Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames

  title={Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames},
  author={Gitta Kutyniok and Jakob Lemvig and Wang-Q Lim},
  journal={SIAM J. Math. Anal.},
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… 

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