Quincunx fundamental refinable functions and quincunx biorthogonal wavelets

Han, Bin; Jia, Rong-Qing

doi:10.1090/S0025-5718-00-01300-4

Quincunx fundamental refinable functions and quincunx biorthogonal wavelets
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by Bin Han and Rong-Qing Jia;

Math. Comp. 71 (2002), 165-196

DOI: https://doi.org/10.1090/S0025-5718-00-01300-4

Published electronically: October 17, 2000

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Abstract:

We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in $\mathbb {R}^2$. Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks, we prove that their symbols are nonnegative. Finally, a general way of constructing quincunx biorthogonal wavelets is presented. Several examples of quincunx interpolatory masks and quincunx biorthogonal wavelets are explicitly computed.

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