B-spline based weighting functions for helical CT

Spatially variant longitudinal aliasing plagues most volumes reconstructed from single-slice helical computed tomography data, and its presence can degrade resolution and distort image structures. We have recently developed a Fourier-based approach to longitudinal interpolation in helical CT that can, under certain conditions, essentially eliminate this longitudinal abasing by exploiting a generalization of the sampling theorem whose conditions are satisfied by the interlaced pairs of direct and complementary longitudinal samples. However, the algorithm is computationally intensive and cannot be pipelined. In the present work, we address this shortcoming by deriving a spatial-domain, projection-data weighting function that approximates the application of the Fourier-based approach, and preserves its aliasing suppression properties to some degree, while allowing for a pipelined implementation. The approach, which we call 180BSP, is based on an approximate, generalized interpolation approach making use of B-splines. Studies of aliasing and resolution properties indicate that while the 180BSP approach does not perfectly replicate the favorable aliasing suppression and resolution properties of the 180FT approach, it is considerably more computationally efficient and it does represent a distinct improvement over the clinically standard 180LI approach on these fronts.