静态CT因其独特的多源多探结构，在成像速度、系统稳定性与场景适应性方面展现出显著优势。然而，非传统的源探几何结构也带来了成像建模与图像重建中的一系列数学挑战，目前尚缺乏系统的理论支持。在多种静态CT几何形式中，源探异面成像模式因其采样完备性与成像效率而具有潜在优势。本文以源探异面锥束静态CT为对象，围绕其解析重建方法、锥束数据不完备性及多源散射校正等核心问题，系统开展建模分析与算法研究，旨在推动该成像模式的理论发展与工程落地。针对源探异面锥束静态CT中异面排布与多源同步出束的成像特性，本文系统建立了其成像过程的数理模型，并深入分析了“多线分布”采样特性、锥束数据不完备、多源通量不一致及多源散射伪影等关键问题。在解析重建方面，本文从源探异面锥束静态CT出发，提出了广义等角几何CT（GEGCT）成像模式，并建立了基于径向偏移比率的直接加权滤波反投影算法（DW-FBP）。相比重排解析重建算法，DW-FBP算法在面对“多线分布”的投影数据时，具有更高的重建分辨率。虽然DW-FBP算法是近似的FBP算法，但其重建精度与精确的FBP重建算法精度相当。DW-FBP算法有效解决了平移不变性失效和动态采样问题，实现了几何建模、重建过程与系统设计参数间的协同优化。针对锥束数据的不完备性，本文提出了一种结合解析重建先验的隐式神经表示方法（FDK-INR）。该方法融合三维解析重建结果与隐式神经表示的优势，较传统的直接隐式方法具备更高的重建精度与更快的收敛速度。此外，针对源探异面锥束静态CT中数据缺失引起的半扫描环状伪影，本文提出一种几何约束策略，有效抑制伪影并显著拓展成像覆盖范围。在多源散射校正方面，本文创新性地引入了康普顿图概念，用于刻画视场外的大角度散射信号的分布，并根据源探异面静态CT的成像特点设计了基于深度学习的多源散射估计网络ComptoNet，通过康普顿图先验引导和解耦建模实现高精度多源散射估计，显著提升了图像质量。本研究系统性地分析了源探异面锥束静态CT的数理特性与关键技术问题，围绕解析重建、锥束重建及散射校正等方面提出了相应的建模方法与创新算法，为该技术的理论发展与工程实现奠定了坚实基础。
Stationary CT, with its unique multi-source, multi-detector static configuration, demonstrates significant advantages in imaging speed, system stability, and adaptability to various scenarios. However, its non-traditional source-detector geometry introduces a series of mathematical challenges in imaging modeling and image reconstruction, and currently lacks systematic theoretical support. Cone-Beam stationary CT with off-plane distributed sources offers comparative advantages in both sampling completeness and acquisition speed. This study focuses on key issues of this imaging mode, including analytical reconstruction methods, cone-beam data incompleteness, and multi-source scatter correction, through comprehensive modeling analysis and algorithm development, aiming to advance its theoretical foundation and engineering applications.Based on the distinctive imaging characteristics of cone-Beam stationary CT with off-plane distributed sources, namely its off-plane source-detector arrangement and simultaneous multi-source emission, this work systematically establishes a mathematical model of the imaging process. It conducts an in-depth analysis of its "multi-line distributed" sampling characteristics, cone-beam data incompleteness, multi-source flux inconsistency, and scatter-induced artifacts.For analytical reconstruction, this study proposes a novel imaging mode termed Generalized Equiangular Geometry CT (GEGCT), and develops a Directly Weighted Filtered Backprojection algorithm (DW-FBP) based on radial offset ratios. Compared to rebinning-based analytical reconstruction methods, DW-FBP achieves higher spatial resolution when dealing with "multi-line distributed" projection data. Although DW-FBP is an approximate form of the FBP algorithm, its reconstruction accuracy is comparable to that of exact FBP. It effectively addresses issues of translational invariance loss and dynamic sampling, enabling coordinated optimization among geometric modeling, reconstruction processes, and system design parameters.To address the problem of cone-beam data incompleteness, this work further proposes an implicit neural representation method with analytical priors (FDK-INR). By integrating the advantages of 3D analytical reconstruction and implicit neural representations, FDK-INR achieves higher reconstruction accuracy and faster performance than direct neural representation methods. In addition, to suppress ring artifacts caused by incomplete data in off-plane cone-beam stationary CT, a geometric constraint strategy is proposed, significantly extending the imaging coverage.In terms of multi-source scatter correction, this study introduces the novel concept of a Compton map to characterize large-angle scatter signals from outside the field of view. Leveraging the imaging characteristics of off-plane stationary CT, a deep learning-based scatter estimation framework called ComptoNet is designed. Guided by the Compton map prior and decoupled modeling, ComptoNet enables high-precision estimation of multi-source scatter, significantly improving image quality.This study systematically analyzes the mathematical properties and critical challenges of cone-Beam stationary CT with off-plane distributed sources. By developing mathematical models and innovative algorithms for analytical reconstruction, cone-beam recovery, and scatter correction, it lays a solid foundation for the theoretical advancement and practical application of this imaging modality.
