Improved Analyses for SP and CoSaMP Algorithms in Terms of Restricted Isometry Constants

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.