3D-FRP: Direct fourier reconstruction with Fourier reprojection for fully 3-D PET
3D-FRP: Direct fourier reconstruction with Fourier reprojection for fully 3-D PET
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DOI：
10.1109/23.958359
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发表时间：
2001-08-01
影响因子：
1.8
通讯作者：
Lewitt, RM
中科院分区：
文献类型：
--
作者：
Matej, S;Lewitt, RM
直接傅立叶方法(DIM)是基于三维傅立叶变换(FT)和平行射线投影的二维傅立叶变换(2-D)之间的关系来重建三维物体的。直接傅立叶方法有可能实现非常快速的重建，但直接实现该方法会导致不满意的结果。本文提出了一种直接傅立叶方法用于具有不完全倾斜投影的全三维正电子发射断层扫描(PET)数据(3D-FRP)，其结果与慢得多的三维过滤反投影法(3DRP)相同或更好，同时也是一种快速但精度较低的方法，该方法使用傅立叶反投影(FORE)然后逐层重建。与3DRP一样，3D-FRP基于反演公式的离散化，因此对于大斜角是几何精确的，并且这两种方法都涉及对初始图像的重新投影。3D-FRP方法的两个关键步骤是从通过傅立叶空间原点的平面上投影的二维变换的样本估计图像的三维变换的样本，反之亦然。这些步骤使用网格化策略，并结合了在变换和图像域中加权的新方法。实验结果表明，该方法可以在较短的重建时间内获得较好的图像精度。
The direct Fourier method (DIM) for three-dimensional (3-D) reconstruction of a 3-D volume is based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The direct Fourier method has the potential for very fast reconstruction, but a straightforward implementation of the method leads to unsatisfactory results. This paper presents an implementation of the direct Fourier method for fully 3-D positron emission tomography (PET) data with incomplete oblique projections (3D-FRP) that gives results as good as, or better than, those of a much slower 3-D filtered backprojection method (3DRP), and in the same time as a fast but less accurate method using Fourier rebinning (FORE) followed by slice-by-slice reconstruction. In common with 3DRP, 3D-FRP is based on a discretization of an inversion formula, so it is geometrically accurate for large oblique angles, and both methods involve reprojection of an initial image. The critical two steps in the 3D-FRP method are the estimations of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for reprojection. These steps use a gridding strategy, combined with new approaches for weighting in the transform and image domains. Our experimental results confirm that good image accuracy can be achieved together with a short reconstruction time.