Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator.

@article{Ozoli2014CompressedPW,
  title={Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator.},
  author={Vidvuds Ozoliņ{\vs} and Rongjie Lai and R. Strebel Caflisch and Stanley Osher},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={2014},
  volume={111 5},
  pages={1691-6}
}
This paper describes an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves, that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities. 

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