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摘要: 合成孔径雷达三维成像技术(3D SAR)能通过孔径维度扩展实现三维成像能力，但数据维度大、系统实现难、成像分辨率低。压缩感知稀疏重构技术在简化3D SAR系统、提升成像质量等方面展现出巨大潜力，但面临计算复杂度高、参数设置困难、弱稀疏场景适应差等新问题，制约了其实际应用。针对上述问题，该文结合卷积神经网络的特征学习及迭代算法的深度展开理论，提出了基于自学习稀疏先验的3D SAR成像方法。首先，探讨了常规3D SAR稀疏成像中矩阵向量线性表征模型的局限性，引入成像算子提升成像算法处理效率。其次，讨论了迭代算法映射网络的深度展开模型和实现方式，包括网络拓扑结构设计、算法参数的优化约束及网络的训练方法。最后，通过仿真数据和地面实验，证明了所提方法在提升成像精度的同时，其运行时间较传统稀疏成像算法降低一个数量级。Abstract: The development of 3D Synthetic Aperture Radar (SAR) imaging is currently hampered by issues such as high data dimension, high system complexity, and low imaging processing efficiency. Sparse SAR imaging has grown in importance as a research branch in SAR imaging due to the high potential of sparse signal processing techniques based on Compressed Sensing (CS) to show high potential in reducing system complexity and improving imaging quality. However, traditional sparse imaging methods are still constrained by high computational complexity, nontrivial parameter tuning, and poor adaptability to weakly sparse scenes. To address these issues, we propose a new 3D SAR imaging method based on learned sparse priors inspired by the deep unfolding concept. First, the limitations of the matrix-vector linear representation model are discussed, and an imaging operator is introduced to improve the algorithm’s imaging efficiency. Furthermore, this research focuses on algorithm network details, such as network topology design, the problem of complex-valued propagations, optimization constraints of algorithm parameters, and network training details. Finally, through simulations and measured experiments, it is proved that the proposed method can improve the imaging accuracy while reducing the running time by more than one order of magnitude compared with the conventional sparse imaging algorithms.
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Key words:
- 3D SAR /
- Deep learning /
- Deep unfolding /
- Sparse representation /
- Sparse imaging
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图 3 各算法在采样率分别为70%和30%时的重构结果
Figure 3. Reconstructions of different algorithms in cases of sampling rate being 70% and 30%, respectively
图 4 各算法在SNR分别为10 dB和0 dB时的重构结果
Figure 4. Reconstructions of different algorithms in cases of SNR being 10 dB and 0 dB, respectively
图 6 各算法在采样率为50%和30%时的三维仿真成像结果
Figure 6. 3D imaging results of different algorithms in cases of sampling rate being 50% and 30%
图 7 各算法在信噪比分别为10 dB和0 dB时的三维仿真成像结果
Figure 7. 3D imaging results of different algorithms in cases of SNR being 10 dB and 0 dB
图 9 各算法在采样率为50%和30%时钢片测试板的三维成像结果
Figure 9. 3D imaging results of the testing steel chip by different algorithms when sampling rate are 50% and 30%
图 10 各算法在采样率为50%和30%时隐匿刀具的成像结果
Figure 10. Imaging results of conceal knives by different algorithms when sampling rate are 50% and 30%
图 11 各稀疏成像算法在不同目标点数时的成像结果
Figure 11. Imaging results of different algorithms in cases of the different number of scatterers
算法1 基于核函数的ISTA稀疏成像算法 Alg. 1 ISTA sparse imaging algorithm based on
kernel functions输入：稀疏降采样回波E，相位传播矩阵P，迭代步长$\tau $，迭代
层数T输出：稀疏成像结果$ {{\boldsymbol{X}}^{\left( T \right)}} $ 初始化：$t = 1$, ${{\boldsymbol{X}}^{\left( 0 \right)}} = {\mathcal{M}^{\text{H}}}\left( {{\boldsymbol{E}},{{\bar {\boldsymbol{P}}}}} \right)$； 循环开始 (1) 更新迭代残差：$ {{\boldsymbol{V}}^{\left( t \right)}} = {\boldsymbol{E}} - \mathcal{M}\left( {{{\boldsymbol{X}}^{\left( {t - 1} \right)}},{\boldsymbol{\bar P}}} \right) $； (2) 梯度下降粗估计：$ {{\boldsymbol{R}}^{\left( t \right)}} = {{\boldsymbol{X}}^{\left( {t - 1} \right)}} + \tau {\mathcal{M}^{\text{H}}}\left( {{{\boldsymbol{V}}^{\left( t \right)}},{\boldsymbol{P}}} \right) $； (3) 软阈值收缩去噪： ${ {\boldsymbol{X} }^{\left( t \right)} } = {{\rm{soft}}} \left( { { {\boldsymbol{R} }^{\left( t \right)} },\lambda } \right)$, $t = t + 1$； (4) 迭代判定：若$t \le T$，则重复步骤(1)—步骤(4)；否则，结束循环。 循环结束 
