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Data consistency conditions for truncated fanbeam and parallel projections

机译：截断的扇形光束和平行投影的数据一致性条件

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摘要

In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections.
机译：在根据投影进行图像重建时，数据一致性条件（DCC）是表达理想投影之间信息重叠的数学关系。 DCC已合并到用于正电子发射断层扫描，单光子发射计算机断层扫描和X射线计算机断层扫描（CT）的图像重建程序中。基于已发布的扇状线DCC，用于沿直线的非截断投影，作者最近宣布了新的DCC，可将其应用于经典（二维）图像重建中的截断平行投影。这些DCC采取多项式的形式进行投影的加权反投影。这项工作的目的是为截断的平行投影提供新的DCC，将这些条件扩展到圆形轨迹上的截断的扇形束投影，以数值示例验证条件，并提出如何将DCC应用于模型的模型。带有截断投影的患者运动估计中的玩具问题。

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