Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach
Classical Analysis and ODEs
2026-01-21 v2
Abstract
This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard conditions of smoothness, compact support, and orthonormality. To solve the resulting feasibility problems, we employ a product space formulation of the Douglas-Rachford algorithm. This approach yields novel examples of nonseparable, multiresolution, compactly supported, smooth, and orthonormal quaternion-valued wavelets on the plane. Additionally, by introducing a symmetry-promoting constraint, we construct symmetric quaternion-valued scaling functions on the plane.
Keywords
Cite
@article{arxiv.2311.12614,
title = {Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach},
author = {Neil D. Dizon and Jeffrey A. Hogan},
journal= {arXiv preprint arXiv:2311.12614},
year = {2026}
}