A Review of Progress in Super-Resolution Reconstruction of Polarimetric Radar Image Target
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摘要: 成像雷达具有全天时、全天候的观测能力，能够通过成像处理获得目标雷达图像信息，是对地观测、侦察监视等民用和军用领域中的重要遥感设备。高分辨率雷达图像能够提供目标的详细轮廓和精细结构，有利于后续目标分类识别等应用。对获取的雷达图像，如何利用信号和信息处理等理论方法进一步提升分辨率，突破分辨率瑞利极限，具有重要的科学研究和实际应用价值。另一方面，作为电磁波的重要属性之一，极化在目标特性的获取和挖掘中发挥着重要作用，能够为目标超分辨率重建带来丰富信息。为此，该文梳理了极化雷达图像目标超分辨率重建的概念及性能评价指标，并重点归纳整理了极化雷达图像目标超分辨率重建方法及其应用。最后，总结了现有方法的局限性并展望了未来的技术发展趋势。Abstract: Radar possesses the capability for all-day, all-weather observation and can generate radar target images through image processing. It serves as an indispensable piece of remote sensing equipment in various civil and military applications, including earth observation, and surveillance. High-resolution radar images can provide a detailed outline and fine structure of the target, which is conducive to subsequent applications such as target classification and recognition. For the acquired radar images, how to use theoretical methods such as signal and information processing to further improve the resolution and break through the Rayleigh limit has important scientific research and practical application value. On the other hand, polarization, a crucial attribute of electromagnetic waves, plays a significant role in the acquisition and analysis of target characteristics, and can provide rich information for super-resolution reconstruction. Accordingly, this work initially elucidates the concept of polarimetric radar image super-resolution reconstruction, summarizes the performance evaluation metrics, and primarily focuses on the methods of polarimetric radar image super-resolution reconstruction and their applications. Lastly, the limitations of existing methods are summarized and potential future trends in technology are forecasted.
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Key words:
- Radar image /
- Polarization /
- Super-resolution reconstruction /
- Signal processing /
- Deep learning
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表 1 基于点目标的极化雷达图像目标超分辨率重建定量评价指标
