Robust and Efficient Sparse-feature Enhancementfor Generalized SAR Imagery
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摘要: 针对合成孔径雷达(SAR)成像中的稀疏特征增强问题，传统方法难以在精度与效率之间实现有效的平衡。该文提出基于复数交替方向多乘子方法(C-ADMM)，针对SAR稀疏特征增强建立增广的拉格朗日优化方程，并引入复数
${\ell _1}$ 范数邻近算子，基于高斯-赛德尔思想进行对偶迭代运算，从而在复数回波数据域内对多种SAR模式的实测数据进行成像。实验部分首先通过仿真数据的相变图(PTD)验证C-ADMM算法对于复数数据的稀疏恢复性能，然后选取地面静止场景和地面运动目标的原始SAR图像和逆SAR图像实测数据，与凸优化(CVX)方法和贝叶斯压缩感知(BCS)方法进行对比试验，最后验证了该文所提算法在稀疏特征增强应用中的稳健性、高效性和通用性。-
关键词:
- 合成孔径雷达 /
- 稀疏特征增强 /
- 复数交替方向多乘子方法 /
- 增广拉格朗日优化方程
Abstract: For the problem of sparse feature enhancement in Synthetic Aperture Radar (SAR) imagery, conventional methods are difficult to achieve a preferable balance between accuracy and efficiency. In this paper, a robust and efficient SAR imaging algorithm based on Complex Alternating Direction Method of Multipliers(C-ADMM) is proposed for general SAR imaging feature enhancement within complex raw data domain. The problem is firstly imposed by an augmented Lagrange function, and the complex${\ell _1}$ -norm of the intended SAR image is jointly formulated within the C-ADMM framework. Then, the proximal mapping of the sparse feature is derived as a soft-thresholding operator. Further, an iterative processing procedure is designed according to Gaussian-Deidel principle, and the convergence of the proposed algorithm is analyzed. In the experiment, the performance of the proposed algorithm is firstly examined by the simulated data in terms of Phase Transition Diagram (PTD) under different under-sampling rate and degree of sparsity. Then, various raw SAR and Inverse SAR(ISAR) data, for both stationary ground scene and Ground Moving Target Imaging(CMTIm), are applied to further verifying the proposed C-ADMM, and comparisons with classical Convex(CVX) and Bayesian Compress Sensing(BCS) algorithms are performed, so that both the effectiveness and superiority of the C-ADMM algorithm can be verified. -
表 1 C-ADMM稀疏特征增强算法流程
(1) 初始化，输入SAR原始数据； (2) 信号预处理，得到通用信号模型$S\left( {\hat r,t} \right)$或$S\left( {\hat r,{t'}} \right)$； (3) 设定初值${{X}^0} = {{Z}^0} = {{U}^0} = 0$，构造字典${A}$=${{A}_0}$或${A}\left( {{\gamma _d}} \right)$； (4) 设定迭代次数与目标精度，若停止准则不满足，进行循环； (5) 更新目标图像
${{X}^{k + 1}} = {\left( {{{A}^{\rm{H}}}{A} + \rho {I}} \right)^{ - 1}}\left\{ {{{A}^{\rm{H}}}{Y} + \rho \left( {{{Z}^k} - {{U}^k}} \right)} \right\}$;(6) 更新软阈值${{Z}^{k + 1}} = {S_{\lambda /\rho }}\left( {{{X}^{k + 1}} + {{U}^k}} \right)$; (7) 更新对偶变量${{U}^{k + 1}} = {{U}^k} + {{X}^{k + 1}} - {{Z}^{k + 1}}$; (8) 若不满足停止准则，继续步骤5—步骤7，若满足停止准则，跳 出循环； (9) 输出稀疏特征增强后的图像。 
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