Multichannel Image Decomposition by using Pseudo-Linear Haar Wavelets

Recently it has been shown that in image processing, the usual sum and product of the reals are not the only operations that can be used. Several other operations provided by fuzzy logic perform well in this application. We continue this line of research and we study the possibility to use some pairs of pseudo-operations. We define in the present paper pseudo-linear Haar wavelets, and we perform multi-channel decomposition of images. We study some pairs of pseudo-operations determined by a continuous, strictly increasing generator instead of the classical sum and multiplication and Haar-type wavelets based on these operations. The results show us that pseudo-linear Haar wavelets can be used as an alternative of classical Haar wavelets since the perfect reconstruction property is conserved.