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

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Abstract
This paper addresses the long object problem in helical cone-beam computed tomography. We 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, Noo, and Defrise in issue 43 of journal Physics in Medicine and Biology. The key novelty of the PHI-method is the introduction of a virtual object fpsi(x) for each value of the azimuthal angle psi in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI omegam. We show that, for each psi, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of fpsi(x) onto the meridian plane of angle psi. Given an angular range of length pi of such parallel-beam projections, the ROI omegam can be exactly reconstructed because f(x) is identical to fpsi(x) in Omegam. 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.