Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm

@article{Mo2011RemarksOT,
title={Remarks on the Restricted Isometry Property in Orthogonal Matching Pursuit algorithm},
author={Qun Mo and Yi Shen},
journal={CoRR},
year={2011},
volume={abs/1101.4458}
}

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… CONTINUE READING