Resolution recoverable statistical listmode reconstruction using depth dependent point spread function for Compton camera

A Compton camera is an imaging system for three-dimensional (3D) distribution of gamma emitting sources based on Compton scattering interaction. The measurement error on energies and positions directly leads to uncertainties on the formation of cones and degrades the spatial resolution of the reconstructed images. Mostly the limited energy resolution, Doppler broadening and position segmentation of detectors cause angular and positional uncertainties on measurements. Since the conical surfaces are delocalized by angular and positional uncertainties into image space, degradation of spatial resolution may be severe depending on the distance (or depth) from the Compton camera. In order to enhance the deteriorated spatial resolution due to angular and positional uncertainties, this study investigates 3D Gaussian point spread function (PSF) incorporable into listmode ordered subset expectation maximization (LMOSEM) as a part of system matrix. Especially the depth-dependent PSF is applied as resolution recovery (RR) technique by image-space convolution operation. We investigated two different RR approaches: one (denoted by LMOSEM-RR-F) is when the convolution is performed in forward projection step only, and the other (denoted by LMOSEM-RR-FB) is when it is performed in both forward and backward projection steps. Using Monte Carlo data for 7 point sources at different depth from the Compton camera, the fitted axial and radial FWHM functions were obtained as FWHM_axial (i)=0.2442i+1.054 and FWHM_radial (i)=0.2369i-1.005, respectively. The simulation results showed that both RR approaches with depth dependent PSF gave an improvement on spatial resolution comparing to LMOSEM without RR techniques. Although LMOSEM-RR-F provided better resolution than LMOSEM-RR-FB, LMOSEM-RR-FB could still be useful for low counting statistics in measurement.