A cone-beam FBP reconstruction algorithm for short-scan and super-short-scan source trajectories

Conventionally, the FDK algorithm is used to reconstruct images from cone-beam projections in many imaging systems. One advantage of this algorithm is its shift-invariant feature in the filtering process. In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory. Examples of the arc trajectory include the full circular scan mode, a short-scan mode and a super-short-scan mode depending upon the angular range of the scanning path. Since the single arc does not satisfy Tuy's data sufficiency condition, there is no mathematically exact algorithm. However, one advantage of this reconstruction is that the shift-invariance property has been preserved despite the lack of a mathematically complete data set. The new algorithm includes backprojections from three adjacent segments of the arc denned by T ₁(→x),T ₂(→x) and T ₃(→x). Each backprojection step consists of a weighted combination of ID Hilbert filtering of the modified cone-beam data along horizontal and non-horizontal directions. The non-horizontal filtering is a new feature of this FBP algorithm. For the full circle scanning path, this algorithm reduces to the conventional FDK algorithm plus a term involving a first order derivative filter. Numerical simulations have been performed to validate the algorithm.