On efficiency of Orthogonal Matching Pursuit

We show that if a matrix $\mathrm{\Phi }$ satisfies the RIP of order $[C{K}^{1.2}]$ with isometry constant $\text{dt}=c{K}^{-0.2}$ and has coherence less than $1\mathrm{/}(20K^{0.8})$, then Orthogonal Matching Pursuit (OMP) will recover $K$-sparse signal $x$ from $y=\mathrm{\Phi }x$ in at most $[C{K}^{1.2}]$ iterations. This result implies that $K$-sparse signal can be recovered via OMP by $M=O(K^{1.6}\log N)$ measurements.