3D Forward and Back-Projection for X-Ray CT Using Separable Footprints

The greatest impediment to practical adoption of iterative methods for X-ray CT is the computation burden of cone-beam forward and back-projectors. Moreover, forward and back-projector accuracy is also crucial to iterative reconstruction methods. We previously described a computationally efficient projector that approximates the voxel footprint functions by the 2D separable products of trapezoid functions in the transaxial plane and rectangular functions in the axial direction [1], [2]. The separability of these footprint functions simplifies calculating their integrals over rectangular detector cells. We showed that this separable footprint (SF-TR) method was more accurate than the distance-driven (DD) method but with comparable computation time. This paper describes a new extension of that projector, called the SF-TT projector, that uses trapezoid functions in both directions. We show that using a trapezoid along the axial direction improves projector accuracy for voxels associated w...

• Type: Journal
• Year: 2010
• Where: TMI
• Authors: Yong Long, Jeffrey A. Fessler, James M. Balter
• Keywords: Axial Direction, Footprint Functions, Management, TMI 2010, Trapezoid Functions