Three-dimensional image reconstruction from axially truncated helical cone beam projections has been under active investigation. It is known that exact helical cone beam reconstruction can be achieved using only the data in the Tarn window. Based on a property of filtering truncated cone beam projections discovered by Kudo et al, we proposed a simple helical cone beam algorithm for the long object problem by invoking virtual infinite detectors at both ends of the helix. However, Tarn has suggested that the derivation using virtual infinite detectors were imprecise as well as the calculated overscan and complexity analysis. In this paper, we provide a new derivation to validate the simple algorithm based on a novel definition of a short object within the long object. We show that the proposed algorithm is essentially a simplified version of Defrise's ZB method. The minimal overscan we derive for the simple algorithm is the same as that of ZB method. Although simulation results indicate that a smaller overscan is required for the proposed algorithm relative to the ZB method, we lack an analytical verification. A modified 3D Shepp-Logan phantom and a disc phantom are used to validate the algorithm.
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