# Holistic Processing of Colour Images Using Novel Quaternion-Valued Wavelets on the Plane

arXiv: https://arxiv.org/abs/2308.16875 · HTML: https://mlsanity.com/paper/2308.16875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 3 of 3)

- [The Douglas-Rachford Algorithm for Convex and Nonconvex Feasibility Problems](https://mlsanity.com/paper/1904.09148/) (2019)
- [A general framework for constrained convex quaternion optimization](https://mlsanity.com/paper/2102.02763/) (2021)
- [A Lyapunov-type approach to convergence of the Douglas-Rachford algorithm](https://mlsanity.com/paper/1706.04846/) (2017)

## Abstract (arXiv)

Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable and truly quaternionic. However, they have not been tested in application. In this paper, we introduce a methodology for decomposing and reconstructing colour images using quaternionic wavelet filters associated to recently developed quaternion-valued wavelets on the plane. We investigate its applicability in compression, enhancement, segmentation, and denoising of colour images. Our results demonstrate these wavelets as promising tools for an end-to-end quaternion processing of colour images.