文提出的理论和方法的有效性。

The CT with linearly distributed sources is a new architecture of computed tomography developed rapidly in the recent years, in which the projection data is acquired through the sequential firing of multiple X-ray sources in an ultra-fast manner. Without the gantry rotation, such a new concept of stationary CT has great advantages in improving the speed of CT scans and simplifying the system design, which will make a breakthrough in the research field of CT. This thesis focuses on the novel stationary CT with linearly distributed sources, in which imaging theory, reconstruction algorithms and imaging optimization strategies will be investigated and included. The novel stationary CT with linearly distributed sources involves important non-standard scanning trajectory and special projection sampling, for which there are no effective analytic reconstruction methods. Therefore, it's urgent to break through the existing imaging theory and make innovation of key technologies. Based on the mathematical modeling and in-depth analysis of the novel stationary CT with linearly distributed sources, geometry weighting of projection and deformation of object are introduced. The Fourier slice theorem of the stationary CT with linearly distributed sources is firstly derived, and the mapping relation between the projection data and scanned object is then established in the Fourier space. The theorem provides a sound theoretical basis for the image reconstruction algorithms, and it's of great significance for understanding and analysis of projection data sampling as well as design and optimization of the system. In the aspect of reconstruction algorithms: This thesis proposes a direct fileted backprojection (FBP) reconstruction method, and presents a weighting strategy to deal with the redundancy problems which can maximize the usage of projection data. Compared with the rebinning-to-parallel-beam algorithm, the proposed FBP method can obtain a higher spatial resolution, and is less sensitive to truncated projection data; In addition, based on the important property that the geometry weighted projection is the linogram sampling of the deformed object, this thesis derives and develops a Linogram reconstruction method which is a direct Fourier reconstruction method. The Linogram method is faster than the FBP method; In order to transfer the powerful learning ability of neural network to the task of image reconstruction, through mathematical modeling, the Linogram reconstruction theory is introduced into the design of neural network as prior knowledge. As a result, the first end-to end, data-driven and parameter-learnable Linogram reconstruction neural network (Linogram-Net) is established in this thesis, which can suppress the artifacts and improve the image quality for the limited-angel reconstruction through the network training. In the aspect of imaging optimization strategies: To reduce the adverse effect of the truncated projection on the FBP and Linogram reconstruction methods, a completion strategy for truncated projection is proposed in this thesis which can alleviate the truncation artifacts and expand the reconstruction ROI; To achieve 3D scanning and imaging, a tiling straight-line scanning mode is explored and the corresponding reconstruction algorithm is then derived. The above imaging optimization strategies are beneficial for increasing the feasibility and expanding the application scope for reconstruction methods. The findings of this thesis fill in the blank of the analytic reconstruction theory and method for the stationary CT with linearly distributed sources, which further provides important algorithms and key technology support for its development and application. The numerical and real experiments both validate the effectiveness of the proposed theories and methods in this thesis.