A Simple Quincunx Wavelet with Support on Triangles

Abstract

We give a simple orthonormal wavelet system associated to the quincunx matrix. That system has four generators and those generators are sum of two constant functions on triangles. Our construction is based on the structure of a multiresolution analysis. Moreover, we prove that such a system is complete in $$L^p({\mathbb {R}}^2)$$ , $$1< p < \infty $$ . Finally, we give a filter bank algorithm associated to the proposed wavelet system.