The spatial resolution from Compton cameras suffers from measurement uncertainties in interaction positions and energies. The degree of degradation in spatial resolution is shift-variant (SV) over the field-of-view (FOV) because the imaging principle is based on the conical surface integration. In our study, the shift-variant point spread function (SV-PSF) is derived from point source measurements at various positions in the FOV and is incorporated into the system matrix of a fully three-dimensional, accelerated reconstruction, i.e. the listmode ordered subset expectation maximization (LMOSEM) algorithm, for resolution recovery. Simulation data from point sources were used to estimate SV and asymmetric parameters for Gaussian, Cauchy, and general parametric PSFs. Although little difference in the fitness accuracy between Gaussian and general parametric PSFs was observed, the general parametric model showed greater flexibility over the FOV in shaping the curve between that for Gaussian and Cauchy functions. The estimated asymmetric SV-PSFs were incorporated into the LMOSEM for resolution recovery. For simulation data from a single point source at the origin, all LMOSEM-SV-PSFs improved the spatial resolution by 2.6 times over the standard LMOSEM. For two point-source simulations, reconstructions also gave a two-fold improvement in spatial resolution and resulted in a greater recovered activity ratio at different positions in the FOV.

Although the ordered subset expectation maximization (OSEM) algorithm does not converge to a true maximum likelihood solution, it is known to provide a good solution if the projections that constitute each subset are reasonably balanced. The Compton scattered data can be allocated to subsets using scattering angles (SA) or detected positions (DP) or a combination of the two (AP (angles and positions)). To construct balanced subsets, the data were first arranged using three ordering schemes: the random ordering scheme (ROS), the multilevel ordering scheme (MLS) and the weighted-distance ordering scheme (WDS). The arranged data were then split into J subsets. To compare the three ordering schemes, we calculated the coefficients of variation (CVs) of angular and positional differences between the arranged data and the percentage errors between mathematical phantoms and reconstructed images. All ordering schemes showed an order-of-magnitude acceleration over the standard EM, and their computation times were similar. The SA-based MLS and the DP-based WDS led to the best-balanced subsets (they provided the largest angular and positional differences for SA- and DP-based arrangements, respectively). The WDS exhibited minimum CVs for both the SA- and DP-based arrangements (the deviation in mean angular and positional differences between the ordered subsets was smallest). The combination of AP and WDS yielded the best results with the lowest percentage errors by providing larger and more uniform angular and positional differences for the SA and DP arrangements, and thus, is probably optimal Compton camera reconstruction using OSEM.

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