List-mode reconstruction for TOF PET by estimating annihilation positions

To date, iterative image reconstruction methods are often preferred over analytic methods for position emission tomography (PET) because the former can allow the use of accurate physical and statistical models of the imaging system, as well as a priori information, to produce images having better resolution and statistics than the latter. Iterative methods typically model the image by using voxels and seek to solve the unknown image intensity inside each voxel by employing a certain optimization criterion. In this approach, the image voxel needs to be carefully selected as the spatial resolution of the resulting image is inherently limited by the voxel size. When using large voxels, the image may not have adequate resolution for visualizing small abnormalities; however, identifying small lesions is of critical significance for achieving early diagnosis of disease. On the other hand, using small voxels can greatly increase the computation complexity of the reconstruction process. Moreover, it can lead to greater image noise and obscure small and low-contrast structures. In this paper, we propose an alternative image representation to enable reconstructing time-of-flight (TOF) PET data without employing image voxels. We will present the theoretical derivation and develop a fixed-point algorithm for finding the maximum-likelihood solution. We will also show promising initial results when applying the developed algorithm to reconstruct one-dimensional (lD) TOF PET data.