基于L1 & TV正则化的低过采样Staggered SAR成像方法

doi:10.12305/j.issn.1001-506X.2023.09.09

系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (9): 2718-2726.doi: 10.12305/j.issn.1001-506X.2023.09.09

基于L₁ & TV正则化的低过采样Staggered SAR成像方法

刘鸣谦¹^,²^,³^,*, 徐仲秋¹^,²^,³, 陈天成¹^,²^,³, 张冰尘¹^,²^,³, 吴一戎¹^,²

1. 中国科学院空天信息创新研究院, 北京 100094
2. 中国科学院大学电子电气与通信工程学院, 北京 101408
3. 空间信息处理与应用系统技术重点实验室, 北京 100190

收稿日期:2022-01-13 出版日期:2023-08-30 发布日期:2023-09-05
通讯作者: 刘鸣谦
作者简介:刘鸣谦 (1994—), 男, 博士研究生, 主要研究方向为稀疏微波成像、合成孔径雷达成像、新体制雷达
徐仲秋 (1996—), 男, 博士研究生, 主要研究方向为稀疏微波成像、合成孔径雷达成像
陈天成 (1999—), 男, 博士研究生, 主要研究方向为稀疏微波成像、合成孔径雷达成像
张冰尘 (1973—), 男, 研究员, 博士, 主要研究方向为雷达系统与雷达信号处理、新体制雷达
吴一戎 (1963—), 男, 中国科学院院士, 博士, 主要研究方向为稀疏微波成像、合成孔径雷达成像
基金资助:
国家自然科学基金(61991421)

Low oversampling Staggered SAR imaging method based on L₁ & TV regularization

Mingqian LIU¹^,²^,³^,*, Zhongqiu XU¹^,²^,³, Tiancheng CHEN¹^,²^,³, Bingchen ZHANG¹^,²^,³, Yirong WU¹^,²

1. Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
2. School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 101408, China
3. Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Beijing 100190, China

Received:2022-01-13 Online:2023-08-30 Published:2023-09-05
Contact: Mingqian LIU

摘要/Abstract

摘要：

高分辨率宽测绘带(high-resolution and wide-swath, HRWS)成像是星载合成孔径雷达(synthetic aperture radar, SAR)发展的重要趋势。Staggered SAR通过改变脉冲重复频率(pulse repetition frequency, PRF)将盲区分散在整个成像带内, 可以将距离向幅宽扩展为传统体制的数倍。针对变PRF模式存在的非均匀采样和回波数据丢失问题, 提出了一种基于L₁ & TV正则化的低过采样Staggered SAR成像方法。所提方法可以在不恢复丢失数据的情况下实现方位模糊抑制, 并且在稀疏重构模型中引入TV正则化项, 从而实现分布式目标的精确重构。仿真和实际数据实验验证了所提方法的有效性。

关键词: 合成孔径雷达, 交错模式, 非均匀采样, 稀疏信号处理, L₁ & TV正则化

Abstract:

High-resolution and wide-swath (HRWS) imaging is an important trend in the development of spaceborne synthetic aperture radar (SAR). Staggered SAR distributes the blind areas into the whole imaging range by using the variable pulse repetition frequency (PRF), which can widen the swath to several times the size of the traditional system. Aiming at the problems of nonuniform sampling and echo data loss in variable PRF mode, a low oversampling staggered SAR imaging method based on L₁ & TV regularization is proposed. The proposed method can suppress the azimuth ambiguities without recovering the lost data, and introduce TV regularization term into the sparse reconstruction model to achieve the accurate reconstruction of distributed targets. Simulation and real data experiments verify the effectiveness of the proposed method.

Key words: synthetic aperture radar (SAR), staggered mode, nonuniform sampling, sparse signal processing, L₁ & TV regularization

中图分类号:

TN95

刘鸣谦, 徐仲秋, 陈天成, 张冰尘, 吴一戎. 基于L₁ & TV正则化的低过采样Staggered SAR成像方法[J]. 系统工程与电子技术, 2023, 45(9): 2718-2726.

