Defrise Michel, Casey Michael E, Michel Christian, Conti Maurizio
Department of Nuclear Medicine, Vrije Universiteit Brussel, AZ-VUB, B-1090 Brussels, Belgium.
Phys Med Biol. 2005 Jun 21;50(12):2749-63. doi: 10.1088/0031-9155/50/12/002. Epub 2005 May 25.
This paper explores fast reconstruction strategies for 3D time-of-flight (TOF) positron emission tomography (PET), based on 2D data rebinning. Starting from pre-corrected 3D TOF data, a rebinning algorithm estimates for each transaxial slice the 2D TOF sinogram that would have been acquired by a single-ring scanner. The rebinned sinograms can then be reconstructed using any algorithm for 2D TOF reconstruction. We introduce TOF-FORE, an approximate rebinning algorithm obtained by extending the Fourier rebinning method for non-TOF data. In addition, we identify two partial differential equations that must be satisfied by consistent 3D TOF data, and use them to derive exact rebinning algorithms and to characterize the degree of the approximation in TOF-FORE. Numerical simulations demonstrate that TOF-FORE is more accurate than two different TOF extensions of the single-slice rebinning method, and suggest that TOF-FORE will be a valuable tool for practical TOF PET in the range of axial apertures and time resolutions typical of current scanners.
本文基于二维数据重排，探索了用于三维飞行时间（TOF）正电子发射断层扫描（PET）的快速重建策略。从预校正的三维TOF数据开始，一种重排算法为每个横断面切片估计单环扫描仪本应采集到的二维TOF正弦图。然后，可以使用任何二维TOF重建算法对重排后的正弦图进行重建。我们引入了TOF-FORE，这是一种通过扩展用于非TOF数据的傅里叶重排方法获得的近似重排算法。此外，我们确定了一致的三维TOF数据必须满足的两个偏微分方程，并使用它们来推导精确的重排算法，并刻画TOF-FORE中的近似程度。数值模拟表明，TOF-FORE比单切片重排方法的两种不同TOF扩展更准确，并表明TOF-FORE将成为当前扫描仪典型轴向孔径和时间分辨率范围内实际TOF PET的一个有价值的工具。
