A 3D Forward and Back-Projection Method for X-Ray CT Using Separable Footprint

The computation burden of cone-beam forward and back-projectors is one of the greatest challenges facing iterative methods for 3D image reconstruction in CT. This paper describes a new separable footprint (SF) projector. It takes advantage of small polar angles of X-rays in cone-beam geometry to approximate the voxel footprint functions as 2D separable functions with simple rectangular functions in the axial direction. Due to rotation of the source, a more accurate function is adopted to approximate the footprint function in the transaxial direction, such as a trapezoid function. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. Simulations and experiments showed that the SF projector is more accurate with similar computational speed than the distance-driven (DD) projector, which is a current state-of-the-art method in the field.