A short-scan reconstruction for cone-beam CT using shift-invariant FBP and equal weighting

A 3D reconstruction formula has been derived for a circular cone-beam (CB) short scan using ID shift-invariant filtering, CB backprojection, and equal weighting. By first converting the divergent projections to parallel projections, we analyze the circular CB data using the classic central slice theorem. The sampling density in Fourier space is investigated and 1D shift-invariant filtering before backprojection can be used to compensate for the nonuniformity. The final formula consists of a conventional FDK reconstruction and a correction term using differential backprojection and the 1D Hilbert transform in the image domain. On a full scan, the approach reduces to the FDK algorithm, while for a short scan, the CB artifacts are suppressed by the second term. This algorithm outperforms the modified FDK algorithm with Parker's weighting, as illustrated by computer simulations and experimental results. Due to its shift-invariant filtered-backprojection structure, the proposed algorithm is implemented efficiently, and requires a simple adaptation of the FDK algorithm.