Mingqian LIU, Zhongqiu XU, Tiancheng CHEN, Bingchen ZHANG, Yirong WU. Low oversampling Staggered SAR imaging method based on L₁ & TV regularization[J]. Systems Engineering and Electronics, 2023, 45(9): 2718-2726.

图/表 11

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参考文献 30

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参数	参数值
轨道高度/km	760
平台速度/(m/s)	7 473
中心频率/GHz	10
斜距范围/km	868~1 097
发射信号带宽/MHz	20
多普勒带宽/Hz	1 440
方位向过采样率	1.1
最大的PRI/s	1/1 487
最小的PRI/s	1/1 714

评价指标	算法
评价指标	CSA	BLU	L₁
ISLR	-7.14	-7.73	-16.88
AASR	-17.85	-18.03	-22.16

参数	参数值
平台速度/(m/s)	7 538.340 124
波长/m	0.055 517
采样率/MHz	66.67
信号带宽/MHz	60
脉冲持续时间/μs	45
脉冲重复频率/Hz	1 149.45

算法	区域
算法	区域1	区域2	区域3
CSA	0.979 8	0.980 3	0.978 6
L₁ & TV	6.453 5	6.461 2	6.447 8

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基于L₁ & TV正则化的低过采样Staggered SAR成像方法

Low oversampling Staggered SAR imaging method based on L₁ & TV regularization

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输入二维回波数据Y, 场景的稀疏度K, 迭代步长参数δ, 最大迭代步数k_max, 误差参数ε, 拉格朗日乘子ξ₁, ξ₂, 图像大小N, 噪声方差σ
初始化 X⁽⁰⁾=0, k=0, dp=(0, 0), z₁⁽⁰⁾=0, z₂⁽⁰⁾=0
迭代 while k < k_max & & Res>ε
1. $\begin{aligned} {\boldsymbol{X}}^{(k+1)}=\left[\mathcal{R}(\mathcal{M}({\boldsymbol{I}}))+\left(\xi_1+\xi_2\right) {\boldsymbol{I}}\right]^{-1}\left[\mathcal{R}\left({\boldsymbol{B}}^* \odot {\boldsymbol{Y}}\right)+\right. \\ \left.\xi_1 {\boldsymbol{z}}_1^{(k)}+{\xi}_2 {\boldsymbol{z}}_2^{(k)}\right]\end{aligned}$
2. λ₁^{(k + 1)}=2ξ₁(\|X^{(k + 1)}\|_{K + 1})
3. ${\boldsymbol{z}}_1^{(k+1)}=\rm{sign}\left({\boldsymbol{X}}^{(k+1)}\right) \cdot \max \left(0, \left\|{\boldsymbol{X}}^{(k+1)}\right\|-\frac{\lambda_1^{(k+1)}}{2 {\xi}_1}\right)$
4. $\lambda_2^{(k+1)}=\lambda_2^{(k)} \frac{N_\sigma}{\left\\|{\boldsymbol{z}}_2^{(k)}-{\boldsymbol{X}}^{(k+1)}\;\right\\|_2}$
5. $\lambda_{\mathrm{TV}}=\frac{\lambda_2^{(k+1)}}{2 \xi_2}$
6. $\begin{array}{l} {\rm{dp}}_{i, j}^{(k+1)}= \\ \frac{\mathrm{dp}_{i, j}^{(k)}+\delta\left(\nabla\left({\rm{divdp}}^{(k)}-\left\|{\boldsymbol{x}}^{(k+1)}\right\| / \lambda_{\mathrm{TV}}\right)\right)_{i, j}}{\max \left\{\left\|{\rm{dp}}_{i, j}^{(k)}+\delta\left(\nabla\left({\rm{divdp}}^{(k)}-\left\|{\boldsymbol{x}}^{(k+1)}\;\right\| / \lambda_{\mathrm{TV}}\right)\right)_{i, j}\;\right\|, 1\right\}} \end{array}$
7. z₂^{(k + 1)}=sign(X^{(k + 1)})(\|X^{(k + 1)}\|-λ_TVdiv(dp^{(k + 1)}))
8. Res=‖X^(k+1)－X^(k)‖₂/‖X^(k)‖₂
9. k=k+1
end while
输出重构后的图像X^(k)