Polyharmonic multiresolution analysis: an overview and some new results

被引：7

作者：

Rabut, Christophe ^{[1
]}

Rossini, Milvia ^{[2
]}

机构：

[1] Univ Toulouse, INSA, IMT, F-31077 Toulouse 4, France

[2] Univ Milan, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

来源：

NUMERICAL ALGORITHMS | 2008年 / 48卷 / 1-3期

关键词：

polyharmonic splines; wavelets; MRA filters;

D O I：

10.1007/s11075-008-9173-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper first presents a condensed state of art on multiresolution analysis using polyharmonic splines: definition and main properties of polyharmonic splines, construction of B-splines and wavelets, decomposition and reconstruction filters; properties of the so-obtained operators, convergence result and applications are given. Second this paper presents some new results on this topic: scattered data wavelet, new polyharmonic scaling functions and associated filters. Fourier transform is of extensive use to derive the tools of the various multiresolution analysis.

引用

页码：135 / 160

页数：26

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