Variable Scale Iterative SAR Imaging Algorithm Based on Sparse Representation

Abstract

In this paper, we discuss the problem of sparse recovery in compressed sensing (CS) in the presence of measurement noise, and present a variable iterative synthetic aperture radar (SAR) imaging method based on sparse representation. In this paper, the sparse reconstruction theory is applied to SAR imaging. The SAR imaging problem is equivalent to solving the sparse solution of the underdetermined equation, and the imaging result of the target scene is obtained. Compared with the previous algorithms using \( l_{1} \)-norm or \( l_{2} \)-norm as cost function model, this paper combines \( l_{p} \)-norm \( (0 < p < 1) \) and \( l_{2} \)-norm as cost function model to obtain more powerful performance. In addition, a smoothing strategy has been adopted to obtain the convergence method under the non-convex case of \( l_{p} \)-norm term. In the framework of this iterative algorithm, the proposed algorithm is compared with some traditional imaging algorithms through simulation experiments. Finally, the simulation results show that the proposed algorithm improves the SAR signal recovery performance to a certain extent and has a certain anti-noise ability. In addition, the improvement is more evident when the SAR signal is block sparse.