Fast cosine transform for FCC lattices

TL;DR

This paper introduces a fast cosine transform tailored for face-centered cubic (FCC) lattices, leveraging algebraic signal processing and Lie group geometry to improve 3D data processing efficiency.

Contribution

It presents the first discrete cosine transform analog for FCC lattices, utilizing multivariate Chebyshev polynomials and a novel fast algorithm based on algebraic signal processing theory.

Findings

Developed a new cosine transform for FCC lattices.

Derived a fast algorithm with reduced computational complexity.

Demonstrated potential applications in 3D imaging and volumetric data processing.

Abstract

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.