A direct filtered back-projection reconstruction method for inverse geometry CT without gridding: a simulation study

Inverse geometry computed tomography (IGCT) uses a small detector and a set of widely distributed x-ray sources. Standard filtered backprojection (FBP) reconstruction for a conventional CT geometry cannot be directly used in IGCT, due to data truncation and redundancy of the sinograms acquired by different sources. Current IGCT algorithms use gridding or iterations during reconstruction, leading to degraded spatial resolution or increased computational cost. In this work, we propose a direct FBP reconstruction method for IGCT without gridding. A reconstruction algorithm is first derived for a full-size sinogram acquired by a single source with a known offset distance to the central line passing through the rotational axis and perpendicular to the detector. A weighting scheme is then developed on the projections to remove the data redundancy of different sinograms acquired by different sources. The final reconstruction is obtained as the summation of CT images reconstructed from different sources, in a form of FBP on weighted projections. The performance of the proposed algorithm is evaluated via simulation studies on the Shepp-Logan phantom. Results show that our algorithm substantially improves the image spatial resolution over the gridding method. The spatial resolution increases by 32.08% and 23.26% at 50% and 10% of the modulation transfer function, respectively. Finally, we demonstrate the advantages of volumetric IGCT compared with circular cone-beam CT in a pilot study.