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 雷达学报  0, Vol. 0 Issue (0): 0-0  DOI: 10.12000/JR15114 0

### 引用本文 [复制中英文]

[复制中文]
Jin Tian. An Enhanced Imaging Method for Foliage Penetration Synthetic Aperture Radar[J]. Journal of Radars, 0, 0(0): 0-0. DOI: 10.12000/JR15114.
[复制英文]

### 文章历史

(国防科学技术大学电子科学与工程学院 长沙 410073)

An Enhanced Imaging Method for Foliage Penetration Synthetic Aperture Radar

(College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China)
Abstract: FOliage PENetration Synthetic Aperture Radar (FOPEN SAR) is used in low Signal-to-Clutter Ratio (SCR) conditions to detect targets hidden in forests, which introduces difficulties in target detection. In this study, an enhanced imaging method based on the scattering aspect variability of the target is proposed, which improves the SCR of the formed images of hidden targets while maintaining high spatial resolution. In the case of a vehicle target, the dihedral is formed by its main side and the ground. The echo is strongest when the incident electromagnetic wave is along the normal direction of the dihedral. A high-resolution image corresponding to this aspect angle is formed by the proposed enhanced imaging method to increase the SCR of the target and improve the detection performance. Airborne FOPEN SAR data were used to validate the efficiency of the proposed method.
Key words: FOliage PENetration (FOPEN)     Synthetic Aperture Radar (SAR)     Enhanced imaging
1 引言

2 FOPEN SAR回波模型

 图 1 正侧视条带工作方式成像几何示意图 Fig. 1  Imaging geometry of broadside trip-map operation mode

 ${\theta }=\arctan \left(\frac{u-y}{r} \right)$ (1)

 $\begin{array}{*{20}{c}} {s(t,u) = \int {\int {\frac{1}{{{{(u - y)}^2} + {r^2}}}{\cal F}_{f \to t}^{\; - 1}\left[ {{g_{\rm{A}}}(f,\theta ){{\rm{g}}_{\rm{T}}}\left( {r,y,f,\theta } \right)} \right]} } }\\ {{ \otimes _t}\;p\left( {t - \frac{{\rm{2}}}{{\rm{c}}}\sqrt {{{\left( {u - y} \right)}^{\rm{2}}}{\rm{ + }}{r^{\rm{2}}}} } \right){\rm{drdy}}} \end{array}$ (2)

 $s(t,u)=\mathcal{F}_{f\to t}^{\ -1}[{{g}_{_ \rm{\Large A}}}(f,{\theta }){{A}_{_ \rm{\Large T}}}(f,{\theta })] \\ \quad\quad\quad \quad {{\otimes }_{t}} \ p \left(t-\frac{2}{\rm{c}}\sqrt{{{(u-{{y}_{n}})}^{2}}+r_{n}^{2}} \right)$ (3)

 $S(k,u)=P(k){{g}_{_ \rm{\Large A}}}(k,{\theta }){{A}_{_ \rm{\Large T}}}(k,{\theta }) \\ \quad\quad\quad\quad \cdot \exp \left[{ - {\rm{j}}2k\sqrt {r_n^2 + {{({u_n} - y)}^2}} } \right]$ (4)

 $\begin{array}{*{20}{l}} {S'(k,{k_u}) \approx }&{\frac{{\exp ( - {\rm{j}}\pi /4)}}{{\sqrt {4{k^2} - k_u^2} }}P(k){g_{\rm{A}}}\left( {k,\frac{{ - {k_u}}}{{\sqrt {{\rm{4}}{k^{\rm{2}}} - k_u^{\rm{2}}} }}} \right)}\\ {}&{ \cdot {{\rm{A}}_{\rm{T}}}\left( {k,\frac{{ - {k_u}}}{{\sqrt {{\rm{4}}{k^{\rm{2}}} - k_u^{\rm{2}}} }}} \right)}\\ {}&{ \cdot \exp \left( { - {\rm{j}}{r_n}\sqrt {{\rm{4}}{k^{\rm{2}}} - k_u^{\rm{2}}} - {\rm{j}}{y_n}{k_u}} \right)} \end{array}$ (5)

