The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing

@article{Tillmann2014TheCC,
  title={The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing},
  author={Andreas M. Tillmann and Marc E. Pfetsch},
  journal={IEEE Transactions on Information Theory},
  year={2014},
  volume={60},
  pages={1248-1259}
}
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several such conditions have been introduced. The most well-known ones are the mutual coherence, the restricted isometry property (RIP), and the nullspace property (NSP). While evaluating the mutual coherence of a given matrix is easy, it has been suspected for some… CONTINUE READING
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