Improved area-simulating-volume method for 3D X-ray CT re-projection and back-projection operations

Many studies have reported that the volume-weighting technique has advantages over the ray-tracing method in re-projection modality and the linear interpolation in back-projection operation for three-dimensional (3D) X-ray computed tomography (CT) imaging. However, the calculation of the intersecting volumes requires a high arithmetic complexity and can be difficult to implement practically. In this work, inspired by the previous work in area-simulating-volume (ASV) projector for 3D positron emission tomography, we developed an improved ASV (IASV) technique, which can fast and accurately calculate the intersection volume between the pencil-ray and the object for 3D cone-beam CT. In our re-projection study, a 3D Shepp-Logan digital phantom was performed to simulate projection data by the IASV and ray-tracing techniques, respectively. An analytical solution of the projection data was calculated based on the known densities and intersection length of the ray with the 3D phantom and used as a ground truth. The results demonstrated that the simulated projection data by IASV technique is smoother than the results from ray-tracing technique and closer to the analytical solution or ground truth. In addition to the comparison in re-projection, a series of digital and physical phantoms were performed to compare the IASV technique with conventional linear-interpolation technique for back-projection operation. Digital phantom study demonstrated that a uniformly distributed noise image was achieved by the proposed volume-weighting technique in stationary noise case. This observation was also verified in a study using repeated scans on a physical phantom.