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Shearlets pp 39-67 | Cite as

Shearlets and Microlocal Analysis

  • Philipp Grohs
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Although wavelets are optimal for describing pointwise smoothness properties of univariate functions, they fail to efficiently characterize the subtle geometric phenomena of multidimensional singularities in high-dimensional functions. Mathematically these phenomena can be captured by the notion of the wavefront set which describes point- and direction-wise smoothness properties of tempered distributions. After familiarizing ourselves with the definition and basic properties of the wavefront set, we show that the shearlet transform offers a simple and convenient way to characterize the wavefront set in terms of the decay properties of the shearlet coefficients.

Key words

Microlocal analysis Radon transform Representation formulas Wavefront set 

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Notes

Acknowledgements

This work was supported by the European Research Council under grant ERC AdG 247277.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland

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