Holistic Processing of Color Images Using Novel Quaternion-Valued Wavelets on the Plane: A promising transformative tool [Hypercomplex Signal and Image Processing]

Abstract

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