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Quincunx fundamental refinable functions and quincunx biorthogonal wavelets

Authors: Bin Han and Rong-Qing Jia
Journal: Math. Comp. 71 (2002), 165-196
MSC (2000): Primary 42C40, 41A25, 41A63, 65D05, 65D17
Published electronically: October 17, 2000
MathSciNet review: 1862994
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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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Additional Information

Bin Han
Affiliation: Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544
Address at time of publication: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Rong-Qing Jia
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Keywords: Fundamental refinable functions, biorthogonal wavelets, quincunx lattice, approximation order, smoothness, coset by coset (CBC) algorithm
Received by editor(s): July 13, 1999
Received by editor(s) in revised form: April 20, 2000
Published electronically: October 17, 2000
Additional Notes: The research of the first author was supported by a postdoctoral fellowship and Grant G121210654 from NSERC Canada.
The research of the second author was partially supported by NSERC Canada under Grant OGP 121336
Article copyright: © Copyright 2000 American Mathematical Society

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