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Interpolatory Biorthogonal Wavelets and CBC Algorithm

### Bin Han and Sherman D. Riemenschneider

## Abstract

In this paper, we shall discuss how to construct multidimensional
biorthogonal wavelets by employing a coset by coset (CBC)
algorithm.
We shall construct biorthogonal wavelets on the hexagonal lattice by
CBC algorithm.
In particular, we shall propose a CBC algorithm to
construct interpolatory biorthogonal wavelets which are derived from
pairs of fundamental refinable functions. More precisely, given an
interpolatory primal mask $a$, we shall characterize when there exists
an interpolatory dual mask $a^d$ of $a$ such that $a^d$ satisfies the
sum rules of order $k$ for some positive integer $k$.
We shall prove that for any dilation matrix $M$ with $ |\det M|>2$,
there exist an interpolatory primal mask $a$ and an interpolatory dual
mask $a^d$ of $a$ such that $a$ and $a^d$ satisfy any preassigned
orders of sum rules. Finally, we
shall give some examples of
interpolatory biorthogonal wavelets.

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