基于半正定规划的压缩感知线阵三维SAR自聚焦成像算法

韦顺军 田博坤 张晓玲 师君

韦顺军, 田博坤, 张晓玲, 师君. 基于半正定规划的压缩感知线阵三维SAR自聚焦成像算法[J]. 雷达学报, 2018, 7(6): 664-675. doi: 10.12000/JR17103
引用本文: 韦顺军, 田博坤, 张晓玲, 师君. 基于半正定规划的压缩感知线阵三维SAR自聚焦成像算法[J]. 雷达学报, 2018, 7(6): 664-675. doi: 10.12000/JR17103
Wei Shunjun, Tian Bokun, Zhang Xiaoling, Shi Jun. Compressed Sensing Linear Array SAR Autofocusing Imaging via Semi-definite Programming[J]. Journal of Radars, 2018, 7(6): 664-675. doi: 10.12000/JR17103
Citation: Wei Shunjun, Tian Bokun, Zhang Xiaoling, Shi Jun. Compressed Sensing Linear Array SAR Autofocusing Imaging via Semi-definite Programming[J]. Journal of Radars, 2018, 7(6): 664-675. doi: 10.12000/JR17103

基于半正定规划的压缩感知线阵三维SAR自聚焦成像算法

doi: 10.12000/JR17103
基金项目: 国家自然科学基金(61501098),博士后面上基金(2015M570778),高分青年基金项目(GFZX04061502),中央高校科研基本业务费(ZYGX2016KYQD107)
详细信息
    作者简介:

    韦顺军(1983–),男,广西柳州人,博士,2013年获电子科技大学工学博士学位,目前为电子科技大学信息与通信工程学院副教授,主要从事合成孔径雷达成像、阵列雷达3维成像等技术研究,已发表论文30余篇。E-mail: weishunjun@uestc.edu.cn

    田博坤(1993–),男,河北沧州人,电子科技大学博士生,主要从事合成孔径雷达成像研究。E-mail: 3544348143@qq.com

    张晓玲(1964–),女,四川成都人,博士,2002年获电子科技大学工学博士学位,目前为电子科技大学信息与通信工程学院教授,博士生导师,主要从事SAR成像技术、雷达探测技术研究,已发表论文50余篇。E-mail: xlzhang@uestc.edu.cn

    师 君(1979–),男,河南南阳人,博士,2009年获电子科技大学工学博士学位,目前为电子科技大学信息与通信工程学院副教授,博士生导师,主要从事SAR成像技术、雷达信号处理研究,已发表论文50余篇。E-mail: shijun@uestc.edu.cn

    通讯作者:

    韦顺军  weishunjun@uestc.edu.cn

  • 中图分类号: TN957.52

Compressed Sensing Linear Array SAR Autofocusing Imaging via Semi-definite Programming

Funds: The National Natural Science Foundation of China (61501098), The China Postdoctoral Science Foundation (2015M570778), The High Resolution Earth Observation Youth Foundation (GFZX04061502), The Fundamental Research Funds for the Central Universities (ZYGX2016KYQD107)
  • 摘要: 线阵合成孔径雷达(Linear Array Synthetic Aperture Radar, LASAR)3维成像技术是一种具有重要潜在应用价值的新体制成像雷达,压缩感知稀疏重构是近几年实现LASAR高分辨3维成像的热点研究之一。但相对于传统2维SAR,受线阵稀疏分布及阵列-平台2维联动,压缩感知LASAR成像面临回波数据欠采样、多维度高阶相位误差等问题,传统SAR自聚焦算法难以适用于压缩感知LASAR 3维稀疏自聚焦成像。为克服欠采样条件下多维度高阶相位误差对LASAR成像的影响,该文提出了一种基于半正定规划的压缩感知LASAR自聚焦成像算法。首先,结合压缩感知成像理论、图像最大锐度及最小均方误差准则,构造欠采样条件下稀疏目标的相位误差估计模型;其次,利用松弛半正定规划方法估计相位误差;最后,利用迭代逼近方法提高相位误差估计精度,实现压缩感知LASAR高精度稀疏自聚焦成像。另外,通过主散射目标区域提取,仅采用主散射区域进行相位误差估计,进一步提高自聚焦算法运算效率。仿真数据和实测数据验证了该文算法的有效性。

     

  • 图  1  LASAR正下视3维成像的几何模型

    Figure  1.  The geographic model of down-looking LASAR imaging

    图  3  沿航迹及切航迹随机分布相位误差下仿真点目标成像结果(上:全部回波数据;中:50%回波数据;下:25%回波数据)

