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Fourier-based approach to interpolation in helical CT exploiting redundant fan-beam information

We present two new approaches to single-slice helical computed tomography image reconstruction that exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fan-beam sinograms corresponding to equispaced transverse slices. Slice-by-slice reconstruction is then performed by use of two-dimensional fan-beam algorithms. The first approach, called 360 FT, makes us only of the directly measured projection data, but an extension called 180 FT exploits the redundancy of fan-beam data acquired over 360 degree to generate a second set of longitudinal samples at each projection angle and bin. The proposed approaches are compared to their counterparts based on the use of linear interpolation -- the 360 LI and 180 LI approaches. Particular attention is paid to the spatially variant aliasing that has recently been shown to be an important consideration in helical CT, and which affects the 360 LI and 180 LI approaches equally despite the latter's use of the additional fan-beam redundancy samples. Remarkably, because of the way it makes use of the fan-beam redundancy data, the proposed 180 FT approach is found to eliminate this spatially variant aliasing under certain conditions. This is a clear advantage of the approach and represents a step toward the desirable goal of achieving isotropic resolution in reconstructed helical CT volumes.