Stable, linear spline wavelets on nonuniform knots with vanishing moments

In wavelet analysis on nonuniform grids it is desirable that the wavelet scheme is stable in some norm independently of the grid spacing (grid stability). It is known that this kind of stability is difficult to achieve for spline wavelets based on orthogonal complements, with stability measured in t...

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Bibliographic Details
Published inComputer aided geometric design Vol. 26; no. 2; pp. 203 - 216
Main Authors Lyche, Tom, Mørken, Knut, Pelosi, Francesca
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.02.2009
Elsevier
Subjects
Applied sciences
Computer aided design
Computer science; control theory; systems
Exact sciences and technology
Linear splines
Mechanical engineering. Machine design
Moments
Multiresolution analysis
Nonuniform knots
Software
Stability
Uniform norm
Wavelets
Linear splines
Wavelets
Stability
Nonuniform knots
Moments
Uniform norm
Multiresolution analysis
Linear interpolation
Grid
L2 approximation
Spacing
Spline approximation
Wavelet transformation
Orthogonal function
Computer aided design
Piecewise linearization
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Summary:In wavelet analysis on nonuniform grids it is desirable that the wavelet scheme is stable in some norm independently of the grid spacing (grid stability). It is known that this kind of stability is difficult to achieve for spline wavelets based on orthogonal complements, with stability measured in the L 2 -norm. On the other hand, a wavelet scheme based on piecewise linear interpolation (Faber decomposition) is known to be grid stable in the L ∞ norm. In this paper we show that Faber decomposition can be extended with preservation of moments, without sacrificing grid stability in the L ∞ norm.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2008.04.002