Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm

Qun Mo; Yi Shen

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arXiv · 1101.4458

Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm

Qun Mo·Yi Shen

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Abstract

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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Qun Mo, Yi Shen. 2011-01-24. Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm. https://arxiv.org/abs/1101.4458

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