A comparison of direct reconstruction algorithms in proton computed tomography.

Several direct algorithms have been proposed to take into account the non-linear path of protons in the reconstruction of a proton CT (pCT) image. This paper presents a comparison between five of them, in terms of spatial resolution and relative stopping power (RSP) accuracy. Our comparison includes (1) a distance-driven algorithm extending the filtered backprojection to non-linear trajectories (DD), (2) an algorithm reconstructing a pCT image from optimized projections (ML), (3) a backproject-then-filter approach using a 2D cone filter (BTF), (4) a differentiated backprojection algorithm based on the inversion of the Hilbert transform (DBP), and (5) an algorithm using a 2D directional ramp filter (DR). We have simulated a single tracking pCT set-up using Geant4 through GATE, with a proton source and two position, direction and energy detectors upstream and downstream from the object. Tracker uncertainties were added on the position and direction measurements. A Catphan 528 phantom and a spiral phantom were simulated to measure the spatial resolution and a Gammex 467 phantom was used for the RSP accuracy. Each proton's trajectory was estimated using a most likely path (MLP) formalism. The spatial resolution was evaluated using the frequency corresponding to a modulation transfer function of 10% of its peak value and the RSP accuracy using the mean values in the inserts of the Gammex phantom. In terms of spatial resolution, it was shown that, for ideal trackers, the DR and BTF methods offer a slightly better resolution since each proton is directly binned in the image grid according to its MLP. However, all methods but the ML show comparable resolution when using realistic trackers. Regarding the RSP, three algorithms (DR, DD and BTF) show a mean relative error inside the inserts about 0.1%. As the DR and BTF methods are more computationally expensive, the DD-which allows the same spatial resolution in realistic conditions and the same accuracy-and the DBP-which has a fairly good accuracy (<0.2%) and allows reconstruction from truncated data-can be used for a reduced reconstruction time.