EPFL | Biomedical Imaging Group | Rotation Covariance

Shift-Invariant Spaces from Rotation-Covariant Functions

B. Forster, T. Blu, D. Van De Ville, M. Unser

Applied and Computational Harmonic Analysis, in press.

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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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