Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm

Details Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm

2011-01-24

arxiv.org/abs/1101.4458v4

Computer Science

Information Theory

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Scientific paper

This paper demonstrates theoretically that if the restricted isometry constant $\delta_K$ of the compressed sensing matrix satisfies $$ \delta_{K+1} < \frac{1}{\sqrt{K}+1}, $$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover a signal with $K$ nonzero entries in $K$ iterations. In contrast, matrices are also constructed with restricted isometry constant $$ \delta_{K+1} = \frac{1}{\sqrt{K}} $$ such that OMP can not recover $K$-sparse $x$ in $K$ iterations. This result shows that the conjecture given by Dai and Milenkovic is ture.

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