Shift-Invariant Spaces from Rotation-Covariant Functions
B. Forster, T. Blu, D. Van De Ville, M. Unser
Applied and Computational Harmonic Analysis, vol. 25, no. 2, pp. 240-265, September 2008.
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.
@ARTICLE(http://bigwww.epfl.ch/publications/forster0801.html, AUTHOR="Forster, B. and Blu, T. and Van De Ville, D. and Unser, M.", TITLE="Shift-Invariant Spaces from Rotation-Covariant Functions", JOURNAL="Applied and Computational Harmonic Analysis", YEAR="2008", volume="25", number="2", pages="240--265", month="September", note="")