# 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} }

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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