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Research Acknowledging KAUST Support
Research Acknowledging KAUST Support
Publications Acknowledging KAUST Support
Continuous Shearlet Tight Frames
Continuous Shearlet Tight Frames
Type
Article
Authors
Grohs, Philipp
Online Publication Date
2010-10-22
Print Publication Date
2011-06
Date
2010-10-22
Abstract
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.
Citation
Grohs P (2010) Continuous Shearlet Tight Frames. Journal of Fourier Analysis and Applications 17: 506–518. Available:
http://dx.doi.org/10.1007/s00041-010-9149-y.
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.
Publisher
Springer Nature
Journal
Journal of Fourier Analysis and Applications
DOI
10.1007/s00041-010-9149-y
Permanent link to this record
http://hdl.handle.net/10754/597848
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