Towards an Efficient Two-Step Hilbert Algorithm for Helical Cone-Beam CT

We investigate helical cone-beam reconstruction using differentiated backprojection on π-lines and a subsequent inverse Hilbert transform. We report in particular on an implementation scheme that allows efficient reconstruction in the geometry of current Multi-Slice-CT scanners. This scheme is based on reconstruction on “theoretical” π-lines (π-lines that would have been measured in a continuous measurement system but are not actually measured because only a finite number of projections are measured in practice) and thus allows us to specify the sampling of the backprojection grid independently of the sampled source positions. We have identified six significant variations within our implementation scheme, which differ mainly in the way the DBP is implemented. We provide a description of all six variants of the algorithm and evaluate their advantages and disadvantages and give examples of reconstructions of the FORBILD thorax phantom.