Unitary transformation between Cartesian- and polar-pixellated screens

摘要

A unitary transformation between Cartesian and polar pixellations of finite two-dimensional images is obtained from the su(2) model for discrete and finite signals. This transformation analyzes the original image into its finite Cartesian "Laguerre-Kravchuk" modes (involving Wigner little-d functions) and synthesizes it back using a polar mode basis with the same set of mode coefficients. The polar basis is derived from the quantum angular momentum theory, and its modes are given by Clebsch-Gordan coefficients.