Stable and efficient shift-variant algorithm for circle-plus-lines orbits in cone-beam CT

Defrise and Clack (see IEEE Trans. Med. Imag., vol.13, p.186-95, 1994) , and also Kudo and Saito (see IEEE Trans. Med. Imag., vol.13, p.196-211, 1994), have derived an exact algorithm suited to accurately reconstruct cone-beam data acquired from any complete orbit. These algorithms are written in the form of a shift-variant filtered backprojection. Their main characteristic is their capability to handle in many different ways the redundancy inherent to cone-beam data sets. We investigate the interplay between the redundancy handling and the stability and efficiency of the algorithm. Specifically, we show how to handle the redundancy to turn shift-variant filtering of some projections into shift-invariant filtering. Invoking this result, we define then a new algorithm suited to accurately and efficiently reconstruct data acquired from circle-plus-lines orbits. The new algorithm is tested on simulated data and real data from industrial imaging of waste containers