Perturbation Analysis of Orthogonal Matching Pursuit
  Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for sparse approximation. Previous studies of OMP have mainly considered the exact recovery of a sparse signal $\bm x$ through $\bm \Phi$ and $\bm y=\bm \Phi \bm x$, where $\bm \Phi$ is a matrix with more columns than rows. In this paper, based on Restricted Isometry Property (RIP), the performance of OMP is analyzed under general perturbations, which means both $\bm y$ and $\bm \Phi$ are perturbed. Though exact recovery of an almost sparse signal $\bm x$ is no longer feasible, the main contribution reveals that the exact recovery of the locations of $k$ largest magnitude entries of $\bm x$ can be guaranteed under reasonable conditions. The error between $\bm x$ and solution of OMP is also estimated. It is also demonstrated that the sufficient condition is rather tight by constructing an example. When $\bm x$ is strong-decaying, it is proved that the sufficient conditions can be relaxed, and the locations can even be recovered in the order of the entries' magnitude. 
Jie Ding, Laming Chen, and Yuantao Gu
cs.IT math.IT