基于稀疏匹配滤波的TomoSAR三维成像

刘慧; 赵春萌; 陈鹏飞; 王彦植; 屈明昊; 肖宁

doi:10.12000/JR25038

基于稀疏匹配滤波的TomoSAR三维成像

DOI: 10.12000/JR25038 CSTR: 32380.14.JR25038

刘慧^{1, 2, ,},
赵春萌¹,
陈鹏飞¹,
王彦植¹,
屈明昊¹,
肖宁^{1, 2}

1.
北京建筑大学智能科学与技术学院北京 102616
2.
城市建筑超级智能技术北京市重点实验室北京 102616

基金项目: 国家自然科学基金(61501019)，中国高校产学研创新基金(2022IT229)

详细信息

作者简介:
刘　慧，副教授，硕士生导师，主要研究方向为SAR成像、InSAR、TomoSAR、雷达信号处理等

赵春萌，硕士生，主要研究方向为TomoSAR成像、SAR三维解模糊等

陈鹏飞，硕士生，主要研究方向为星载SAR三维成像

王彦植，硕士生，主要研究方向为D-TomoSAR成像

屈明昊，硕士生，主要研究方向为多模态多维信号处理

肖　宁，讲师，主要研究方向为信号处理、计算视觉等

通讯作者:
刘慧 liuhui@bucea.edu.cn

责任主编：毕辉 Corresponding Editor: BI Hui
中图分类号: TN957.5
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出版历程
- 收稿日期: 2025-02-25
- 修回日期: 2025-08-17
- 网络出版日期: 2025-09-11

Sparse Matching Filtering Algorithm for Tomographic SAR Imaging

1.
School of Intelligence Science and Technology, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
2.
Beijing Key Laboratory of Super Intelligent Technology for Urban Architecture, Beijing University of Civil Engineering and Architecture, Beijing 102616, China

Funds: The National Natural Science Foundation of China (61501019), China Higher Education Institution Industry-University-Research Innovation Fund (2022IT229)

More Information

Corresponding author: LIU Hui, liuhui@bucea.edu.cn

摘要

摘要: 层析SAR (TomoSAR)成像技术已经成为获取三维SAR点云的关键技术。然而，如果忽略斜距垂向的二次相位，可能会导致目标在高程方向的散焦问题，这是由于层析SAR成像中第三维也可能存在菲涅耳衍射所导致的。该文利用光学成像中的衍射原理解释了SAR成像中的衍射问题同样在第三维存在，并提出采用稀疏匹配滤波方法对第三维进行聚焦。第三维稀疏匹配滤波的关键在于构建稀疏相位补偿因子，进而构建稀疏匹配滤波器。首先根据TomoSAR影像的空间几何基线，构建第三维归一化的稀疏频率；然后，结合波长、距离、孔径等参数，根据菲涅耳积分特性构建频域稀疏匹配滤波器；最后，使用频域稀疏滤波器对稀疏采样的SAR图像进行相位补偿，再利用经典的稀疏成像算法(如压缩感知、似然比检测方法等)进行高程即第三维目标检测。该文采用中国科学院空天信息创新研究院的机载SAR数据，运用该文构建的频域稀疏匹配滤波器对其进行实验，实验结果验证了该文所提的方法能够解决层析SAR在菲涅耳衍射情况下导致的散焦问题，从而改善散焦引起的目标位置和后向散射信息不准确的问题。
- SAR层析成像 /
- 稀疏匹配滤波 /
- 稀疏相位补偿 /
- 后向散射 /
- 菲涅耳衍射
Abstract: Synthetic Aperture Radar Tomography (TomoSAR) has emerged as the primary technique for generating 3D SAR point clouds. In practice, ignoring the quadratic phase distribution in the elevation dimension causes defocusing artifacts due to inherent Fresnel diffraction in tomographic SAR processing. By comparing with optical diffraction theory, this paper identifies similar diffraction effects in the third dimension of SAR images and introduces a sparse matched filtering technique for tomographic focusing. Our method is based on deriving a sparse phase compensation factor to construct the matched filter. The proposed processing chain includes three key steps. First, a normalized sparse frequency profile in the tomographic dimension is constructed using the spatial geometric baseline of TomoSAR acquisitions. Next, we derive a frequency-domain sparse matched filter based on Fresnel integral properties incorporating system parameters such as wavelength, range, and aperture size. Finally, phase compensation is applied through the designed sparse filter, enabling elevation target detection using established sparse imaging techniques, including compressed sensing and likelihood ratio detection. This study employs airborne SAR data acquired by the Aerospace Information Research Institute, Chinese Academy of Sciences, to validate the proposed frequency-domain sparse matched filter. Experimental results demonstrate that our method effectively reduces tomographic defocusing artifacts caused by Fresnel diffraction, substantially improving the accuracy of both target localization and backscattering coefficient estimation.
- SAR tomography imaging /
- Sparse matching filtering /
- Sparse phase compensation /
- Backscattering /
- Fresnel diffraction

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图 1 TomoSAR系统的几何模型

Figure 1. Geometric model of TomoSAR system

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图 2 光的衍射几何

Figure 2. Diffraction geometry of light

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图 3 机载TomoSAR系统参数仿真结果(菲涅耳N_F≈0.01)

Figure 3. Simulation results by parameters of airborne TomoSAR system (N_F≈0.01)

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图 4 TerraSAR-X系统参数仿真结果(菲涅耳N_F≈4.28)

Figure 4. Simulation results by parameters of TerraSAR-X system (N_F≈4.28)

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图 5 稀疏匹配滤波三维成像流程图

Figure 5. Flowchart of sparse matched filtering 3D imaging

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图 6 单点目标情况下匹配滤波验证(菲涅耳N_F≈0.01)

Figure 6. Verification of matched filtering under the condition of single target (N_F≈0.01)

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图 7 两点目标情况下匹配滤波验证(菲涅耳N_F≈0.01)

Figure 7. Verification of matched filtering under the condition of two targets (N_F≈0.01)

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图 8 天津临港商务大厦

Figure 8. Tianjin Lingang Business Building

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图 9 不做匹配滤波时方位向为500的切片处进行TomoSAR成像结果

Figure 9. TomoSAR imaging results at the 500th slice in azimuth without matched filtering

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图 10 匹配滤波后方位向为500的切片处进行TomoSAR成像结果

Figure 10. TomoSAR imaging results at the 500th slice in azimuth with matched filtering

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图 11 不同长度基线干涉相位图

Figure 11. Interferograms with different baselines

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图 12 干涉相位图去噪结果

Figure 12. Denoised interferograms

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图 13 不同区域的模糊值

Figure 13. Ambiguity value indifferent regions

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图 14 方位向为500的切片处TomoSAR点云

Figure 14. TomoSAR point clouds at the 500th slice in azimuth with matched filtering

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图 15 观测场景TomoSAR点云

Figure 15. TomoSAR point clouds of the observed scene

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表 1 两组TomoSAR数据参数

Table 1. Two sets of TomoSAR data parameters

参数	符号	机载数据(m)	星载数据(m)
最小基线间隔	${B_{\min }}$	0.1071	20
最大基线长度	${B_{\max }}$	0.442	400
波长	$\lambda $	0.0197	0.031
斜距	r	482.0413	603638.971

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