Computational Complexity of Certifying Restricted Isometry Property

@inproceedings{Natarajan2014ComputationalCO,
  title={Computational Complexity of Certifying Restricted Isometry Property},
  author={Abhiram Natarajan and Yi Wu},
  booktitle={APPROX-RANDOM},
  year={2014}
}
  • Abhiram Natarajan, Yi Wu
  • Published in APPROX-RANDOM 2014
  • Mathematics, Computer Science
  • Given a matrix $A$ with $n$ rows, a number $k<n$, and $0<\delta < 1$, $A$ is $(k,\delta)$-RIP (Restricted Isometry Property) if, for any vector $x \in \mathbb{R}^n$, with at most $k$ non-zero co-ordinates, $$(1-\delta) \|x\|_2 \leq \|A x\|_2 \leq (1+\delta)\|x\|_2$$ In many applications, such as compressed sensing and sparse recovery, it is desirable to construct RIP matrices with a large $k$ and a small $\delta$. Given the efficacy of random constructions in generating useful RIP matrices, the… CONTINUE READING

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