Fourier-based approach to interpolation in single-slice helical computed tomography

It has recently been shown that longitudinal aliasing can be a significant and detrimental presence in reconstructed single-slice helical computed tomography (CT) volumes. This aliasing arises because the directly measured data in helical CT are generally undersampled by a factor of at least 2 in the longitudinal direction and because the exploitation of the redundancy of fanbeam data acquired over 360 degrees to generate additional longitudinal samples does not automatically eliminate the aliasing. In this paper we demonstrate that for pitches near 1 or lower, the redundant fanbeam data, when used properly, can provide sufficient information to satisfy a generalized sampling theorem and thus to eliminate aliasing. We develop and evaluate a Fourier-based algorithm, called 180FT, that accomplishes this. As background we present a second Fourier-based approach, called 360FT, that makes use only of the directly measured data. Both Fourier-based approaches exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fanbeam sinograms corresponding to equispaced transverse slices. Slice-by-slice reconstruction is then performed by use of two-dimensional fanbeam algorithms. The proposed approaches are compared to their counterparts based on the use of linear interpolation-the 360LI and 180LI approaches. The aliasing suppression property of the 180FT approach is a clear advantage of the approach and represents a step toward the desirable goal of achieving uniform longitudinal resolution properties in reconstructed helical CT volumes.