Application of Pack and Noo´s Cone-Beam Inversion Formula to a Wide Class of Trajectories

In this paper, the cone-beam inversion formula of Pack and Noo [2005] is applied to a wide class of important trajectories such as two-circles, circle-and-line, and closed sinusoid. The inversion formula can be applied if the intersection points between the scanning trajectory and each reconstructed slice construct a convex polygon, and the adjacent vertices of the polygon are connected by a part of the scanning trajectory. To reconstruct a single slice, the inversion formula applies a shift-invariant filtration followed by a backprojection of cone-beam data. When we take a 3D FOV as a family of parallel slices, the shift-invariant filtered backprojection (FBP) structure is also kept if the convex polygons are semi-similar for all the slices.