Shearlets and Microlocal Analysis
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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 wordsMicrolocal analysis Radon transform Representation formulas Wavefront set
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This work was supported by the European Research Council under grant ERC AdG 247277.
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