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Precise Reconstruction Method for Hidden Targets Based on Non-line-of-sight Radar 3D Imaging
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摘要: 非视距(NLOS)三维成像雷达是一种利用多径散射回波探测隐藏目标的新技术，但存在多路径回波分离、孔径遮蔽缩减、反射面相位误差等问题，传统视距雷达三维成像方法难以实现非视距隐藏目标的高精度成像。为此，该文提出了一种基于迭代稀疏重构的非视距隐藏目标三维成像雷达精确成像方法(NSIR)。在该方法中，首先构建非视距毫米波雷达三维成像的多径信号模型，利用视距/非视距回波特性，通过模型驱动方法提取非视距隐藏目标的多路径回波，实现视距/非视距回波信号的分离；其次，构建耦合多径反射面相位误差的全变分多约束隐藏目标重构优化问题，利用分裂Bregman全变分(TV)正则化算子和最小均方误差的相位误差估计准则，联合求解多约束最优化问题，实现非视距目标的精确成像及轮廓重构。最后，搭建平面扫描的三维成像雷达试验平台，完成了拐角非视距场景下刀具、铁架等目标的实验验证，验证了非视距毫米波三维成像雷达隐匿目标探测能力及该文方法的有效性。Abstract: Non-Line-Of-Sight (NLOS) 3D imaging radar is an emerging technology that utilizes multipath scattering echoes to detect hidden targets. However, this technology faces challenges such as the separation of multipath echoes, reduction of aperture occlusion, and phase errors of reflective surfaces, which hinder the high-precision imaging of hidden targets when using traditional Line-Of-Sight (LOS) radar imaging methods. To address these challenges, this paper proposes a precise imaging method for NLOS hidden targets based on Sparse Iterative Reconstruction (NSIR). In this method, we first establish a multipath signal model for NLOS millimeter-wave 3D imaging radar. By exploiting the characteristics of LOS/NLOS echoes, we extract the multipath echoes from hidden targets using a model-driven approach to realize the separation of LOS/NLOS echo signals. Second, we formulate a total variation multiconstraint optimization problem for reconstructing hidden targets, integrating multipath reflective surface phase errors. Using the split Bregman Total Variation (TV) regularization operator and the phase error estimation criterion based on the minimum mean square error, we jointly solve the multiconstraint optimization problem. This approach facilitates precise imaging and contour reconstruction of NLOS targets. Finally, we construct a planar scanning 3D imaging radar experimental platform and conduct experimental verification of targets such as knives and iron racks in a corner NLOS scenario. Results validate the capability of NLOS millimeter-wave 3D imaging radar in detecting hidden targets and the effectiveness of the method proposed in this paper.
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图 7 金属刀具及金属花架非视距及视距成像结果对比(第1行为非视距成像结果，第2行为视距成像结果，采样率均为100%)
Figure 7. Comparison of the NLOS and LOS imaging results of the metal knives and the metal flower stands (the first line is the NLOS imaging result, the second line is the LOS imaging result, the sampling rate is 100%)
图 8 不同采样率下，4种算法的非视距金属刀具成像结果对比(从左至右：采样率分别为100%, 70%, 50%和30%)
Figure 8. Comparison of NLOS metal knives imaging results of four algorithms with different sampling rates (from left to right: sampling rates of 100%, 70%, 50%, and 30%, respectively)
图 9 不同采样率下，4种算法的非视距金属花架成像结果对比((从左至右：采样率分别为100%, 70%, 50%和30%)
Figure 9. Comparison of NLOS metal flower stands imaging results of four algorithms with different sampling rates (from left to right: sampling rates of 100%, 70%, 50%, and 30%, respectively)
