In a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. Analytical image reconstruction algorithm exits for TOF PET which emulates the iterative Landweber algorithm. This paper introduces such an algorithm, focusing on two-dimensional (2D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first, and then a 2D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and a profile function may be used along the projection LOR. The 2D filter depends on the TOF timing resolution as well as the backprojection profile function. In order to emulate the iterative algorithm effects, a Fourier-domain window function is suggested. This window function has a parameter, k, which corresponds to the iteration number in an iterative algorithm.

中文翻译：

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飞行时间正电子发射断层扫描成像重建：二维情况

在正电子发射断层扫描（PET）扫描仪中，飞行时间（TOF）信息为我们提供了沿响应线（LOR）的大致事件位置。使用TOF信息进行PET图像重建可以减少图像噪声。最新的TOF PET图像重建使用迭代算法。存在用于TOF PET的分析图像重建算法，该算法模拟了迭代的Landweber算法。本文介绍了这样一种算法，着重于二维（2D）重建。所提出的算法采用反投影滤波的形式，其中先执行反投影，然后将2D滤波器应用于反投影图像。对于列表模式数据，以逐个事件的方式执行反投影，并且可以沿投影LOR使用配置文件功能。2D滤波器取决于TOF时序分辨率以及反投影轮廓函数。为了模拟迭代算法的效果，建议使用傅立叶域窗函数。该窗口函数具有一个参数k，它对应于迭代算法中的迭代次数。