Certifying the Restricted Isometry Property is Hard

@article{Bandeira2013CertifyingTR,
  title={Certifying the Restricted Isometry Property is Hard},
  author={A. Bandeira and Edgar Dobriban and Dustin G. Mixon and William F. Sawin},
  journal={IEEE Transactions on Information Theory},
  year={2013},
  volume={59},
  pages={3448-3450}
}
  • A. Bandeira, Edgar Dobriban, +1 author William F. Sawin
  • Published 2013
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided P ≠ NP. 

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