Exact cone beam reconstruction for a saddle trajectory

We propose an exact shift-invariant filtered backprojection (FBP) algorithm for inversion of cone beam (CB) data in the case where the source trajectory is a saddle. The algorithm allows for axial truncation of the cone beam data. The algorithm involves only one family of filtering lines on the detector plane, and it does not depend on the existence of π-lines. The algorithm is derived from a general formula in Pack and Noo (2005 Inverse Problems 21 1105–20). We also give the steps to implement the algorithm for planar detector geometry and discuss how to select the parameter of the saddle and the size of the detector when the trajectory is a standard saddle. The algorithm is tested by simulation studies.