Static CT With Sources and Detectors Distributed in a Multi-Segment Manner: System Analysis and Analytical Reconstruction

In this work, we investigate the feature of projection sampling and analytical reconstruction algorithms for a Static CT with sources and detectors distributed in a Multi-Segment manner (MS-StaticCT). MS-StaticCT is a generalized configuration of previous static linear CT systems offering enhanced design flexibility and utilization efficiency in both X-ray source and detector components. By analyzing the imaging geometry of single-segment source and detector pairs, we delved into the Radon space properties of MS-StaticCT and proposed a data sufficiency condition for system design. To explore the impact of the unique sampling characteristics of MS-StaticCT on reconstruction quality, we derived analytical algorithms under two popular pipelines filtered-backprojection (MS-FBP) and differentiated backprojection filtration (MS-DBF), and assessed their performance. Due to the non-uniform sampling and singular points between segments, the global filtration process of MS-FBP requires local rebinning. The local nature of differentiation enables convenient filtration without rebinning. Besides, to address insufficient data caused by optical obstruction by sources and detectors, we incorporated multiple imaging planes and designed a generalized weighting function that efficiently utilizes conjugate projections. Simulation studies on numerical phantoms and clinical CT data demonstrate the feasibility of MS-StaticCT and the proposed reconstruction algorithms. The results highlighted MS-DBF's superiority in accuracy and spatial resolution for multi-segment geometries without compromising noise performance compared to MS-FBP whose performance depends on the number of detector segments involved for each focal spot. Our study provides a comprehensive understanding of the essential data structure and basic reconstruction tailored for systems characterized by linear source trajectories and detectors.