  In the context of compressed sensing (CS), both Subspace Pursuit (SP) and
Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative
greedy recovery algorithms which could reduce the recovery complexity greatly
comparing with the well-known $\ell_1$-minimization. Restricted isometry
property (RIP) and restricted isometry constant (RIC) of measurement matrices
which ensure the convergency of iterative algorithms play key roles for the
guarantee of successful reconstructions. In this paper, we show that for the
$s$-sparse recovery, the RICs are enlarged to $\delta_{3s}<0.4859$ for SP and
$\delta_{4s}<0.5$ for CoSaMP, which improve the known results significantly.
The proposed results also apply to almost sparse signal and corrupted
measurements.
