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

@article{Kutyniok2012OptimallySA,
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.},
year={2012},
volume={44},
pages={2962-3017}
}
• Published 27 September 2011
• Computer Science
• 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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