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

Abstract

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.