An Accurate Sparse SAR Imaging Method for Enhancing Region-Based Features Via Nonconvex and TV Regularization

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, ℓ
₁
optimization induces sparsity the most effectively, and the ℓ
₁
-norm penalty is usually combined with the total variation norm (TV-norm) penalty to construct a compound regularizer in order to enhance the point-based features as well as the region-based features. However, as a convex optimizer, the analytic solution of ℓ
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 ℓ
₁
regularization, nonconvex regularization can reduce the average relative bias from 10.88% to 0.25%; compared with the matched filtering method and ℓ
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.