Exact image reconstruction with triple-source saddle-curve cone-beam scanning.

In this paper, we propose an exact shift-invariant filtered backprojection (FBP) algorithm for triple-source saddle-curve cone-beam CT. In this imaging geometry, the x-ray sources are symmetrically positioned along a circle, and the trajectory of each source is a saddle curve. Then, we extend Yang's formula from the single-source case to the triple-source case. The saddle curves can be divided into four parts to yield four datasets. Each of them contains three data segments associated with different saddle curves, respectively. Images can be reconstructed on the planes orthogonal to the z-axis. Each plane intersects the trajectories at six points (or three points at the two ends) which can be used to define the filtering directions. Then, we discuss the properties of these curves and study the case of 2N+1 sources (N>or=2). A necessary condition and a sufficient condition are given to find efficient curves. Finally, we perform numerical simulations to demonstrate the feasibility of our triple-source saddle-curve approach. The results show that the triple-source geometry is advantageous for high temporal resolution imaging, especially important for cardiac imaging and small animal imaging.