Fast High-resolution Imaging Method for Wideband Spinning Targets under Sub-Nyquist Sampling
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摘要: 逆合成孔径雷达(ISAR)观测自旋目标时，自旋目标回波的距离-多普勒时变性会导致传统成像方法失效。针对此问题，该文提出一种基于分布式匹配稀疏表示模型的宽带自旋目标快速高分辨成像方法。首先，通过自旋目标回波在距离频域表征出的稀疏性，构建分布式匹配稀疏表示模型；其次，研究快速分布式同步多正交匹配追踪算法，并通过减少算法总的迭代次数和每次迭代运算量来提高算法的重构效率，同时设计相关阈值抑制虚假重构散射点，实现鲁棒成像；最后，从理论上分析该方法在欠采样及低信噪比条件下依然可获得高质量图像的机理。仿真结果证明了该方法的有效性。Abstract: When using Inverse Synthetic Aperture Radar (ISAR) to observe the spinning targets, the range-Doppler time-varying characteristics of spinning target echo would lead to the inefficiency of traditional imaging methods. To solve this problem, a fast high-resolution imaging method based on distributed matching sparse representation model is proposed for wideband spinning targets imaging. Firstly, a distributed matching sparse representation model is constructed based on the sparsity of spinning target echo. Secondly, a Fast Distributed Simultaneous Multiple Orthogonal Matching Pursuit (FDSMOMP) algorithm is proposed for achieving the fast robust imaging of the spinning parts. The proposed algorithm can significantly improve the reconstruction efficiency by reducing the iteration times and computational complexity of each iteration. Additionally, in order to enhance the robustness of FDSMOMP, a related threshold is designed to suppress the false reconstruction. Finally, the mechanism of the presented method is analyzed theoretically, and it is proved that the high quality imaging result can still be obtained under the conditions of sub-Nyquist sampling and lower (SNR Signal Noise Ratio). Simulation results show the validation of the proposed method.
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Key words:
- High-resolution sparse imaging /
- Sparsity /
- Spinning target /
- Sub-Nyquist sampling /
- Low SNR
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表 1 FDSMOMP算法
输入：量测数据 ${{Y}}$，感知矩阵 ${{Θ}}$，预置稀疏度 ${k_0}$，组选支撑集 $s$。 输出：重构结果 ${\tilde {{X}}_{{\rm{Finaset}}}}$。 算法初始化：初始残差 ${{{R}}^{\left( 0 \right)}} = {{Y}}$，预重构结果 $\tilde {{X}} = 0$，初始支
撑集 $\tilde {{S}} = \varnothing $。第1步 多原子识别：根据式(11)计算新原子支撑集 ${\rm{pos}}$，以此为 索引构建新的原子组； 第2步 投影计算：更新支撑集 ${\tilde S^j} = {\tilde S^{j - 1}} \cup {\rm{pos}}$，依据式(12)进 行投影值计算，得到 $\tilde {{X}}{({{{{{f}}}_p})_{\tilde S}}$； 第3步 残差更新： ${{R}}{\left( {{f_p}} \right)^{\left( j \right)}} = {{y}}\left( {{f_p}} \right) - {{Θ}}_{\tilde S}^{\left( j \right)}\tilde {{X}}{\left( {{{{f}_p}} \right)_{\tilde S}}$，判断迭代 停止条件是否满足，若满足则执行第4步，否则循环迭代 第1至第3步； 第4步 利用最小二乘估计最终结果 ${\tilde {{X}}_{{\rm{Finaset}}}}$。 
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表 2 不同算法的图像熵值和运算时间对比
欠采样倍数 DCS-SOMP FDSMOMP 图像熵值 运算时间(s) 图像熵值 运算时间(s) $\delta = 2$ 3.162 15.287 3.151 4.202 $\delta = 4$ 3.169 8.125 3.168 2.222 $\delta = 8$ 3.189 4.995 3.182 1.740
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