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Shearlets and microlocal analysis

by P. Grohs

(Report number 2011-27)

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.

Keywords:

@Techreport{G11_137,
  author = {P. Grohs},
  title = {Shearlets and microlocal analysis},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-27},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-27.pdf },
  year = {2011}
}

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