评价指标 是否需要参考图像 含义 计算公式 变量与符号说明 距离向3 dB主瓣宽度[17,39–43] 否 距离向瑞利极限值 ${\delta _{\text{r}}} = \left\{ {y\left| {{{{\hat {\boldsymbol{I}}}}_{\max }} \ge {\hat {\boldsymbol{I}}}\left( y \right) \ge 0.707{{{\hat {\boldsymbol{I}}}}_{\max }}} \right.} \right\}$ ${\hat {\boldsymbol{I}}}$为超分辨率重建图像幅度特征图，$ {{\hat {\boldsymbol{I}}}_{\max }} $为主瓣峰值，$y$为距离向坐标 方位向3 dB主瓣宽度[17,39–43] 否 方位向瑞利极限值 ${\delta _{\text{a}}} = \left\{ {x\left| {{{{\hat {\boldsymbol{I}}}}_{\max }} \ge {\hat {\boldsymbol{I}}}\left( x \right) \ge 0.707{{{\hat {\boldsymbol{I}}}}_{\max }}} \right.} \right\}$ $x$为方位向坐标 峰值旁瓣比(Peak Side Lobe Ratio, PSLR)[42–44] 否 第一旁瓣与主瓣峰值的比值，能够表征弱目标被强目标旁瓣压制的程度 $ {\text{PSLR}} = 20\lg \left( {{{{{{\hat {\boldsymbol{I}}}}_{{\text{SideLobe}}}}} \mathord{\left/ {\vphantom {{{{{\hat I}}_{{\text{SideLobe}}}}} {{{{\hat I}}_{\max }}}}} \right. } {{{{\hat {\boldsymbol{I}}}}_{\max }}}}} \right) $ $ {{\hat {\boldsymbol{I}}}_{{\text{SideLobe}}}} $为第一旁瓣峰值 积分旁瓣比(Integrate Side Lobe Ratio, ISLR) [42] 否 旁瓣能量与主瓣能量的比值，能够表征对旁瓣的抑制能力 $ {\text{ISLR}} = 20\lg \left( {{{{E_{{\text{SideLobe}}}}} \mathord{\left/ {\vphantom {{{E_{{\text{SideLobe}}}}} {{E_{{\text{MainLobe}}}}}}} \right. } {{E_{{\text{MainLobe}}}}}}} \right) $ $ {E_{{\text{SideLobe}}}} $为旁瓣总能量，$ {E_{{\text{MainLobe}}}} $为主瓣总能量 距离向分辨率增强指数(Intersection Amplitude Value, IAV)[45] 是 参考图像与超分辨率重建图像中两个不完全孤立的点目标距离向回波幅值交叉点取值的差 $ {\text{IA}}{{\text{V}}_{\text{r}}}{\text{ = IAV}}_{\text{r}}^{{\text{hr}}} - {\text{IAV}}_{\text{r}}^{{\text{sr}}} $ $ {\text{IAV}}_{\text{r}}^{{\text{hr}}} $和$ {\text{IAV}}_{\text{r}}^{{\text{sr}}} $分别为参考图像与超分辨率重建图像中两个不完全孤立的点目标距离向回波幅值交叉点取值 方位向分辨率增强指数(Intersection Amplitude Value, IAV)[45] 是 参考图像与超分辨率重建图像中两个不完全孤立的点目标方位向回波幅值交叉点取值的差 $ {\text{IA}}{{\text{V}}_{\text{a}}}{\text{ = IAV}}_{\text{a}}^{{\text{hr}}} - {\text{IAV}}_{\text{a}}^{{\text{sr}}} $ $ {\text{IAV}}_{\text{a}}^{{\text{hr}}} $和$ {\text{IAV}}_{\text{a}}^{{\text{sr}}} $分别为参考图像与超分辨率重建图像中两个不完全孤立的点目标方位向回波幅值交叉点取值 峰值点匹配准确率[46] 是 重建后强散射点位置保持
精度– – 
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表 2 基于面目标的极化雷达图像目标超分辨率重建定量评价指标
评价指标 是否需要参考图像 含义 计算公式 变量与符号说明 图像熵[44,47–51] 否 图像平均信息量 $ {\text{Entropy}} = - \sum\limits_{y = 1}^H {\sum\limits_{x = 1}^W {\frac{{{{\left| {{\hat {\boldsymbol{I}}}\left( {x,y} \right)} \right|}^2}}}{Q} {{\lg }}\frac{{{{\left| {{\hat {\boldsymbol{I}}}\left( {x,y} \right)} \right|}^2}}}{Q}} }$ $ Q $为超分辨率重建图像总能量。$H$与$W$分别为图像距离向与方位向的
像素数图像对比度(Image Contrast, IC)[42,48] 否 超分辨率重建图像强度标准差与方差
