Sampling conditions of 3D parallel and fan-beam x-ray CT with application to helical tomography.

ABSTRACT

We give the sampling conditions of the 3D fan-beam x-ray transform (3DFBXRT). The motivation of this work lies in the fact that helical tomography with a single detector line is simply a sampling of this transform under the helical constraint. We give a precise description of the geometry of the essential support of the 3DFBXRT Fourier transform and show how to derive efficient sampling schemes. We then give efficient sampling schemes in parallel helical tomography. We present numerical experiments showing that efficient sampling on hexagonal interlaced schemes yields better reconstructions than the standard schemes in both parallel helical tomography (using QDO) and 3DFBXRT. We discuss the practical drawbacks and advantages of these efficient schemes and the possible extension to fan-beam helical CT.