Positron emission tomography (PET) has been widely used for the diagnosis of serious diseases including cancer and Alzheimer's disease, based on the uptake of radiolabelled molecules that target certain pathological signatures. Recently, a novel imaging mode known as positronium lifetime imaging (PLI) has been shown possible with time-of-flight (TOF) PET as well. PLI is also of practical interest because it can provide complementary disease information reflecting conditions of the tissue microenvironment via mechanisms that are independent of tracer uptake. However, for the present practical systems that have a finite TOF resolution, the PLI reconstruction problem has yet to be fully formulated for the development of accurate reconstruction algorithms. This paper addresses this challenge by developing a statistical model for the PLI data and deriving from it a maximum-likelihood algorithm for reconstructing lifetime images alongside the uptake images. By using realistic computer simulation data, we show that the proposed algorithm can produce quantitatively accurate lifetime images.

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