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算法2 LSISTA网络稀疏成像算法 Alg. 2 LSISTA network-based sparse imaging algorithm 输入：稀疏降采样回波E，相位传播矩阵P； 输出：稀疏成像结果$ {{\boldsymbol{X}}^{\left( T \right)}} $ 初始化：加载卷积核预训练权重，$ \left\{ {{w_1},{b_1},{w_2},{b_2}} \right\} $； 循环开始 (1) 根据式(14)，由$ \left\{ {{w_1},{b_1},{w_2},{b_2}} \right\} $计算$ {\tau ^{\left( t \right)}} $和$ {\lambda ^{\left( t \right)}} $； (2) 更新迭代残差：$ {{\boldsymbol{V}}^{\left( t \right)}} = {\boldsymbol{E}} - \mathcal{M}\left( {{{\boldsymbol{X}}^{\left( {t - 1} \right)}},{\boldsymbol{\bar P}}} \right) $； (3) 梯度下降粗估计：$ {{\boldsymbol{R}}^{\left( t \right)}} = {{\boldsymbol{X}}^{\left( {t - 1} \right)}} + {\tau ^{\left( t \right)}}{\mathcal{M}^{\text{H}}}\left( {{{\boldsymbol{V}}^{\left( t \right)}},{\boldsymbol{P}}} \right) $； (4) 软阈值收缩去噪：
${ {\boldsymbol{X} }^{\left( t \right)} } = \tilde {\mathcal{T} }\left( {{\rm{soft}}} \left( {\mathcal{T}\left( { { {\boldsymbol{R} }^{\left( t \right)} } } \right),{\lambda ^{\left( t \right)} } } \right) \right)$, $t = t + 1$；(5) 迭代判定：若$t \le T$，则重复步骤(1)—步骤(5)；否则，结束循环。 循环结束
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表 1 各算法在不同采样率情况下的MAE值
Table 1. MAEs of different algorithms in cases of sampling rate being 70% and 30%, respectively
算法 Profile #1 Profile #2 Profile #3 70% 30% 70% 30% 70% 30% RMA 0.064 0.104 0.075 0.118 0.063 0.105 ISTA 0.024 0.038 0.037 0.058 0.025 0.041 RMIST-Net 0.014 0.022 0.023 0.034 0.015 0.024 LSISTA 0.005 0.012 0.006 0.017 0.005 0.013
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表 2 各算法在不同SNR情况下的MAE值
Table 2. MAEs of different algorithms in cases of SNR being 10 dB and 0 dB, respectively
算法 Profile #1 Profile #2 Profile #3 10 dB 0 dB 10 dB 0 dB 10 dB 0 dB RMA 0.089 0.118 0.102 0.135 0.085 0.118 ISTA 0.038 0.071 0.056 0.093 0.038 0.072 RMIST-Net 0.018 0.026 0.030 0.046 0.020 0.029 LSISTA 0.005 0.008 0.006 0.015 0.005 0.009
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表 3 仿真和实测系统参数
Table 3. Parameters in simulations and real experiments
参数 三维SAR仿真值 实测系统值 载频(GHz) 77 78.8 带宽(GHz) 4 3.6 孔径尺寸(cm) 100×100 40×40 采样间隔(mm) x : 7.8; z : 7.8 x : 1; z : 2 距离(m) 15 具体指定
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表 4 三维SAR成像仿真在不同降采样率下各算法的图像熵评估
Table 4. Image entropy of different algorithms with different sampling rates in simulated 3D SAR imaging
算法 50% 30% Time (s) (CPU/GPU) RMA 2.757 3.128 0.336/— ISTA 0.363 0.387 13.561/— RMIST-Net 0.087 0.062 1.522/0.026 LSISTA 0.299 0.289 7.054/0.033
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表 5 三维SAR成像仿真在信噪比下各算法的图像熵评估
Table 5. Image entropy of different algorithms with different SNRs in simulated 3D SAR imaging
算法 10 dB 0 dB Time (s) (CPU/GPU) RMA 2.789 3.155 0.337/— ISTA 0.548 0.884 14.523/— RMIST-Net 0.377 0.632 1.630/0.030 LSISTA 0.379 0.419 6.931/0.036
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表 6 图9成像实验中各算法的图像熵评估
Table 6. Image entropy of different algorithms in the experiment of Fig. 9
算法 50% 30% Time (s) (CPU/GPU) RMA 4.530 4.761 0.176/— ISTA 1.125 0.948 6.604/— RMIST-Net 0.749 0.584 0.156/0.010 LSISTA 0.586 0.429 3.461/0.013
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表 7 图10成像实验中各算法的图像熵评估
Table 7. Image entropy of different algorithms in the experiment of Fig. 10
算法 50% 30% Time (s) (CPU/GPU) RMA 6.141 5.960 0.135/— ISTA 3.567 3.058 6.086/— RMIST-Net 2.719 2.159 0.115/ 0.009 LSISTA 2.376 1.845 3.103/0.013
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表 8 各算法计算复杂度
Table 8. Computational complexity of different algorithms
算法 FLOPs RMA ${N_y}{N_s}\left( {10{{\log }_2}{N_s} + 12} \right)$ ISTA ${N_{{\rm{iter}}} }{N_y}{N_s}\left( {10{ {\log }_2}{N_s} + 12} \right)$ RMIST-Net $ T{N_y}{N_s}\left( {10{{\log }_2}{N_s} + 12} \right) $ LSISTA $ T{N_s}\left( {{N_y}\left( {10{{\log }_2}{N_s} + 12} \right) + 2846} \right) $
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表 9 各算法在不同目标点数时的MAE评估值
Table 9. MAEs in cases of the different number of target points
目标点数 ISTA RMIST-Net LSISTA 99422(37.9%) 0.125 0.121 0.094 24896(9.5%) 0.027 0.026 0.022 6203(2.4%) 0.005 0.005 0.003
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