Generalized orthonormal piecewise constant wavelet bases with 1-4 splitting (Q2893480)
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scientific article; zbMATH DE number 6048363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized orthonormal piecewise constant wavelet bases with 1-4 splitting |
scientific article; zbMATH DE number 6048363 |
Statements
20 June 2012
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orthonormal wavelets
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bivariate wavelets
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piecewise constant wavelets
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wavelets on manifolds
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reconstruction error
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Haar wavelets
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Generalized orthonormal piecewise constant wavelet bases with 1-4 splitting (English)
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The author constructs orthonormal piecewise constant wavelets on 2-dimensional manifolds, in the case when the refinement process consists in dividing a domain into four subdomains of equal area. It is shown that the Haar wavelets minimize the \(\infty\)-norm of the reconstruction error, but not the 1-norm. This construction of wavelets applies not only to planar domains, but also to surfaces of revolution, like sphere, cone, or paraboloid. Examples are not given.
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