Liu X, Defrise M, Michel C, Sibomana M, Comtat C, Kinahan P, Townsend D
Division of Nuclear Medicine, Vrije Universiteit Brussel, Belgium.
IEEE Trans Med Imaging. 1999 Aug;18(8):657-64. doi: 10.1109/42.796279.
The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.
容积式正电子发射断层显像（PET）成像中数据处理的高计算成本仍然阻碍着这项成功技术的常规应用，尤其是在动态研究的情况下。本文描述了基于精确重排方程的两种新算法，可用于加速三维（3 - D）PET数据的处理。第一种算法FOREPROJ是一种快速前向投影算法，它允许直接从二维（2 - D）透射扫描计算三维衰减校正因子（ACF），而无需先重建衰减图然后再进行三维前向投影。FOREPROJ的使用将三维ACF的估计速度提高了五倍多。第二种算法FOREX是一种重排算法，与标准重投影算法（3DRP）相比，其速度也快了五倍多，并且在大轴向孔径情况下不会出现由更快的近似傅里叶重排（FORE）方法产生的图像失真。然而，对于大多数现有的扫描仪来说，可能不需要FOREX，因为轴向孔径不够大，在临床数据上无法显示出比FORE更好的效果。这两种算法都已实现，并应用于为具有大轴向孔径（30度）的扫描仪模拟的数据，以及用ECAT HR和ECAT HR +扫描仪采集的数据。结果表明，这些算法具有出色的准确性，并且在正弦图大小为2的幂次方时能显著加速。
