Orthogonal Multiwavelet Frames in L 2 R d

Abstract

We characterize the orthogonal frames and orthogonal multiwavelet frames in $L^2\left(R^d\right)$ with matrix dilations of the form $\left(Df\right)\left(x\right)=\sqrt{\left|\text{d}\text{e}\text{t}A\right|}f\left(Ax\right)$, where $A$ is an arbitrary expanding $d\{\backslash times\}d$ matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.