合成孔径雷达（SAR)图像可使用随机欠采样数据进行重建。平滑l0范数法（SL0)作为一种压缩感知SAR图像重建方法，具有重建速度快、算法简单等优点,但也存在一些缺点。其使用的最速下降法在迭代方向上出现“锯齿现象”，会增大SAR图像重构时间；且其使用的高斯拟合函数对于离散l0范数的匹配程度欠佳，影响重建精度，导致重建后的SAR图像分辨率不高。针对上述问题，通过引入近似双曲正切函数和混合优化算法，提出了一种重建效果更好的A-HNSL0 SAR图像重建方法。实验表明，在相同外部条件下，所提SAR图像重建方法在重建速度及重建精度上都有一定程度的提高。

Synthetic Aperture Radar (SAR) images can be reconstructed by using random undersampled data.The smoothed l0 norm (SL0) method is a compressed sensing SAR image reconstruction method with fast reconstruction speed and a simple algorithm.However,the steepest descent technique used in the method may result in the phenomenon of contour jaggies in the iteration direction,which greatly increases the time consumption of SAR image reconstruction.In addition,the Gaussian fitting function that is used in the method has a poor matching degree to the discrete l0 norm,which will affect the accuracy of image reconstruction,and the resolution of the reconstructed SAR image is not high enough.To solve the above problems,an SAR image reconstruction method based on Almost-Hybird Newton Smoothed l0 norm (A-HNSL0) is proposed by introducing the approximate hyperbolic tangent function and the hybrid optimization algorithm.Experimental results show that the proposed method makes certain improvements to both the reconstruction speed and the reconstruction accuracy under the same external conditions.