A comparison study on ray-driven approximation in re-projection and back-projection for CT reconstruction

Ray-driven technique is very important for computed tomography (CT) image reconstruction. It has been reported that the weighting factor in ray-driven technique can be obtained by calculating the intersection length (distance-weighting) or area (area-weighting) of a projection line or strip with an image pixel. Recently, we presented a method which considers the intersection volume as weighting factor (volume-weighting) in fully three-dimensional (3D) imaging. In this work, we presented the performances of these three different weighting techniques by computer simulation studies. We first generated a 3D continuous Shepp-Logan phantom and computed the sinogram data analytically as the reference. Then the sinogram data with the three different weighting techniques were simulated. It can be observed that the profile obtained by the analytical solution is smooth while the three weighting methods show noticeable unevenness. The unevenness is inevitable due to the induced error by the digitalization process and finite image resolution. While the volume weighting achieved slightly better performance than the area weighting and both of them showed noticeable improvements compared to the distance weighting. We also compared their reconstruction performances using filtered backprojection (FBP) and Feldkamp (FDK) algorithms for 2D and 3D cases, respectively. The gain by the use of volume-weighting was measured, as compared to others, by the standard variation in selected regions of interest in the reconstructions. One drawback about the volume weighting is the need of intensive computation. It costs about ten times more computation as compared to the distance weighting and about three times more computation to the area weighting. Though this should not be a major concern for sinogram restoration and analytical reconstruction, it might limit the use when using iterative algorithms. Optimization of the volume weighting for fast computation and comparison of the ray-driven technique with other methods are under investigation.