Cone-beam tomography from 12 pinhole vertices

We have devised a simple model of inherent tomographic capability for a limited cone-beam system consisting of a few unordered cone-vertex locations. The projections are assumed to not be truncated, and represent ideal line-integrals (no noise or physical effects, and perfect sampling and resolution). The model can easily be applied, and is intended to predict which resolution features can not be recovered from the cone-beam projection data, independent of the reconstruction algorithm applied. Our model tells us about tomographic capability outside the convex hull of the vertex set, whereas conventional theory (Tuy's condition) says nothing for this case. We tested our model with a system consisting of 12 vertices. The results have motivated us to successively refine our reconstruction algorithm, striving for the bounds claimed by our model.