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基于深度迭代网络的穿墙雷达成像方法

王玉皞 张玥 周辉林 刘且根 蔡琦

王玉皞,张玥,周辉林,等. 基于深度迭代网络的穿墙雷达成像方法[J]. 电波科学学报,xxxx,x(x): x-xx. DOI: 10.12265/j.cjors.2021325
引用本文: 王玉皞,张玥,周辉林,等. 基于深度迭代网络的穿墙雷达成像方法[J]. 电波科学学报,xxxx,x(x): x-xx. DOI: 10.12265/j.cjors.2021325
WANG Y H, ZHANG Y, ZHOU H L, et al. Deep iterative network for through-the-wall radar imaging[J]. Chinese journal of radio science,xxxx,x(x): x-xx. (in Chinese). DOI: 10.12265/j.cjors.2021325
Citation: WANG Y H, ZHANG Y, ZHOU H L, et al. Deep iterative network for through-the-wall radar imaging[J]. Chinese journal of radio science,xxxx,x(x): x-xx. (in Chinese). DOI: 10.12265/j.cjors.2021325

基于深度迭代网络的穿墙雷达成像方法

doi: 10.12265/j.cjors.2021325
基金项目: 国家自然科学基金(62061030)
详细信息
    作者简介:

    王玉皞:(1977—),男,湖北人,南昌大学信息工程学院教授,博士生导师,研究方向为通信与雷达波形一体化

    张玥:(1997—),女,江西人,南昌大学信息工程学院硕士研究生,研究方向为雷达传感信号处理、穿墙雷达成像方法研究

    周辉林:(1979—),男,江西人,南昌大学信息工程学院教授,博士生导师,研究方向为超宽带雷达成像、雷达信号处理

    刘且根:(1983—),男,江西人,南昌大学信息工程学院教授,博士生导师,研究方向为成像探测、图像处理及信息检测

    蔡琦:(1994—),女,湖北人,南昌大学信息工程学院硕士研究生,研究方向为毫米波雷达成像信号处理及定位跟踪

    通讯作者:

    周辉林 E-mail: zhouhuilin@ncu.edu.cn

  • 中图分类号: TN957.52

Deep iterative network for through-the-wall radar imaging

  • 摘要: 联合墙杂波去除及图像重建迭代求解方法为当前较前沿的穿墙雷达成像(through-the-wall radar imaging, TWRI)算法,能够同时滤除墙体杂波和重构目标图像,但仍存在收敛速度慢、人工干预过多以及对初值的选取敏感等问题,难以快速精确地进行目标成像. 针对上述问题,本文提出一种联合低秩与稀疏分解驱动的可学习深度迭代网络的TWRI方法. 该方法利用穿墙雷达场景下墙体杂波的低秩特性以及待重建目标图像的稀疏特性,首先将问题建模为联合低秩与稀疏分解的正则化优化问题,然后采用变分框架和轮换策略将优化问题转化成两个准线性优化子问题并推导其更新公式,最后将上述迭代更新公式映射到网络结构中,展开成深度迭代网络模型并采用端到端学习策略,形成融合物理模型的可学习深度迭代网络框架. 仿真结果表明该方法能够有效去除墙体杂波,相对于其他方法显著提高了目标成像精度和速度.
  • 图  1  TWRI系统探测示意图

