In compressed sensing, most previous researches have studied the recovery performance of a sparse signal x based on the acquired model y=Φx+n, where n denotes the noise vector. There are also related studies for general perturbation environment, i.e., y=(Φ+E)x+n, where E is the measurement perturbation. IHT and HTP algorithms are the classical algorithms for sparse signal reconstruction in compressed sensing. Under the general perturbations, this paper derive the required sufficient conditions and the error bounds of IHT and HTP algorithms.

In the context of compressed sensing (CS), simultaneous orthogonal matching pursuit (SOMP) algorithm is an important iterative greedy algorithm for multiple measurement matrix vectors sharing the same non-zero locations. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the convergence of CS algorithms. Based on the RIP of measurement matrix, this paper shows that for the K-row sparse recovery, the restricted isometry constant (RIC) is improved to $delta_{K+1}<rac{sqrt{4K+1}-1}{2K}$ for SOMP algorithm. In addition, based on this RIC, this paper obtains sufficient conditions that ensure the convergence of SOMP algorithm in noisy case.