Orthogonal Multiwavelet Frames in L2Rd

Abstract EN

We characterize the orthogonal frames and orthogonal multiwavelet frames in L2Rd with matrix dilations of the form (Df)(x)=detAf(Ax), where A is an arbitrary expanding d×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.