改进的L<sub>1/2</sub>阈值迭代高分辨率SAR成像算法

高志奇; 孙书辰; 黄平平; 乞耀龙; 徐伟

doi:10.12000/JR22243

改进的L_1/2阈值迭代高分辨率SAR成像算法

DOI: 10.12000/JR22243

高志奇^{1, 2},
孙书辰^{1, 2},
黄平平^{1, 2, ,},
乞耀龙^{1, 2},
徐伟^{1, 2}

1.
内蒙古工业大学信息工程学院呼和浩特 010080
2.
内蒙古自治区雷达技术与应用重点实验室呼和浩特 010051

基金项目: 国家自然科学基金(61761037, 62071258)，内蒙古自治区自然科学基金(2021MS06005, 2020ZD18)，内蒙古自治区直属高校基本科研业务费项目(JY20220147)

详细信息

作者简介:
高志奇，博士，副教授，主要研究方向为阵列信号处理、SAR成像

孙书辰，硕士生，主要研究方向为SAR成像算法

黄平平，博士，教授，主要研究方向为新体制雷达系统、雷达信号处理和微波遥感应用

乞耀龙，博士，副教授，主要研究方向为阵列成像、地基合成孔径雷达系统

徐　伟，博士，教授，主要研究方向为新体制星载SAR系统仿真与信号处理

通讯作者:
黄平平 hpp@imut.edu.cn

责任主编：张群 Corresponding Editor: ZHANG Qun
中图分类号: TN957.5
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出版历程
- 收稿日期: 2022-12-28
- 修回日期: 2023-02-05
- 网络出版日期: 2023-02-22
- 刊出日期: 2023-10-28

Improved L_1/2 Threshold Iterative High Resolution SAR Imaging Algorithm

GAO Zhiqi^{1, 2},
SUN Shuchen^{1, 2},
HUANG Pingping^{1, 2
, ,},
QI Yaolong^{1, 2},
XU Wei^{1, 2}

1.
College of Information Engineering, Inner Mongolia University of Technology, Hohhot 010080, China
2.
Inner Mongolia Key Laboratory of Radar Technology and Application, Hohhot 010051, China

Funds: The National Natural Science Foundation of China (61761037, 62071258), The Natural Science Foundation of Inner Mongolia (2021MS06005, 2020ZD18), Basic Scientific Research Business Cost Project of Colleges Directly under the Inner Mongolia (JY20220147)

More Information

Corresponding author: HUANG Pingping, hpp@imut.edu.cn

摘要

摘要: 针对合成孔径雷达(SAR)在稀疏采样条件下方位向分辨率低、易受噪声干扰等问题，提出改进的高分辨率SAR成像算法。该文在现有的L_1/2正则化理论及其阈值迭代算法的基础上，改进了其表达式中的梯度算子，提高重构图像的求解精度，降低计算量。然后，在全采样和欠采样条件下，将原有L_1/2阈值迭代算法与所提改进L_1/2阈值迭代算法，分别结合近似观测模型对SAR回波信号进行成像处理和性能对比。实验结果表明，改进的算法具有更加优越的收敛性能，并且对于SAR图像方位向分辨率有一定的改善。
- 合成孔径雷达 /
- 近似观测模型 /
- 压缩感知 /
- L_1/2正则化理论
Abstract: An improved Synthetic Aperture Radar (SAR) imaging algorithm is proposed to address the issues of low azimuth resolution and noise interference in the sparse sampling condition. Based on the existing L_1/2 regularization theory and iterative threshold algorithm, the gradient operator is modified, which can improve the solution accuracy of the reconstructed image and reduce the load of calculation. Then, under full sampling and under-sampling conditions, the original and improved L_1/2 iterative threshold algorithm are combined with the approximate observation model to image SAR echo signals and compare their imaging performance. The experimental findings demonstrate that the improved algorithm improves the azimuth resolution of SAR images and has higher convergence performance.
- Synthetic Aperture Radar (SAR) /
- Approximate observation model /
- Compressed sensing /
- L_1/2 regularization theory

