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Orthogonal Multiwavelet Frames in L2(Rd)
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We characterize the orthogonal frames and orthogonal multiwavelet frames in L2(Rd) with matrix dilations of the form , 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.
Title: Orthogonal Multiwavelet Frames in L2(Rd)
Description:
We characterize the orthogonal frames and orthogonal multiwavelet frames in L2(Rd) with matrix dilations of the form , 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.
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