双层稀疏组Lasso高分辨SAR结构特征增强成像

针对合成孔径雷达(synthetic aperture radar, SAR)成像中,基于?₁正则化线性回归(简称为Lasso)的凸优化类算法在进行稀疏特征增强时会导致弱散射体结构特征丢失，进而影响稀疏信号恢复精度的问题,本文提出一种基于双层稀疏组Lasso罚高斯回归模型的交替方向多乘子算法。该算法以散射体的块结构(组)特征为先验,首先针对SAR数据分类特征引入?₁范数对应的近端算子,通过在交替方向多乘子方法框架中利用高斯-赛德尔思想对其近端算子进行对偶迭代运算,实现第一层和第二层SAR组间的稀疏特征增强。另外混合范数中的?_F范数为高斯惩罚项,可对SAR回波复数据整体进行平滑,实现SAR结构特征增强成像。因此，所提算法可在SAR回波复数据处理中同时实现稀疏特征和结构特征联合增强。实验选取SAR、SAR地面动目标成像(SAR ground moving target imaging, SAR-GMTIm)和逆SAR的仿真数据与实测数据,分别从定性和定量两种角度对所提算法和传统算法进行对比,其中定量分析时采用相变图(phase transition diagram, PTD)方法来验证所提算法的重建能力，从而验证了本文所提算法应用于SAR稀疏与结构特征增强的有效性与优越性。

High resolution SAR imagery with structural feature enhancement under two-layer sparse group Lasso

In synthetic aperture radar(SAR) imagery,the conventional convex optimization algorithms based on least absolute shrinkage and selection operator(Lasso shorted) may lead to the loss of structural features in weak scattering and affect the accuracy of the sparse signal recovery when sparsity enhancement is carried out.To solve this problem,a novel algorithm based on two-layer sparse group Lasso of alternating direction method of multipliers(SGL-ADMM) is proposed in this paper.Based on the block structure(group)feature of the scatterer as a prior,the proposed method firstly introduces the proximal operator corresponding to ■ norm according to the classified feature of the SAR data.Then,it realizes the sparse feature enhancement in the first-layer and second-layer SAR group by using the Gauss-Seidel strategy to perform dual iterative operation for the proximal operators in the ADMM framework.In addition,the ■ norm in the mixed norm is the Gaussian penalty item,which can smooth the SAR echo data for realizing the enhanced structural features of SAR,accordingly.Therefore,the proposed algorithm can realize the joint enhancement of sparse feature and structure feature during echoed complex SAR data processing.In the experiments,the simulation data and the measured data of SAR,SAR ground moving target imaging(SAR-GMTIm) and inverse SAR are selected to compare the proposed algorithm with the traditional algorithm from the qualitative and quantitative perspectives.The phase transition diagram(PTD) method is used to verify the reconstruction ability of the proposed algorithm in the qualitative analysis,so as to verify the effectiveness and superiority of the proposed algorithm in SAR sparese and structural feature enhancement.