Spatially Variant Resolution Modelling for Iterative List-Mode PET Reconstruction

A spatially variant resolution modelling technique is presented which estimates the system matrix on-the-fly during iterative list-mode reconstruction. This is achieved by redistributing the endpoints of each list-mode event according to derived probability density functions describing the detector response function and photon acollinearity, at each iteration during the reconstruction. Positron range is modelled using an image-based convolution. When applying this technique it is shown that the maximum-likelihood expectation maximisation (MLEM) algorithm is not compatible with an obvious acceleration strategy. The image space reconstruction algorithm (ISRA), however, after being adapted to a list-mode based implementation, is well-suited to the implementation of the model. A comparison of ISRA and MLEM is made to confirm that ISRA is a suitable alternative to MLEM. We demonstrate that this model agrees with measured point spread functions and we present results showing an improvement in resolution recovery, particularly for off-centre objects, as compared to commercially available software, as well as the standard technique of using a stationary Gaussian convolution to model the resolution, for equal iterations and only slightly higher computation time.