Defrise M, Kinahan P E, Townsend D W, Michel C, Sibomana M, Newport D F
Division of Nuclear Medicine, Free University of Brussels AZ-VUB, Belgium.
IEEE Trans Med Imaging. 1997 Apr;16(2):145-58. doi: 10.1109/42.563660.
This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18 degrees axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.
本文提出了两种用于三维正电子发射断层扫描（PET）数据重建的新重排算法。重排算法是一种先将三维数据整理成普通二维数据集的算法，该二维数据集中包含要重建的每个横断面切片的一幅正弦图；然后通过对每个切片应用二维重建方法（如滤波反投影）来恢复三维图像。这种方法能显著加快三维重建速度，这对于涉及动态采集或全身成像的应用尤为有用。第一种新算法是通过离散精确的解析反演公式得到的。第二种算法称为傅里叶重排算法（FORE），它是近似算法，但基于对数据进行二维傅里叶变换可实现高效实现。第二种算法已被实现，并应用于使用新一代PET系统采集的数据以及具有18度轴向孔径的扫描仪的模拟数据。将重建图像与使用三维重投影算法（3DRP）获得的图像进行比较，3DRP是标准的“精确”三维滤波反投影方法。结果表明，FORE为3DRP提供了可靠的替代方案，同时处理时间减少了一个数量级。
