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Forster, B. ; Blu, T.* ; van de Ville, D.* ; Unser, M.*

Shift-invariant spaces from rotation-covariant functions.

Appl. Comput. Harmon. Anal. 25, 240-265 (2008)
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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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter 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 Band: 25, Heft: 2, Seiten: 240-265 Artikelnummer: , Supplement: ,
Verlag Academic Press
Verlagsort San Diego, Calif. [u.a.]
Begutachtungsstatus Peer reviewed