Image reconstruction in positron emission tomography (PET) is conventionally regarded as the algorithm applied to the acquired data to produce images used for estimation of physiological parameters, or to determine the presence of disease. There are numerous approaches to image reconstruction, and the method chosen has a significant impact on the utility of PET. The use of iterative image reconstruction algorithms and the use of resolution modelling ("resolution recovery") are two specific advances from recent years which have demonstrated marked improvements in image quality. This paper considers three main aspects of PET image reconstruction in which there are still promising possibilities for further advance: (i) full consideration of the raw acquired PET data (with minimal pre-processing), (ii) careful selection of the parameters to estimate and (iii) accurate definition of the system matrix, which maps the parameters to the measurement space. Specific examples for these three areas include (i) the full use of timing, position and energy information, (ii) selecting physiological parameters as the unknowns to estimate and (iii) using Monte Carlo simulation to model the PET scanner and patient, in conjunction with time-dependent MRI or CT anatomical information to render the model more accurate. Present computational constraints mean that limited but practical methods have to be used, which to some extent compromise the full capabilities of image reconstruction in all of the aforementioned areas of promise. Nonetheless, this paper comments on possible ways forward without being overly concerned about the current limitations.
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