Some compactly supported dual wavelets associated to the Quincunx matrix in ℝ3

Abstract

In this paper, we construct a family of compactly supported dual wavelets associated to the Quincunx matrix on [Formula: see text]. Our family will have dual wavelets with any desired number of vanishing moments, any fixed degree of regularity and symmetry with respect to some point. Finally, we also present dual wavelets on [Formula: see text] associated to some dilation matrices with determinant [Formula: see text].