Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry

This paper investigates cone-beam tomography for a wide class of x-ray source trajectories called saddles. In particular, a mathematical analysis of the number of intersections between a saddle and an arbitrary plane is given. This analysis demonstrates that axially truncated cone-beam projections acquired along a saddle can be used for exact reconstruction at any point in a large volume. The reconstruction can be achieved either using a new algorithm presented herein or using a formula recently introduced by Katsevich (2003 Int. J. Math. Math. Sci. 21 1305-21). The shape of the reconstructed volume and the properties of saddles make saddles attractive for cardiac imaging. Three examples of saddles are presented with a discussion of implementation on devices similar to modern C-arm systems and multislice CT scanners. Reconstruction with one of these saddles has been tested using computer-simulated data, with and without truncation. The imaged phantom for the truncated data is a FORBILD head phantom (representing the heart) that has been modified and embedded inside the FORBILD thorax phantom. The non-truncated data were generated by excluding the thorax. The reconstructed images demonstrate the accuracy of the mathematical results.