Hexagonal Basis Projectors for Model-Based Iterative CT Reconstruction

Image representation affects both the forward model and quantitative feature recovery in model-based iterative CT reconstruction. For isotropically bandlimited signals, the hexagonal lattice is the most sampling-efficient lattice in two dimensions, with greater directional isotropy and a larger alias-free bandwidth than the Cartesian grid at equal density. We develop constant and linear hexagonal projectors for two-dimensional fan-beam CT using box spline calculus. Both bases form a partition of unity on common coefficient centers; the linear tent also reproduces affine functions. We derive analytic ray footprints and effective detector-blur expressions and implement efficient GPU forward and backprojection. On simulated FORBILD data, the linear model improves on Cartesian and hexagonal pixels, with its best noisy-data accuracy at the coarser resolution. Real-world 2DeteCT comparisons use high-dose, high-resolution Cartesian reconstructions as pseudo ground truth and show competitive image and feature agreement. These results establish a practical hexagonal representation for quantitative CT.