Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimally sparse approximations of 3D functions by compactly supported
  shearlet frames   We study efficient and reliable methods of capturing and sparsely
representing anisotropic structures in 3D data. As a model class for
multidimensional data with anisotropic features, we introduce generalized
three-dimensional cartoon-like images. This function class will have two
smoothness parameters: one parameter \beta controlling classical smoothness and
one parameter \alpha controlling anisotropic smoothness. The class then
consists of piecewise C^\beta-smooth functions with discontinuities on a
piecewise C^\alpha-smooth surface. We introduce a pyramid-adapted, hybrid
shearlet system for the three-dimensional setting and construct frames for
L^2(R^3) with this particular shearlet structure. For the smoothness range
1<\alpha =< \beta =< 2 we show that pyramid-adapted shearlet systems provide a
nearly optimally sparse approximation rate within the generalized cartoon-like
image model class measured by means of non-linear N-term approximations.

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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