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图 1 条带式SAR空间模型图

Figure 1. Strip SAR spatial model diagram

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图 2 点目标位置

Figure 2. Point target position

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图 3 Chirp-Scaling算法成像结果

Figure 3. Imaging results of Chirp-Scaling algorithm

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图 4 L_1/2阈值迭代算法成像结果

Figure 4. Imaging results of L_1/2 threshold iterative algorithm

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图 5 改进L_1/2阈值迭代算法成像结果

Figure 5. Imaging results of improved L_1/2 threshold iterative algorithm

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图 6 点目标剖面图

Figure 6. Cross section of point targets

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图 7 Chirp-Scaling算法成像结果

Figure 7. Imaging results of Chirp-Scaling algorithm

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图 8 L_1/2阈值迭代算法成像结果

Figure 8. Imaging results of the L_1/2 threshold iterative algorithm

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图 9 改进L_1/2阈值迭代算法成像结果

Figure 9. Imaging results of the improved L_1/2 threshold iterative algorithm

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图 10 不同信噪比下成像效果对比

Figure 10. Imaging results for different SNR

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图 11 不同算法的重建结果

Figure 11. Reconstruction results of different algorithms

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表 1 SAR成像仿真参数

Table 1. Simulation parameters of SAR imaging

参数	数值
载频(GHz)	5.3
飞行速度(m/s)	150
脉冲宽度(μs)	2.5
距离向采样率(MHz)	60
方位向采样率(Hz)	200
平台离场景中心斜距(km)	20
斜视角(°)	0
距离向调频率(MHz/μs)	20000

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表 2 3种算法中5个点目标成像分辨率分析(m)

Table 2. Imaging resolution analysis of five targets in three algorithms (m)

算法	点目标1	点目标2	点目标3	点目标4	点目标5
Chirp-Scaling算法	1.6104	1.6225	1.6235	1.6235	1.6235
L_1/2阈值迭代算法	1.1425	1.1143	1.1425	1.1425	1.1425
改进L_1/2阈值迭代算法	0.9389	0.9382	0.9623	0.9623	0.9623

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表 3 3种算法中方位向数据缺失60％时5个点目标的分辨率(m)

Table 3. The resolution of five targets with 60% azimuth data missed for three algorithms (m)

算法	点目标1	点目标2	点目标3	点目标4	点目标5
Chirp-Scaling算法	1.6619	1.6522	1.6484	1.6484	1.6484
L_1/2阈值迭代算法	1.1494	1.1005	1.1494	1.1494	1.1494
改进L_1/2阈值迭代算法	1.0759	1.0502	1.0599	1.0599	1.0599

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表 4 3种算法中方位向数据缺失70％时5个点目标的分辨率(m)

Table 4. The resolution of five targets with 70% azimuth data missed for three algorithms (m)

算法	点目标1	点目标2	点目标3	点目标4	点目标5
Chirp-Scaling算法	1.6719	1.7801	1.7768	1.7768	1.7768
L_1/2阈值迭代算法	1.1604	1.2054	1.1604	1.1604	1.1604
改进L_1/2阈值迭代算法	1.1049	1.0619	1.0627	1.0627	1.0627

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表 5 不同模型的运算量分析

Table 5. Calculation amount analysis of different models

性能分析	匹配滤波	精确观测模型	近似观测模型
空间复杂度	O(MN)	O(M²N²)	O(MN)
时间复杂度	O(MNlog₂MN)	O(IM²N²)	O(IMNlog₂MN)

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表 6 不同采样率下两种算法重建点目标耗时时长(s)

Table 6. Time consuming of point target reconstruction by the two algorithms at different sampling rates (s)

算法	采样率100.0%	采样率75.0%	采样率50.0%	采样率25.0%	采样率12.5%
L_1/2阈值迭代算法	98.560592	74.146809	49.485751	25.464554	13.557194
改进L_1/2阈值迭代算法	53.307587	40.525354	26.610069	13.761923	7.354359

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表 7 RADARSAT-1卫星SAR成像参数

Table 7. Parameters of RADARSAT-1 satellite SAR imaging

参数	数值
载频(GHz)	5.3
飞行速度(m/s)	7062
脉冲宽度(μs)	41.75
距离向采样率(MHz)	32317
脉冲重复频率(Hz)	125.7
平台离场景中心斜距(km)	988.65
图像分辨率单元数(M×N)	2048×3000
距离向调频率(MHz/μs)	5000
成像场景大小(m)	10000×12000

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表 8 3种算法实测数据成像耗时时长

Table 8. Time consuming of measured data imaging by the three algorithms

算法	重建耗时时长(s)
Chirp-Scaling算法	3.143686
L_1/2阈值迭代算法	14.176919
改进L_1/2阈值迭代算法	10.074317

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