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/sub /spl phi//(x) for each value of the azimuthal angle /spl phi/ in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI /spl Omega//sub m/. The authors show that, for each /spl phi/, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of f/sub /spl phi//(x) onto the meridian plane of angle /spl phi/. Given an angular range of length /spl pi/ of such parallel-beam projections, the ROI /spl Omega//sub m/ can be exactly reconstructed because f(x) is identical to f/sub /spl phi//(x) in /spl Omega//sub 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.

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