System models for PET statistical iterative reconstruction: A review

Positron emission tomography (PET) is a nuclear imaging modality that provides in vivo quantitative measurements of the spatial and temporal distribution of compounds labeled with a positron emitting radionuclide. In the last decades, a tremendous effort has been put into the field of mathematical tomographic image reconstruction algorithms that transform the data registered by a PET camera into an image that represents slices through the scanned object. Iterative image reconstruction methods often provide higher quality images than conventional direct analytical methods. Aside from taking into account the statistical nature of the data, the key advantage of iterative reconstruction techniques is their ability to incorporate detailed models of the data acquisition process. This is mainly realized through the use of the so-called system matrix, that defines the mapping from the object space to the measurement space. The quality of the reconstructed images relies to a great extent on the accuracy with which the system matrix is estimated. Unfortunately, an accurate system matrix is often associated with high reconstruction times and huge storage requirements. Many attempts have been made to achieve realistic models without incurring excessive computational costs. As a result, a wide range of alternatives to the calculation of the system matrix exists. In this article we present a review of the different approaches used to address the problem of how to model, calculate and store the system matrix.