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A Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit

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2 Author(s)
Qun Mo ; Dept. of Math., Zhejiang Univ., Hangzhou, China ; Yi Shen

This paper demonstrates that if the restricted isometry constant δK+1 of the measurement matrix A satisfies [δK+1 <; 1 √K+1] then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover every K-sparse signal x in K iterations from Ax. By contrast, a matrix is also constructed with the restricted isometry constant [δK+1 = 1 √K] such that OMP can not recover some K-sparse signal x in K iterations. This result positively verifies the conjecture given by Dai and Milenkovic in 2009.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 6 )