Based on the shearlet transform we present a general construction of continuous tight frames for L2(ℝ2) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From our earlier results in Grohs (Technical report, KAUST, 2009) it follows that these systems enjoy the same desirable approximation properties for directional data as the previous bandlimited and very specific constructions due to Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009). We also show that the representation formulas we derive are in a sense optimal for the shearlet transform. © 2010 Springer Science+Business Media, LLC.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research for this paper has been carried out while the author was working atthe Center for Geometric Modeling and Scientific Visualization at KAUST, Saudi Arabia.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.