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Open Access Green as soon as Postprint is submitted to ZB.
Shift-invariant spaces from rotation-covariant functions.
Appl. Comput. Harmon. Anal. 25, 240-265 (2008)
We consider shift-invariant multiresolution spaces generated by rotation-covariant functions {rho} in R2. To construct corresponding scaling and wavelet functions, {rho} has to be localized with an appropriate multiplier, such that the localized version is an element of L2(R2).We consider several classes of multipliers and show a new method to improve regularity and decay properties of the corresponding wavelets. The wavelets are complex-valued functions, which are approximately rotation-covariant and therefore behave as Wirtinger differential operators. Moreover, our class of multipliers gives a novel approach for the construction of polyharmonic B-splines with better polynomial reconstruction properties.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Complex wavelets, Riesz basis, two-scale relation, multiresolution, scaling functions, shift-invariant spaces, rotation covariance
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Quellenangaben
Volume: 25,
Issue: 2,
Pages: 240-265
Publisher
Academic Press
Publishing Place
San Diego, Calif. [u.a.]
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)