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Polarimetric SAR Target Scattering Interpretation in Rotation Domain: Theory and Application
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摘要: 雷达目标的后向散射敏感于目标姿态与雷达视线的相对几何关系。雷达目标的这种散射多样性给以极化合成孔径雷达(SAR)为代表的成像雷达信息处理与应用造成诸多不便，是当前目标散射机理精细解译和定量应用面临的主要技术瓶颈之一。该文回顾并介绍一种在绕雷达视线旋转域解译目标散射机理的新思路，主要包括新近提出的统一的极化矩阵旋转理论和极化相干特征旋转域可视化解译理论。目标散射旋转域解译方法的核心思想是将特定几何关系下获得的目标信息拓展到绕雷达视线的旋转域，为目标散射信息深度挖掘和利用奠定基础。该文详细分析上述方法导出的一系列新的极化特征参数集，并开展应用验证。对比研究证实了旋转域解译方法在地物辨识与分类等领域的应用潜力。Abstract: Backscattering of radar targets is sensitive to the relative geometry between target orientations and the radar line of sight. This scattering diversity makes imaging radar represented by polarimetric Synthetic Aperture Radar (SAR) information processing and applications very difficult. This situation has become one of the main bottlenecks in the interpretation of the target scattering mechanism and quantitative applications. In this work, we review and introduce a new interpretation of the target scattering mechanism in the rotation domain along the radar line of sight. This concept includes the recently established uniform polarimetric matrix rotation theory and polarimetric coherence pattern visualization and interpretation in the rotation domain. The core idea of target scattering interpretation in the rotation domain is to extend the amount of target information acquired at a given geometry to the rotation domain, which then provides fundamentals for the deep mining and utilization of target scattering information. This work mainly focuses on the investigation of derived new polarimetric feature sets and application demonstrations. Comparison study results validate the promising potential for the application of the established interpretation framework in the rotation domain with respect to target discrimination and classification.
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图 4 极化相干特征旋转域优化前后对比图
Figure 4. Comparison of polarimetric coherence without and with optimization in rotation domain
图 5 极化相干特征旋转域优化前后的统计分布图
Figure 5. Histograms of polarimetric coherence for full scene AIRSAR data
图 6 AIRSAR数据中7种已知地物的旋转域极化相干特征的可视化图。(a1)–(a4) 茎豆，(b1)–(b4) 油菜，(c1)–(c4)豌豆，(d1)–(d4)土豆，(e1)–(e4)紫苜蓿，(f1)–(f4)小麦，(g1)–(g4)甜菜。其中，1–4分别代表 $\left| {{\gamma _{\left( {{\rm{HH}} + {\rm{VV}}} \right) - \left( {{\rm{HH}} - {\rm{VV}}} \right)}}\left( \theta \right)} \right|$, $\left| {{\gamma _{\left( {{\rm{HH}} - {\rm{VV}}} \right) - \left( {{\rm{HV}}} \right)}}\left( \theta \right)} \right|$, $\left| {{\gamma _{{\rm{HH}} - {\rm{VV}}}}\left( \theta \right)} \right|$和 $\left| {{\gamma _{{\rm{HH}} - {\rm{HV}}}}\left( \theta \right)} \right|$
Figure 6. Polarimetric coherence patterns of the seven crop types from AIRSAR data. (a1)–(a4)stembeans, (b1)–(b4)rapeseed, (c1)–(c4)peas, (d1)–(d4)potatoes, (e1)–(e4)lucerne, (f1)–(f4)wheat and (g1)–(g4)beet. The numbers 1–4 indicate $\left| {{\gamma _{\left( {{\rm{HH}} + {\rm{VV}}} \right) - \left( {{\rm{HH}} - {\rm{VV}}} \right)}}\left( \theta \right)} \right|$, $\left| {{\gamma _{\left( {{\rm{HH}} - {\rm{VV}}} \right) - \left( {{\rm{HV}}} \right)}}\left( \theta \right)} \right|$, $\left| {{\gamma _{{\rm{HH}} - {\rm{VV}}}}\left( \theta \right)} \right|$ and $\left| {{\gamma _{{\rm{HH}} - {\rm{HV}}}}\left( \theta \right)} \right|$, respectively
