Post-Reconstruction PET Resolution Modelling by Synthesised Image Reconstruction

Resolution recovery techniques in PET aim to improve spatial resolution, signal-to-noise ratio and quantitative accuracy. Whilst several factors are responsible for the degradation of spatial resolution, image-space point spread function (PSF) modelling has been developed to compensate for resolution losses. For example, the widely used Richardson-Lucy (RL) algorithm can be used to model the PSF and improve spatial resolution. However, when the RL algorithm is applied to post-reconstruction resolution recovery, noise rapidly develops even in early iterations. On the other hand, incorporation of the PSF directly into iterative reconstruction algorithms has shown potential benefits (depending on the task), with less rapid noise accumulation compared to RL, and with resolution improvements compared to conventional reconstruction with no PSF modelling. However, PSF-based reconstruction requires raw projection data and knowledge of the forward/back-projectors relating to the scanner's geometry, and if these are unavailable the technique becomes infeasible. In this proof-of-concept work, we propose a novel post-reconstruction resolution recovery technique based on synthesising an image reconstruction problem. Tomographic data are synthesised from the supplied image and a new inverse problem with embedded PSF resolution modelling is then solved. This work evaluates the proposed method in 2D using a simulated phantom at various count levels. We compare the performance of the proposed method with the RL algorithm and PSF-based maximum likelihood expectation maximisation (MLEM) reconstruction. In conditions which match typical clinical scans (e.g. low iteration numbers and counts), the proposed method achieves a substantially lower root mean square error than the RL algorithm. The performance of the proposed method is comparable to PSF-based reconstruction despite the proposed method having no access to the original sinogram data.