Construction function for three-dimensional sinograms of the time-of-flight positron emission tomograph

Abstract
A new method of image reconstruction for the time-of-flight positron emission tomograph (TOF-PET) has been developed. A construction function was found to reconstruct a positron image by directly convoluting three-dimensional sinograms. This construction function consists of the product of the well-known function for a conventional PET and the response function of time-of-flight measurement system for annihilation γ rays.