Multivariate orthonormal interpolating scaling vectors

Abstract

In this paper we introduce an algorithm for the construction of interpolating scaling vectors on R d with compact support and orthonormal integer translates. Our method is substantiated by constructing several examples of bivariate scaling vectors for quincunx and box–spline dilation matrices. As the main ingredients of our recipe we derive some implementable conditions for accuracy and orthonormality of an interpolating scaling vector in terms of its mask.