  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.
