The l₁-norm based compressed sensing (CS) model cannot fully explore the sparsity property of a signal, and the weighted constraint of the restored coefficients is seldom equally arranged during the reconstruction. Therefore, the characteristic of the non-sparsity of the noise will seriously affect the restoration of the target information in low signal-to-noise (SNR) conditions, which may result in quite many false targets during imaging, leading to a sharp decline of the imaging quality. This paper provided a detailed analysis of the reweighted l₁-norm model for CS reconstruction, and proposed a robust high resolution imaging model with corrupted echo. The main idea is inspired by the canonical reweighted l₁-norm based CS model, but the selection of the weight parameters are improved, which equally penalize the variation and separation of large and small weights, and the noise components can be effectively suppressed during the imaging. Simulation results testify the validity of the proposed model in low SNR conditions.