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   -> Volume 6, Issue 9

Preprint: Multivariate Compactly Supported Wavelets
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"Shen Zuo Wei" (

PostPosted: Thu Aug 14, 1997 10:37 am    
Subject: Preprint: Multivariate Compactly Supported Wavelets
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#2 Preprint: Multivariate Compactly Supported Wavelets

Multivariate Compactly Supported Fundamental Refinable Functions,
Duals and Biorthogonal Wavelets

Hui Ji, Sherman D. Riemenschneider and Zuowei Shen

Abstract: For a given continuous compactly supported refinable
function $phi$ that is fundamental (that means,
$phi(ga)=delta_ga$), this paper presents several methods to
construct, directly from $phi$, compactly supported fundamental
refinable functions with higher regularity. Asymptotic regularity
analyses of the constructions are given. These constructions
immediately provide multivariate interpolatory subdivision schemes
that generate highly smooth surfaces.

These constructions also lead directly to constuctions of a pair of
dual refinable functions with high regularity in any number of
variables. Combined with the biorthogonal wavelet construction
algorithm for a pair of dual refinable functions given in ef{RiS2},
we obtain symmetric multivariate biorthogonal wavelets with
arbitrarily high regularity.

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