Interpolatory Biorthogonal Wavelets and CBC Algorithm

Bin Han and Sherman D. Riemenschneider


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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