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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. 

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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",
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