    Fig.  1  TWRI system detection diagram

    图  2  电磁波传播路径

    Fig.  2  Electromagnetic wave propagation path diagram

    图  3  展开算法的网络架构

    Fig.  3  Unroll the network architecture diagram of the algorithm

    图  4  单层网络架构图

    Fig.  4  Single-layer network architecture diagram

    图  5  单目标仿真及成像结果对比

    Fig.  5  Single target simulation and imaging results comparison

    图  6  双目标仿真及成像结果对比

    Fig.  6  Double target simulation and imaging results comparison

    图  7  不同噪声水平下的TCR和PSNR

    Fig.  7  TCR and PSNR at different noise levels

    表  1  展开迭代深度网络算法流程图

    Tab.  1  Flowchart of expand iterative deep network algorithm

    输入:雷达回波数据${\boldsymbol{B }}$,网络层数$ K $.
    (1) 建模低秩联合稀疏的最小化问题:
    $\mathop {\min }\limits_{ {y^{\text{w} } },s} \frac{1}{2}\left\| { {\boldsymbol{B} } - {\boldsymbol{\varPhi} } {{\boldsymbol{y}}^{\text{w} } } - {\boldsymbol{\varOmega} } {\boldsymbol{s}}} \right\|_{\text{F} }^2 + {\lambda _1}{\left\| { {{\boldsymbol{y}}^{\text{w} } } } \right\|_*} + {\lambda _2}{\left\| {\boldsymbol{s}} \right\|_{1,2} }$
    (2) 转化为两个子问题并得出相应低秩分量和稀疏分量的轮换迭代求解:
    ${\boldsymbol{y} }_{k + 1}^{\text{w} }{\text{ = } }{\Upsilon _{ {\lambda _{\text{1} } }\mu } }\left\{ {(I - \mu { {\boldsymbol{\varPhi} } ^{H} }{\boldsymbol{\varPhi} } ){\boldsymbol{y} }_k^{\text{w} } - { {\boldsymbol{\varPhi} } ^{H} }{\boldsymbol{\varOmega} } { {\boldsymbol{s} }_k} + { {\boldsymbol{\varPhi} } ^{H} }{\boldsymbol{B}}} \right\}$
    ${ {\boldsymbol{s} }_{k + 1} }{\text{ = } }{\mathcal{T}_{ {\lambda _2}\mu } }\left\{ {(I - \mu { {\boldsymbol{\varOmega} } ^{H} }{\boldsymbol{\varOmega} } ){ {\boldsymbol{s} }_k} - { {\boldsymbol{\varOmega} } ^{H} }{\boldsymbol{\varPhi} } {\boldsymbol{y} }_k^{\text{w} } + { {\boldsymbol{\varOmega} } ^{H} }{\boldsymbol{B}}} \right\}$
    (3) 展开可学习迭代网络架构,加入二维卷积核($ \Theta _1^k $,…,$ \Theta _6^k $),初始化$ {\boldsymbol{y}}_0^{\text{w}} = 0 $、$ {{\boldsymbol{s}}_0} = 0 $,网络层$ k = 1 $.
    (4) 当$ k \leqslant K $时,进行网络迭代:
    步骤1 在卷积层中六个卷积核与卷积层输入($ {\boldsymbol{y}}_k^{\text{w}} $,$ {{\boldsymbol{s}}_k} $,${\boldsymbol{B}}$)交替卷积运算得到输出($ {{\boldsymbol{x}}_y} $,$ {{\boldsymbol{x}}_s} $):
    ${ {\boldsymbol{x} }_y} = \Theta _1^k*{\boldsymbol{y} }_k^{\text{w} } + \Theta _3^k*{ {\boldsymbol{s} }_k} + \Theta _2^k*{\boldsymbol{B }}$
    ${ {\boldsymbol{x} }_s} = \Theta _4^k*{\boldsymbol{y} }_k^{\text{w} } + \Theta _6^k*{ {\boldsymbol{s} }_k} + \Theta _5^k*{\boldsymbol{B}}$
    步骤2 进入激活层,独立学习阈值系数$ {\text{thr}}_L^k $、$ {\text{thr}}_S^k $.
    步骤3 对($ {{\boldsymbol{x}}_y} $,$ {{\boldsymbol{x}}_s} $)分别进行奇异值阈值和软阈值操作得到网络低秩输出和稀疏输出:
    $ {\boldsymbol{y}}_{k + 1}^{\text{w}}{\text{ = }}{\Upsilon _{\lambda _{_{\text{1}}}^k}}({{\boldsymbol{x}}_y}) $
    $ {{\boldsymbol{s}}_{k + 1}}{\text{ = }}{\mathcal{T}_{\lambda _{_2}^k}}({{\boldsymbol{x}}_s}) $
    步骤4 $ k = k + 1 $
    (5) 结束
    输出:低秩分量$ {y^{\text{w}}} $,稀疏分量${\boldsymbol{ s}}$(目标重建图像).
    下载: 导出CSV

    表  2  单目标重建性能对比

    Tab.  2  Comparison of single target reconstruction performance

    成像算法TCR /dBPSNR /dBPRT/s
    BP成像10.8751.261.82
    CS成像40.6454.2842.73
    低秩联合稀疏成像42.5859.9816.86
    本文方法成像44.9871.301.34
    下载: 导出CSV

    表  3  双目标重建性能对比

    Tab.  3  Comparison of double target reconstruction performance

    成像算法TCR /dBPSNR /dBPRT/s
    BP成像8.72648.131.90
    CS成像38.94053.9743.71
    低秩联合稀疏成像39.83057.4218.24
    本文方法成像40.84066.281.36
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-12-07
  • 录用日期:  2022-05-11
  • 网络出版日期:  2022-05-11

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