Exact helical reconstruction using native cone-beam geometries

Abstract

This paper is about helical cone-beam reconstruction using the exact filtered backprojection formula recently suggested by Katsevich (2002a Phys. Med. Biol. 47 2583–97). We investigate how to efficiently and accurately implement Katsevich's formula for direct reconstruction from helical cone-beam data measured in two native geometries. The first geometry is the curved detector geometry of third-generation multi-slice CT scanners, and the second geometry is the flat detector geometry of C-arms systems and of most industrial cone-beam CT scanners. For each of these two geometries, we determine processing steps to be applied to the measured data such that the final outcome is an implementation of the Katsevich formula. These steps are first described using continuous-form equations, disregarding the finite detector resolution and the source position sampling. Next, techniques are presented for implementation of these steps with finite data sampling. The performance of these techniques is illustrated for the curved detector geometry of third-generation CT scanners, with 32, 64 and 128 detector rows. In each case, resolution and noise measurements are given along with reconstructions of the FORBILD thorax phantom.