Quartic Box-Spline Reconstruction on the BCC Lattice

This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M_7 that has the same approximation order as the eight-direction quintic box-spline M_8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M_7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.