图 7 旋转域极化相干特征典型值对比图
Figure 7. Errorbar plots of typical polarimetric coherence parameters
图 8 旋转域极化相干度对比图
Figure 8. Errorbar plots for polarimetric coherence degree in rotation domain
图 9 旋转域极化相干起伏度对比图
Figure 9. Errorbar plots of polarimetric coherence fluctuation in rotation domain
图 10 旋转域极化相干对比度对比图
Figure 10. Errorbar plots of polarimetric coherence contrast in rotation domain
图 11 旋转域极化相干宽度对比图
Figure 11. Errorbar plots of polarimetric coherence beamwidth ${\rm{B}}{{\rm{W}}_{0.95}}$ in rotation domain
图 12 旋转域极化相干特征最大化角对比图
Figure 12. Errorbar plots of maximum rotation angles ${\theta _{\gamma {\rm{ - }}\max }}$ (in deg) which produce maximized coherence in rotation domain
图 13 旋转域极化相干特征最小化角对比图
Figure 13. Errorbar plots of minimum rotation angles ${\theta _{\gamma {\rm{ - }}\min }}$ (in deg) which produce minimized coherence in rotation domain
图 14 基于极化特征组合的农作物辨识结果
Figure 14. Crops discrimination results based on combinations of derived polarimetric parameters
表 1 旋转域极化相干矩阵的振荡参数集[40]
Table 1. Oscillation parameter set of polarimetric coherence matrix in rotation domain
元素项 $A = \sqrt \cdot $ B $\omega $ ${\theta _0} = \displaystyle \frac{1}{\omega }{\rm{Angle}}\left\{ \cdot \right\}$ ${\mathop{\rm Re}\nolimits} \left[ {{T_{12}}\left( \theta \right)} \right]$ ${{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{12}}} \right] + {{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{13}}} \right]$ 0 2 ${\mathop{\rm Re}\nolimits} \left[ {{T_{13}}} \right] + j{\mathop{\rm Re}\nolimits} \left[ {{T_{12}}} \right]$ ${\mathop{\rm Re}\nolimits} \left[ {{T_{13}}\left( \theta \right)} \right]$ ${{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{12}}} \right] + {{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{13}}} \right]$ 0 2 $ - {\mathop{\rm Re}\nolimits} \left[ {{T_{12}}} \right] + j{\mathop{\rm Re}\nolimits} \left[ {{T_{13}}} \right]$ ${\mathop{\rm Im}\nolimits} \left[ {{T_{12}}\left( \theta \right)} \right]$ ${{\mathop{\rm Im}\nolimits} ^2}\left[ {{T_{12}}} \right] + {{\mathop{\rm Im}\nolimits} ^2}\left[ {{T_{13}}} \right]$ 0 2 ${\mathop{\rm Im}\nolimits} \left[ {{T_{13}}} \right] + j{\mathop{\rm Im}\nolimits} \left[ {{T_{12}}} \right]$ ${\mathop{\rm Im}\nolimits} \left[ {{T_{13}}\left( \theta \right)} \right]$ ${{\mathop{\rm Im}\nolimits} ^2}\left[ {{T_{12}}} \right] + {{\mathop{\rm Im}\nolimits} ^2}\left[ {{T_{13}}} \right]$ 0 2 $ - {\mathop{\rm Im}\nolimits} \left[ {{T_{12}}} \right] + j{\mathop{\rm Im}\nolimits} \left[ {{T_{13}}} \right]$ ${\mathop{\rm Re}\nolimits} \left[ {{T_{23}}\left( \theta \right)} \right]$ $\frac{1}{4}{\left( {{T_{33}} - {T_{22}}} \right)^2} + {{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{23}}} \right]$ 0 4 $\frac{1}{2}\left( {{T_{33}} - {T_{22}}} \right) + j{\mathop{\rm Re}\nolimits} \left[ {{T_{23}}} \right]$ ${T_{22}}\left( \theta \right)$ $\frac{1}{4}{\left( {{T_{33}} - {T_{22}}} \right)^2} + {{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{23}}} \right]$ $\frac{1}{2}\left( {{T_{22}} + {T_{33}}} \right)$ 4 ${\mathop{\rm Re}\nolimits} \left[ {{T_{23}}} \right] + j\frac{1}{2}\left( {{T_{22}} - {T_{33}}} \right)$ ${T_{33}}\left( \theta \right)$ $\frac{1}{4}{\left( {{T_{33}} - {T_{22}}} \right)^2} + {{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{23}}} \right]$ $\frac{1}{2}\left( {{T_{22}} + {T_{33}}} \right)$ 4 $ - {\mathop{\rm Re}\nolimits} \left[ {{T_{23}}} \right] + j\frac{1}{2}\left( {{T_{33}} - {T_{22}}} \right)$ ${\left| {{T_{12}}\left( \theta \right)} \right|^2}$ ${{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{12}}T_{13}^ * } \right] + \frac{1}{4}{\left( {{{\left| {{T_{13}}} \right|}^2} - {{\left| {{T_{12}}} \right|}^2}} \right)^2}$ $\frac{1}{2}\left( {{{\left| {{T_{12}}} \right|}^2} + {{\left| {{T_{13}}} \right|}^2}} \right)$ 4 ${\mathop{\rm Re}\nolimits} \left[ {{T_{12}}T_{13}^ * } \right] + j\frac{1}{2}\left( {{{\left| {{T_{12}}} \right|}^2} - {{\left| {{T_{13}}} \right|}^2}} \right)$ ${\left| {{T_{13}}\left( \theta \right)} \right|^2}$ ${{\mathop{\rm Re}\nolimits} ^2}\left[ {{T_{12}}T_{13}^ * } \right] + \frac{1}{4}{\left( {{{\left| {{T_{13}}} \right|}^2} - {{\left| {{T_{12}}} \right|}^2}} \right)^2}$ $\frac{1}{2}\left( {{{\left| {{T_{12}}} \right|}^2} + {{\left| {{T_{13}}} \right|}^2}} \right)$ 4 $ - {\mathop{\rm Re}\nolimits} \left[ {{T_{12}}T_{13}^ * } \right] + j\frac{1}{2}\left( {{{\left| {{T_{13}}} \right|}^2} - {{\left| {{T_{12}}} \right|}^2}} \right)$ ${\left| {{T_{23}}\left( \theta \right)} \right|^2}$ $\frac{1}{4}{\left\{ {\frac{1}{4}{{\left( {{T_{33}} - {T_{22}}} \right)}^2} + {{{\mathop{\rm Re}\nolimits} }^2}\left[ {{T_{23}}} \right]} \right\}^2}$ $\begin{array}{l}\frac{1}{2}\left\{ {\frac{1}{4}{{\left( {{T_{33}} - {T_{22}}} \right)}^2} + {{{\mathop{\rm Re}\nolimits} }^2}\left[ {{T_{23}}} \right]} \right\}\\\quad + {{\mathop{\rm Im}\nolimits} ^2}\left[ {{T_{23}}} \right]\end{array}$ 8 $\begin{array}{l}\frac{1}{2}\left( {{T_{33}} - {T_{22}}} \right){\mathop{\rm Re}\nolimits} \left[ {{T_{23}}} \right] \\\quad+ j\frac{1}{2}\left[ {{{{\mathop{\rm Re}\nolimits} }^2}\left[ {{T_{23}}} \right] - \frac{1}{4}{{\left( {{T_{33}} - {T_{22}}} \right)}^2}} \right]\end{array}$ 
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表 2 AIRSAR数据极化相干特征旋转域优化前后对比结果
Table 2. Comparison of polarimetric coherence without and with optimization in rotation domain for AIRSAR data
极化相干特征 原始值均值 最优值均值 增强百分比(%) $\left| {{\gamma _{\left( {{\rm{HH}} + {\rm{VV}}} \right) - \left( {{\rm{HH}} - {\rm{VV}}} \right)}}\left( \theta \right)} \right|$ 0.30 0.33 10.00 $\left| {{\gamma _{\left( {{\rm{HH}} - {\rm{VV}}} \right) - {\rm{HV}}}}\left( \theta \right)} \right|$ 0.11 0.48 336.36 $\left| {{\gamma _{{\rm{HH}} - {\rm{VV}}}}\left( \theta \right)} \right|$ 0.35 0.64 82.86 $\left| {{\gamma _{{\rm{HH}} - {\rm{HV}}}}\left( \theta \right)} \right|$ 0.13 0.45 246.15
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