Separating the object and detector dependent characteristics of projector/backprojector through use of an intermediate stage

A new projector/backprojector pair for iterative reconstruction using an intermediate stage is proposed. The aim was to separate the object-dependent and the detector-dependent characteristics into two separate modules. In two-dimensions (2D) the intermediate stage is a circle surrounding the object. An emission distribution is calculated at the circle from the initial estimate of the source distribution in the object. This leads to the probability that a photon, coming from the source distribution, leaves the circle surrounding the object at a certain point, going in a specific direction. Iterative reconstruction uses the total system sensitivity calculated from the integration over the distribution and the individual sensitivity for a given bin location, derived from the integration over a fraction of the distribution. The fraction is calculated from the geometry of the detection system. This information can be used in the forward and backprojection of an iterative reconstruction method to obtain a more accurate model of the processes involved. By using the intermediate stage the authors obtained a structure that can very easily be adapted to different types of collimators, taking into account the distance dependent resolution, and acquisition protocols. The method can even be used for list-mode reconstruction.