Sparse Recovery With Orthogonal Matching Pursuit Under RIP

@article{Zhang2011SparseRW,
  title={Sparse Recovery With Orthogonal Matching Pursuit Under RIP},
  author={Tong Zhang},
  journal={IEEE Transactions on Information Theory},
  year={2011},
  volume={57},
  pages={6215-6221}
}
  • Tong Zhang
  • Published 12 May 2010
  • Computer Science
  • IEEE Transactions on Information Theory
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level <i>O</i>(k̅), then OMP can stably recover a <i>k̅</i>-sparse signal in 2-norm under measurement noise. For compressed sensing applications, this result implies that in order to uniformly recover a <i>k̅</i>-sparse signal in R<i>d</i>, only <i>O</i>(<i>k̅</i> ln<i>d</i>) random projections are needed. This analysis… 
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