Windowed image reconstruction for time-of-flight positron emission tomography

It has been well recognized that, in comparison with the conventional positron emission tomography (PET), the differential-time measurements made available in time-of-flight (TOF) PET imaging can reduce the propagation of data noise in reconstruction and lead to images having better statistical quality. This observation has been the motivation driving the interest in developing TOF-PET systems. In this paper, we make new observations that can extend the use of TOF-PET. We develop a new mathematical formulation showing that the TOF information can be utilized to achieve new modes of reconstruction. In particular, it enables windowed and regions-of-interest reconstructions by use of TOF-PET measurements having a restricted coverage in the TOF or transverse direction, or both. A class of analytic algorithms is developed to perform such reconstructions. We employ computer-simulated TOF-PET data containing Poisson noise to validate the developed algorithms and evaluate their response to data noise with respect to a confidence-weighting analytic TOF-PET reconstruction method. We also demonstrate that in certain situations, the new reconstruction algorithms can generate images having improved statistics by recruiting suitable subsets of the TOF-PET data to minimize the use of deteriorating measurements in reconstruction. Potential implications of the new reconstruction approach to PET imaging are discussed.