This paper is to investigate the high-quality analytical reconstructions of multiple source-translation computed tomography (mSTCT) under an extended field of view (FOV). Under the larger FOVs, the previously proposed backprojection filtration (BPF) algorithms for mSTCT, including D-BPF and S-BPF, make some intolerable errors in the image edges due to an unstable backprojection weighting factor and the half-scan mode, which deviates from the intention of mSTCT imaging. In this paper, to achieve reconstruction with as little error as possible under the extremely extended FOV, we propose two strategies, including deriving a no-weighting D-BPF (NWD-BPF) for mSTCT and introducing BPFs into a special full-scan mSTCT (F-mSTCT) to balance errors, i.e., abbreviated as FD-BPF and FS-BPF. For the first strategy, we eliminate this unstable backprojection weighting factor by introducing a special variable relationship in D-BPF. For the second strategy, we combine the F-mSTCT geometry with BPFs to study the performance and derive a suitable redundant weighting function for F-mSTCT. The experiments demonstrate our proposed methods for these strategies. Among them, NWD-BPF can weaken the instability at the image edges but blur the details, and FS-BPF can get high-quality stable images under the extremely extended FOV imaging a large object but requires more projections than FD-BPF. For different practical requirements in extending FOV imaging, we give suggestions on algorithm selection.

翻译：本文旨在研究扩展视场（FOV）下多源平移计算机断层扫描（mSTCT）的高质量解析重建。在较大视场下，先前针对mSTCT提出的反投影滤波（BPF）算法（包括D-BPF和S-BPF）因不稳定的反投影加权因子和半扫描模式，在图像边缘产生不可容忍的误差，偏离了mSTCT成像的初衷。为在极度扩展视场下实现尽可能低误差的重建，本文提出两种策略：一是为mSTCT推导无加权D-BPF（NWD-BPF），二是将BPF引入特殊全扫描mSTCT（F-mSTCT）以平衡误差，分别简记为FD-BPF和FS-BPF。对于第一种策略，我们通过引入D-BPF中的特殊变量关系，消除了不稳定的反投影加权因子。对于第二种策略，我们将F-mSTCT几何结构与BPF相结合，研究其性能，并推导适用于F-mSTCT的恰当冗余加权函数。实验验证了所提策略的有效性。其中，NWD-BPF可减弱图像边缘的不稳定性，但会模糊细节；FS-BPF在极度扩展视场下对大物体成像可获得高质量稳定图像，但所需投影数多于FD-BPF。针对扩展视场成像的不同实际需求，本文给出了算法选择建议。