Analytic time-of-flight positron emission tomography reconstruction: two-dimensional case

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.