A Simple Proof of the Restricted Isometry Property for Random Matrices

@inproceedings{Baraniuk2008ASP,
  title={A Simple Proof of the Restricted Isometry Property for Random Matrices},
  author={Richard G. Baraniuk and Mark A. Davenport and Ronald A. DeVore and Michael B. Wakin},
  year={2008}
}
We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property… CONTINUE READING
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