Exact Radon rebinning algorithm for the long object problem in helical cone-beam CT

This paper addresses the long object problem in helical cone-beam computed tomography. The authors present the PHI-method, a new algorithm for the exact reconstruction of a region-of-interest (ROI) of a long object from axially truncated data extending only slightly beyond the ROI. The PHI-method is an extension of the Radon-method, published by Kudo et al. in Phys. in Med. and Biol., vol. 43, p. 2885-909 (1998). The key novelty of the PHI-method is the introduction of a virtual object f _φ(x) for each value of the azimuthal angle φ in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI Ω _m. The authors show that, for each φ, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of f _φ(x) onto the meridian plane of angle φ. Given an angular range of length π of such parallel-beam projections, the ROI Ω _m can be exactly reconstructed because f(x) is identical to f _φ(x) in Ω _m. Simulation results are given for both the Radon-method and the PHI-method indicating that (1) for the case of short objects, the Radon- and PHI-methods produce comparable image quality, (2) for the case of long objects, the PHI-method delivers the same image quality as in the short object case, while the Radon-method fails, and (3) the image quality produced by the PHI-method is similar for a large range of pitch values.