  Voxel representation and processing is an important issue in a broad spectrum
of applications. E.g., 3D imaging in biomedical engineering applications, video
game development and volumetric displays are often based on data representation
by voxels. By replacing the standard sampling lattice with a face-centered
lattice one can obtain the same sampling density with less sampling points and
reduce aliasing error, as well. We introduce an analog of the discrete cosine
transform for the facecentered lattice relying on multivariate Chebyshev
polynomials. A fast algorithm for this transform is deduced based on algebraic
signal processing theory and the rich geometry of the special unitary Lie group
of degree four.
