With the rapid development of compressed sensing theories and applications, sparse signal processing has been widely used in synthetic aperture radar (SAR) imaging during the recent years. As an efficient tool for sparse reconstruction, 1 optimization induces sparsity the most effectively, and the 1 -norm penalty is usually combined with the total variation norm (TV-norm) penalty to construct a compound regularizer in order to enhance the pointbased features as well as the region-based features. However, as a convex optimizer, the analytic solution of 1 regularization-based sparse signal reconstruction is usually a biased estimation. Aiming at this issue, in this article, we quantitatively analyzed the variation of reconstruction bias with respect to the complex reflectivity of targets, the undersampling ratio and the noise power. In order to reduce the bias effect and improve the reconstruction accuracy, we adopted the nonconvex regularization-based sparse SAR imaging method with a nonconvex penalty family. Furthermore, we linearly combined the nonconvex penalty and the TV-norm penalty to form a compound regularizer in the imaging model, which can improve the reconstruction accuracy of distributed targets and maintain the continuity of the backscattering coefficient. Simulation results showed that compared with 1 regularization, nonconvex regularization can reduce the average relative bias from 10.88% to 0.25%; compared with the matched filtering method and 1 and TV regularization, nonconvex & TV regularization can reduce the variance of the uniformly distributed targets by 80% without losing of reconstruction accuracy. Experiments on Gaofen-3 SAR data are also exploited to verify the effectiveness of the proposed method.

Sparse signal processing theory has been applied to synthetic aperture radar (SAR) imaging. In compressive sensing (CS), the sparsity is usually considered as a known parameter. However, it is unknown practically. For many functions of CS, we need to know this parameter. Therefore, the estimation of sparsity is crucial for sparse SAR imaging. The sparsity is determined by the size of regularization parameter. Several methods have been presented for automatically estimating the regularization parameter, and have been applied to sparse SAR imaging. However, these methods are deduced based on an observation matrix, which will entail huge computational and memory costs. In this paper, to enhance the computational efficiency, an efficient adaptive parameter estimation method for sparse SAR imaging is proposed. The complex image-based sparse SAR imaging method only considers the threshold operation of the complex image, which can reduce the computational costs significantly. By utilizing this feature, the parameter is pre-estimated based on a complex image. In order to estimate the sparsity accurately, adaptive parameter estimation is then processed in the raw data domain, combining with the pre-estimated parameter and azimuth-range decouple operators. The proposed method can reduce the computational complexity from a quadratic square order to a linear logarithm order, which can be used in the large-scale scene. Simulated and Gaofen-3 SAR data processing results demonstrate the validity of the proposed method.