Improved Analysis for Subspace Pursuit Algorithm in Terms of Restricted Isometry Constant

In the context of compressed sensing (CS), subspace pursuit (SP) is an important iterative greedy recovery algorithm which could reduce the recovery complexity greatly comparing with
${\ell _1}$
-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of measurement matrices which ensure the convergence of iterative algorithms play key roles for the guarantee of successful reconstructions. In this letter, we show that for the
$s$
-sparse recovery, the RIC is enlarged to
${\delta _{3s}} < 0.4859$
for SP, which improves the known results significantly. The proposed result also applies to almost sparse signals and corrupted measurements.