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This paper investigates 3D image reconstruction from truncated cone-beam (CB) projections acquired with a helical vertex path. First, we show that a rigorous derivation of Grangeat's formula for truncated projections leads to a small additional term compared with previously published similar formulations. This correction term is called the boundary term. Next, this result is used to develop a CB filtered-backprojection (FBP) algorithm for truncated helical projections. This new algorithm only requires the CB projections to be measured within the region that is bounded, in the detector, by the projections of the upper and lower turns of the helix. Finally, simulations with mathematical phantoms demonstrate that: (i) the boundary term is necessary to obtain high-quality imaging of low-contrast structures and (ii) good image quality is obtained even with large values of the pitch of the helix.
Kudo et al. (Thu,) studied this question.