    Figure  3.  The results of the point targets in the case of the along-track random phase errors and cross-track random phase errors(Top: all samples; Middle: 50% samples; Bottom: 25% samples)

    图  4  SDPSA算法MSE变化曲线

    Figure  4.  The MSE curve of SDPSA

    图  2  沿航迹二次项及切航迹随机分布相位误差下仿真点目标成像结果(上:全部回波数据;中:50%回波数据;下:25%回波数据)

    Figure  2.  The results of the point targets in the case of the along-track quadratic phase errors and cross-track random phase errors(Top: all samples; Middle: 50% samples; Bottom: 25% samples)

    图  5  地基等效LASAR成像实验

    Figure  5.  The ground-based LASAR experiment

    图  6  地基LASAR合成阵列平面及回波数据

    Figure  6.  The virtual array antenna and the echo of the ground-based LSAR

    图  8  路灯目标实测数据稀疏自聚焦成像结果(左:BP-PGA算法;中:IRLS-PGA算法;右:SDPSA算法)

    Figure  8.  The sparse autofocusing results of the experimental light data(Left: BP-PGA; Middle: IRLS-PGA; Right: SDPSA)

    表  1  SDPSA算法

    Table  1.   SDPSA algorithm

    输入:代价函数 ${J_{\rm{1}}}\left( {{{{f}}},{{{φ}}} } \right)$和 ${J_{\rm{2}}}\left( {{{{f}}},{{{φ}}} } \right)$
    输出:估计值 $\left( {{{{\stackrel \frown{f}}}} ,{{\stackrel \frown{{φ}}} } } \right)$
    初始化:迭代次数 $i = 0$,相位误差 ${{{{φ}}} ^{\left( {\rm{0}} \right)}} = 0$,门限 ${{δ}} $,迭代总次数 $K$
    若 ${\left\| {{{{{{\stackrel \frown{f}}}} }^{\left( {i + 1} \right)}} - {{{{{\stackrel \frown{f}}}} }^{\left( i \right)}}} \right\|_2}\Bigr/{\left\| {{{{{{\stackrel \frown{f}}}} }^{\left( i \right)}}} \right\|_2} > {{δ}} $和 $i \le K$,循环开始
     步骤1 构造稀疏目标重构的代价函数:
    ${J_{\rm{1}}}\left( {{{{f}}},{{{{{\stackrel \frown{φ}}} } }^{\left( i \right)}}} \right) = {{λ}} {\left\| {{{f}}} \right\|_1}{\rm{ + }} \left\| {{{{y}}} - {{{R}}}\left( {{{{{{\stackrel \frown{φ}}} } }^{\left( i \right)}}} \right){{{Af}}}} \right\|_2^{}$
     步骤2 利用IRLS算法进行稀疏目标重构:
    ${{{{\stackrel \frown{f}}}} ^{\left( {i{\rm{ + 1}}} \right)}} = \arg \mathop {\min }\limits_{f} {J_{\rm{1}}}\left( {{{{f}}},{{{{{\stackrel \frown{φ}}} } }^{\left( i \right)}}} \right)$
     步骤3 构造相位误差估计的代价函数:
    ${J_{\rm{2}}}\left( {{{{{{\stackrel \frown{f}}}} }^{\left( {i + 1} \right)}},{{{φ}}} } \right) \approx {{{γ} }^{\rm H}}{{{{Q}}}^{\left( {i + 1} \right)}}{{γ} }$
     步骤4 利用SDP方法求解最优问题:
    ${{{{\stackrel \frown{X}}}} _{\rm{opt}}} = \arg \mathop {\min }\limits_{X} {\rm tr}\left({{{{Q}}}^{\left( {i + 1} \right)}}{{{X}}}\right),\ {\rm s.t.} \ \ {{{X}}} \succeq 0,{{{{X}}}_{ii}} = {g_n},n = 1,2, ·\!·\!· ,N$
     步骤5 利用 ${{{{\stackrel \frown{X}}}} _{\rm {opt}}}$估计相位误差 ${{{{\stackrel \frown{φ}}} } ^{\left( {i + 1} \right)}}$;
    $i \leftarrow i + 1$
    循环结束
    返回结果: ${{{\stackrel \frown{f}}}} \leftarrow {{{{\stackrel \frown{f}}}} ^{\left( {i + 1} \right)}}$, $\stackrel \frown{{{{φ}}} } \leftarrow {\stackrel \frown{{{{φ}}} } ^{\left( {i + 1} \right)}}$
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出版历程
  • 收稿日期:  2017-11-09
  • 修回日期:  2018-03-28
  • 网络出版日期:  2018-12-28

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