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

TL;DR

This paper introduces a new quaternion-valued wavelet methodology for processing colour images, demonstrating its effectiveness in various image enhancement tasks and establishing its potential as a comprehensive quaternion-based image processing tool.

Contribution

It presents a novel application of recently developed quaternion wavelets for decomposing and reconstructing colour images, filling a gap in practical testing of these wavelets.

Findings

Effective in image compression, enhancement, segmentation, and denoising.

Wavelets show promising results for end-to-end quaternion image processing.

Demonstrates the practical applicability of quaternion wavelets in real-world tasks.

Abstract

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.