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}
}
Given a matrix A with n rows, a number k < n, and 0 < δ < 1, A is (k, δ)-RIP (Restricted Isometry Property) if, for any vector x ∈ R, with at most k non-zero co-ordinates, (1− δ)‖x‖2 ≤ ‖Ax‖2 ≤ (1 + δ)‖x‖2 In other words, a matrix A is (k, δ)-RIP if Ax preserves the length of x when x is a k-sparse vector. In many applications, such as compressed sensing and sparse recovery, it is desirable to construct RIP matrices with a large k and a small δ. It is known that, with high probability, random… CONTINUE READING

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