Continuous Shearlet Tight Frames |
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Authors: | Philipp Grohs |
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Affiliation: | (1) Department of Mathematics, Missouri State University, Springfield, MO 65804, USA;(2) Department of Mathematics, University of Houston, 651 Phillip G Hoffman, Houston, TX 77204-3008, USA |
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Abstract: | Based on the shearlet transform we present a general construction of continuous tight frames for L 2(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. |
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