Construction of Multivariate Tight Frames via Kronecker Products

Abstract

Integer-translates of compactly supported univariate refinable functions φ i , such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions Φ from the φ i 's. The objective of this paper is to introduce a Kronecker-product approach to build compactly supported tight frames associated with Φ, using the two-scale symbols of the univariate tight frame generators associated with the φ i 's. © 2001 Academic Press.