Geometric multiscale analysis: from wavelets to parabolic molecules (Q2803912)
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scientific article; zbMATH DE number 6576501
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometric multiscale analysis: from wavelets to parabolic molecules |
scientific article; zbMATH DE number 6576501 |
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3 May 2016
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geometric multiscale analysis
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wavelets
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anisotropic system
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shearlets
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curvelets
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parabolic molecules
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0.8810898
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0.85042524
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0.8417907
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0.8366036
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0.8357326
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Geometric multiscale analysis: from wavelets to parabolic molecules (English)
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The article discusses several concepts of sparse representation of multivariate functions. First, wavelet systems are introduced. Since an isotropic approach using wavelets is adapted to point out singularities and many phenomena in several variables exhibit also curvilinear singularities, suitable anisotropic systems are needed. In the paper, the requirements on the system are formulated and examples of anisotropic systems, namely shearlets, curvelets and parabolic molecules, are presented. The definition of parabolic molecules is generalized to \(\alpha\)-molecules and it is shown that wavelets are a special case. The framework of shearlets is extended to universal shearlets.
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