图 10 在全采样率下，4种算法的最大投影结果对比(从左往右分别对应BP, RMA, ISTA和NSIR)
Figure 10. At the full sampling rate, the maximum projection results of the four algorithms are compared (from left to right, corresponding to BP, RMA, ISTA and NSIR)
1 NLOS目标多路径回波提取
1. Extraction of NLOS target echoes
输入：LOS环境结构，雷达回波E； 输出：NLOS目标多径回波； RMA粗成像：${{\boldsymbol{I}}_{{\text{RMA}}}} = {\mathcal{G}_{{\text{RMA}}}}\left( {\boldsymbol{E}} \right)$； 结合RMA成像结果与LOS环境布局分析，确定NLOS区域及隐藏
目标：${\varOmega _{{\mathrm{all}}}}\mathop \to \limits^f {\varOmega _{{\mathrm{NLOS}}}}$；距离聚焦：${P_{\text{c}}} = {\text{FFT}}\left( {{\boldsymbol{E}},q} \right)$； 计算隐藏目标对应时延及距离：${y_r} = \left( {\dfrac{{{m_r}}}{{{f_0} \times T \times q}}} \right) \times \dfrac{{\mathrm{c}}}{2}$； 根据镜像对称原理，确定同一目标不同虚像对应的回波； 根据距离历史提取对应回波：${\text{Extra}}\left( {\boldsymbol{E}} \right) \to {{\boldsymbol{E}}_{{\text{NLOS}}}}$； 返回隐藏目标的多径回波。 
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2 三维雷达自聚焦成像算法NSIR
2. 3D radar autofocusing imaging algorithm NSIR
输入：隐藏目标回波${{\boldsymbol{S}}_{\text{e}}} \in {\mathbb{C}^{{N_x} \times {N_z} \times R}}$，参数$\lambda $, ${\gamma _1}$和${\gamma _2}$； 输出：稀疏成像结果$ {\boldsymbol{X}} \in {\mathbb{C}^{R \times N \times N}} $； 初始化：${\boldsymbol{X}}^0 = {\boldsymbol{b}}_1^0 = {\boldsymbol{b}}_2^0 = {\boldsymbol{d}}_1^0 = {\boldsymbol{d}}_2^0 = 0$, ${\boldsymbol{Y}} = {{\boldsymbol{S}}_{\text{e}}}$； 循环开始 (1) 根据式(34)，重构${\boldsymbol{X}}^{k + 1}$； (2) 更新辅助变量：$ {\boldsymbol{d}}_1^{k + 1} = \mathcal{T}\left( {\nabla {\boldsymbol{X}}^{k + 1} + {\boldsymbol{b}}_1^k,1/{\gamma _1}} \right) $,
$ {\boldsymbol{d}}_2^{k + 1} = \mathcal{T}\left( {{\boldsymbol{X}}^{k + 1} + {\boldsymbol{b}}_2^k,1/{\gamma _2}} \right) $；(3) 更新参数：$ {\boldsymbol{b}}_1^{k + 1} = {\boldsymbol{b}}_1^k + \nabla {\boldsymbol{X}}^{k + 1} - {\boldsymbol{d}}_1^{k + 1} $,
$ {\boldsymbol{b}}_2^{k + 1} = {\boldsymbol{b}}_2^k + {\boldsymbol{X}}^{k + 1} - {\boldsymbol{d}}_2^{k + 1} $；(4) 由式(32)、式(33)估计相位误差, $t = t + 1$； (5) 迭代判定：若$k \le T$，则重复(1)—(5)；否则，结束循环。 循环结束
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表 1 实测系统参数
Table 1. Parameters in real experiments
参数 实测系统值 载频(GHz) 79 带宽(GHz) 3.998 孔径尺寸(cm) 40×40 采样间隔(mm) x: 1; z: 2 脉冲发射间隔(ms) 50
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表 2 不同算法下的实测实验数值评估结果
Table 2. Numerical evaluation results of real experiments with different algorithms
目标 采样率(%) BP RMA ISTA NSIR ENT IC Time (s) ENT IC Time (s) ENT IC Time (s) ENT IC Time (s) 金属刀具 100 11.03 8.74 810.56 10.70 8.41 1.05 10.65 8.48 14.69 10.24 11.05 76.94 70 11.15 8.62 625.30 11.06 7.91 1.06 10.944 8.06 17.58 10.78 11.75 124.38 50 11.27 8.50 308.45 11.39 7.30 1.06 11.237 7.54 17.82 10.00 11.64 77.447 30 11.49 8.12 183.67 11.92 6.19 1.15 11.572 6.79 20.49 9.93 12.08 131.58 金属花架 100 11.25 7.25 251.61 11.93 5.23 0.99 11.61 5.73 23.96 10.71 9.07 80.96 70 11.50 6.82 169.20 12.41 4.56 1.00 11.83 5.44 24.61 10.44 12.08 80.18 50 11.75 5.13 120.88 12.78 3.98 0.98 12.05 5.16 24.48 10.06 16.30 77.25 30 11.10 4.23 73.76 13.23 3.04 0.99 12.26 4.76 24.53 8.59 45.89 77.98
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