的比值$ {\text{IC}} = {{{\text{std}}\left( {{{{\hat {\boldsymbol{I}}}}^2}} \right)} \mathord{\left/ {\vphantom {{{\text{std}}\left( {{{{\hat I}}^2}} \right)} {{\text{mean}}\left( {{{{\hat I}}^2}} \right)}}} \right. } {{\text{mean}}\left( {{{{\hat {\boldsymbol{I}}}}^2}} \right)}} $ $ {\text{std}}\left( \cdot \right) $为数据标准差，$ {\text{mean}}\left( \cdot \right) $为数据均值 图像信噪比(Signal-to-noise Ratio, SNR)[48] 否 超分辨率重建图像目标区域强度与背景区域强度的比值 $ {\text{SNR}} = 20\lg \left[ {\dfrac{{{\text{mean}}\left( {{\hat {\boldsymbol{I}}}_{{\text{target}}}^2} \right)}}{{{\text{mean}}\left( {{\hat {\boldsymbol{I}}}_{{\text{background}}}^2} \right)}}} \right] $ $ {\hat {\boldsymbol{I}}}_{{\text{target}}}^2 $为目标区域图像强度，$ {\hat {\boldsymbol{I}}}_{{\text{background}}}^2 $为背景区域图像强度 平均绝对误差(Mean Absolute Error, MAE)[5,43,52,53] 是 超分辨率重建图像与参考图像幅度值之间绝对误差的平均值 $ {\text{MAE}} = {\left\| {{\hat {\boldsymbol{I}}} - {{\boldsymbol{I}}}} \right\|_1} $ $ {{\boldsymbol{I}}} $为参考图像幅度特征图，${\left\| \cdot \right\|_1}$为矩阵1范数 均方误差(Mean Square Error, MSE)[44] 是 超分辨率重建图像与参考图像幅度值之间差值平方的平均值 $ {\text{MSE}} = \left\| {{\hat {\boldsymbol{I}}} - {{\boldsymbol{I}}}} \right\|_2^2 $ ${\left\| \cdot \right\|_2}$为矩阵2范数 均方根误差(Root Mean Square Error, RMSE)[30,43,54] 是 均方误差的算数
平方根$ {\text{RMSE}} = {\left\| {{\hat {\boldsymbol{I}}} - {{\boldsymbol{I}}}} \right\|_2} $ – 平均归一化均方根误差(Average Normalized Root Mean Square Error, NRMSE)[55] 是 归一化的均方根误差 $ {\text{NRMSE}} = \dfrac{{{{\left\| {{\hat {\boldsymbol{I}}} - {{\boldsymbol{I}}}} \right\|}_2}}}{{{{\left\| {{\hat {\boldsymbol{I}}}} \right\|}_2}{{\left\| {{\boldsymbol{I}}} \right\|}_2}}} $ – 峰值信噪比(Peak Signal-to-Noise Ratio, PSNR)[3–5,8,43,44,46,49,51–53,56–59] 是 超分辨率重建图像最大强度与均方误差强度的比值 $ {\text{PSNR = 10lg}}\dfrac{{{{\boldsymbol{I}}}_{\max }^2}}{{{\text{MSE}}}} $ – 结构相似度(Structural Similarity, SSIM)[4,8,43,46,49,57–59] 是 超分辨率重建图像与参考图像结构
相似程度$ {\text{SSIM = }}L\left( {{\hat {\boldsymbol{I}}}{\text{,}}{{\boldsymbol{I}}}} \right){{C}}\left( {{\hat {\boldsymbol{I}}}{\text{,}}{{\boldsymbol{I}}}} \right){{S}}\left( {{\hat {\boldsymbol{I}}}{\text{,}}{{\boldsymbol{I}}}} \right) $ $ {{L}}\left( \cdot \right) $为亮度相似程度，$ {{C}}\left( \cdot \right) $为对比度相似程度，$ {{S}}\left( \cdot \right) $为结构相似
程度[60]特征相似性指标(Feature Similarity Index Metric, FSIM)[61,62] 是 超分辨率重建图像与参考图像特征相似程度，取值越接近1，相似性越高 $ \begin{gathered} {\text{FSIM}} = \\ \frac{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {{\text{S}}'\left[ {{\hat {\boldsymbol{I}}}\left( {x,y} \right){\text{,}}{{\boldsymbol{I}}}\left( {x,y} \right)} \right]{\text{P}}{{\text{C}}_{\text{m}}}\left[ {{\hat {\boldsymbol{I}}}\left( {x,y} \right){\text{,}}{{\boldsymbol{I}}}\left( {x,y} \right)} \right]} } }}{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {{\text{P}}{{\text{C}}_{\text{m}}}\left[ {{\hat {\boldsymbol{I}}}\left( {x,y} \right){\text{,}}{{\boldsymbol{I}}}\left( {x,y} \right)} \right]} } }} \\ \end{gathered} $ $ {\text{S}}'\left( \cdot \right) $为超分辨率重建图像与参考图像的局部相似性，$ {\text{P}}{{\text{C}}_{\text{m}}}\left( \cdot \right) $为对应的最大相位一致性[63] 皮尔逊相关系数[8] 是 参考图像与超分辨率重建图像协方差与标注差的比值 $ {\text{P = }}\frac{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {\left[ {{\hat {\boldsymbol{I}}}\left( {x,y} \right) - {\text{mean}}\left( {{\boldsymbol{I}}} \right)} \right]} } \left[ {{\hat {\boldsymbol{I}}}\left( {x,y} \right) - {\text{mean}}\left( {{\hat {\boldsymbol{I}}}} \right)} \right]}}{{{{\left\| {{\hat {\boldsymbol{I}}}} \right\|}_2}{{\left\| {{\boldsymbol{I}}} \right\|}_2}}} $ – 边缘保持指数(Edge Preservation Index, EPI)[62] 是 针对乘性噪声的图像距离向边缘保持度量 $ \begin{gathered} {\text{EPI = }} \\ \frac{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {\left[ {\Delta {\hat {\boldsymbol{I}}}\left( {x,y} \right) - {\text{mean}}\left( {\Delta {\hat {\boldsymbol{I}}}} \right)} \right]\left[ {\Delta {{\boldsymbol{I}}}\left( {x,y} \right) - {\text{mean}}\left( {\Delta {{\boldsymbol{I}}}} \right)} \right]} } }}{{{{\left\| {\Delta {\hat {\boldsymbol{I}}} - {\text{mean}}\left( {\Delta {\hat I}} \right)} \right\|}_2}{{\left\| {\Delta {{\boldsymbol{I}}} - {\text{mean}}\left( {\Delta {{\boldsymbol{I}}}} \right)} \right\|}_2}}} \\ \end{gathered} $ $ \Delta {\hat {\boldsymbol{I}}} $为超分辨率重建图像的边缘滤波特征图，$ \Delta {{\boldsymbol{I}}} $为参考图像的边缘滤波特征图[64] 距离向边缘保持度量指标(Edge Preservation Index-ROA, EPI-ROA)[57] 是 针对乘性噪声的图像距离向边缘保持度量 $ {\text{EPI - RO}}{{\text{A}}_{\text{r}}}{\text{ = }}\frac{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {\left[ {{{{\hat {\boldsymbol{I}}}\left( {x,y + 1} \right)}/ {{\hat {\boldsymbol{I}}}\left( {x,y} \right)}}} \right]} } }}{{\displaystyle\sum\limits_{y = 1}^H {\sum\limits_{x = 1}^W {\left[ {{{{{\boldsymbol{I}}}\left( {x,y + 1} \right)} \mathord{\left/ {\vphantom {{{I}\left( {x,y + 1} \right)} {{I}\left( {x,y} \right)}}} \right. } {{{\boldsymbol{I}}}\left( {x,y} \right)}}} \right]} } }} $ – 方位向边缘保持度量指标(Edge Preservation Index-ROA, EPI-ROA)[57] 是 针对乘性噪声的图像方位向边缘保持度量 $ {\text{EPI - RO}}{{\text{A}}_{\text{a}}}{\text{ = }}\frac{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {\left[ {{{{\hat {\boldsymbol{I}}}\left( {x + 1,y} \right)} \mathord{\left/ {\vphantom {{{\hat I}\left( {x + 1,y} \right)} {{\hat I}\left( {x,y} \right)}}} \right. } {{\hat {\boldsymbol{I}}}\left( {x,y} \right)}}} \right]} } }}{{\displaystyle\sum\limits_{y = 1}^H {\displaystyle\sum\limits_{x = 1}^W {\left[ {{{{{\boldsymbol{I}}}\left( {x + 1,y} \right)} \mathord{\left/ {\vphantom {{{{\boldsymbol{I}}}\left( {x + 1,y} \right)} {{{\boldsymbol{I}}}\left( {x,y} \right)}}} \right. } {{{\boldsymbol{I}}}\left( {x,y} \right)}}} \right]} } }} $ – Pauli相似性指标[16] 是 全极化雷达图像Pauli矢量重建精度 ${{R}} = \dfrac{{{{\left\| {{{\boldsymbol{k}}}_{{\text{sr}}}^{}{{\boldsymbol{k}}}_{{\text{hr}}}^{\text{H}}} \right\|}_1}}}{{{{\left\| {{{\boldsymbol{k}}}_{{\text{sr}}}^{}} \right\|}_1}{{\left\| {{{\boldsymbol{k}}}_{{\text{hr}}}^{}} \right\|}_1}}}$ ${{\boldsymbol{k}}}_{{\text{sr}}}^{}$为超分辨率重建图像Pauli矢量，${{\boldsymbol{k}}}_{{\text{hr}}}^{}$为参考图像Pauli矢量
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表 3 基于深度学习的极化雷达图像超分辨率重建方法研究现状
极化模式 网络模型结构 文献 学习方式 损失函数 升采样方式 升采样阶段 单极化 Shallow CNN [42] 监督学习 ${L_2}$/${L_{{\text{SSIM}}}}$ Bicubic 前升采 Shallow CNN [73] 监督学习 ${L_2}$ Bicubic 前升采 ResNet [43] 监督学习 ${L_2}$/${L_{{\text{SSIM}}}}$ 反卷积 后升采 ResNet [3] 监督学习 ${L_2}$ 反卷积 后升采 ResNet [4] 监督学习 ${L_1}$ 亚像素卷积重排 后升采 ResNet [57] 监督学习 ${L_2}$/$ {L_{{\text{Content}}}} $ 反卷积 后升采 ResNet [8] 监督学习 ${L_1}$/${L_{{\text{Edge}}}}$ Bicubic 后升采 ResNet [58] 监督学习 ${L_1}$ Bicubic 后升采 GAN [74] 监督学习 ${L_2}$/${L_{{\text{GAN}}}}$/$ {L_{{\text{Content}}}} $/$ {L_{{\text{Style}}}} $ – – GAN [75] 监督学习 ${L_1}$/${L_{{\text{GAN}}}}$ – – GAN [49] 监督学习 ${L_1}$/${L_{{\text{GAN}}}}$/$ {L_{{\text{Content}}}} $ – – GAN [73] 监督学习 ${L_{{\text{GAN}}}}$/$ {L_{{\text{Content}}}} $ – – GAN [46] 监督学习 ${L_{{\text{GAN}}}}$/${L_{{\text{CycleGAN}}}}$ – – GAN [7] 无监督学习 ${L_2}$/${L_{{\text{SSIM}}}}$ – – 双极化 ResNet [52] 监督学习 ${L_1}$/${L_{{\text{Phy}}}}$ 反卷积 前升采 隐式神经表征 [17] 半监督学习 ${L_2}$/${L_{{\text{Self}}}}$/${L_{{\text{Penalty}}}}$/${L_{{\text{CE}}}}$ Bilinear 后升采 全极化 ResNet [5,76] 监督学习 ${L_2}$ 反卷积 前升采 ResNet [53] 监督学习 ${L_{\text{F}}}$/${L_{{\text{Phy}}}}$ 反卷积 前升采 ResNet [77] 监督学习 ${L_{\text{C}}}$/${L_{{\text{Edge}}}}$ 反卷积 前升采 ResNet [15] 监督学习 ${L_1}$ 亚像素卷积重排 后升采 隐式神经表征 [78] 半监督学习 ${L_1}$/${L_{{\text{Self}}}}$ Bilinear 后升采
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