  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.
