Shift-invariant spaces from rotation-covariant functions
Journal
Applied and Computational Harmonic Analysis
Journal Volume
25
Journal Issue
2
Date Issued
2008-09-01
Author(s)
Abstract
We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in R2. To construct corresponding scaling and wavelet functions, ρ 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 scaling functions and 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. © 2007 Elsevier Inc. All rights reserved.
Subjects
Complex wavelets | Multiresolution | Riesz basis | Rotation covariance | Scaling functions | Shift-invariant spaces | Two-scale relation
Type
journal article