Exact 3D cone-beam reconstruction from two short-scans using a C-arm imaging system

In this paper we present a source path for the purpose of exact cone-beam reconstruction using a C-arm X-ray imaging system. The proposed path consists of two intersecting segments, each of which is a short-scan. Any C-arm capable of a short-scan sweep can thus be used to obtain data on our proposed source path as well, since it only requires an additional sweep on a tilted plane. This tilt can be achieved by either using the propeller axis of mobile C-arms, or the vertical axis of ceiling mounted C-arms. While the individual segments are only capable of exact reconstruction in their mid-plane, we show that the combined path is capable of exact reconstruction within an entire volumetric region. In fact, we show that the largest sphere that can be captured in the field of view of the C-arm can be exactly reconstructed if the tilt between the planes is at least equal to the cone-angle of the system. For the purpose of cone-beam inversion we use a generalized cone-beam filtered backprojection algorithm (CB-FBP). The exactness of this method relies on the design of a set of redundancy weights, which we explicitly evaluate for the proposed dual short-scan source path.