FOPEN SAR 2维回波时域和频域(波数域)模型分别如式(3)和式(5)所示，定量表示了回波中目标散射随频率和方位角变化的信息。

3 增强成像机理与实现 3.1 成像模型

FOPEN SAR为了获得与高波段SAR相当的方位分辨率，需要更大的积累角，距离向和方位向存在强耦合。距离迁移(RM)算法针对该特性，利用Stolt变换在2维回波波数域对距离向和方位向解耦。Stolt变换定义为：

 $\left\{ \!\!\! \begin{array}{l} k = \frac{1}{2}\sqrt {k_r^2 + k_y^2} \\ {k_u} = {k_y} \end{array} \right.$ (6)

 $\begin{array}{*{20}{c}} {\tilde S({k_r},{k_y}) = \frac{{\exp ( - {\rm{j}}\pi /4)}}{{{k_r}}}\left| {{J_{{\rm{ST}}}}} \right|{{\left| {P(k)} \right|}^2}{g_{\rm{A}}}\left( {k,\frac{{ - {k_y}}}{{{k_r}}}} \right)}\\ { \cdot {{\rm{A}}_{\rm{T}}}\left( {k,\frac{{ - {k_y}}}{{{k_r}}}} \right)\exp \left( { - {\rm{j}}{r_n}{k_r} - {\rm{j}}{y_n}{k_y}} \right)} \end{array}$ (7)

 ${J_{{\rm{ST}}}} = \left[ {\begin{array}{*{20}{c}} {\frac{{\partial k}}{{\partial {k_r}}}}&{\frac{{\partial k}}{{\partial {k_y}}}}\\ {\frac{{\partial {k_u}}}{{\partial {k_r}}}}&{\frac{{\partial {k_u}}}{{\partial {k_y}}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\frac{{{k_r}}}{{2\sqrt {k_r^2 + k_y^2} }}}&{\frac{{{k_y}}}{{2\sqrt {k_r^2 + k_y^2} }}}\\ 0&1 \end{array}} \right]$ (8)

 $\left| {{J_{{\rm{ST}}}}} \right| = \frac{{{k_r}}}{{2\sqrt {k_r^2 + k_y^2} }}$ (9)

 $\begin{array}{l} \tilde S({k_r},{k_y})\\ = {\left| {P\left( {\frac{1}{2}\sqrt {k_r^2 + k_y^2} } \right)} \right|^2}{{g}_{_\rm{\Large A}}}\left( {\frac{1}{2}\sqrt {k_r^2 + k_y^2} ,\frac{{ - {k_y}}}{{{k_r}}}} \right)\\ \quad \cdot {{A}_{_ \rm{\Large T}}} \left( \! {\frac{1}{2}\sqrt {k_r^2 \! + \! k_y^2} ,\frac{{ - {k_y}}}{{{k_r}}}} \right)\exp ( \! - \! {\rm{j}}{r_n}{k_r} \! - \! {\rm{j}}{y_n}{k_y}) \end{array}$ (10)

RM算法成像结果$f(r,y)$是$\tilde{S}({{k}_{r}},{{k}_{y}})$的2维逆Fourier变换，还可以表示为：

 $f(r,y)={{f}_{\text{psf}}}(r,y){{\otimes }_{r,y}}{{\tilde{g}}_{_ \rm{\Large T}}}(r,y)$ (11)

 $\begin{array}{l} \!\! {f_{{\rm{psf}}}}(r,y) = {\cal F}_{{k_r},{k_y} \to r,y}^{ \ - 1}\left[{{{\left| {P\left( {\frac{1}{2}\sqrt {k_r^2 + k_y^2} } \right)} \right|}^2}} \right.\\ \quad\quad\quad\quad\quad \cdot \left. {{{g}_{_\rm{\Large A}}}\left( {\frac{1}{2}\sqrt {k_r^2 + k_y^2} ,\frac{{ - {k_y}}}{{{k_r}}}} \right)} \right] \end{array}$ (12)
 $\begin{array}{l} {{\tilde g}_{_ \rm{\Large T}}}(r,y) = {\cal F}_{{k_r},{k_y} \to r,y}^{ \ - 1}\left[{{{A}_{_ \rm{\Large T}}} \left( {\frac{1}{2}\sqrt {k_r^2 + k_y^2} ,\frac{{ - {k_y}}}{{{k_r}}}} \right)} \right] \hspace{8pt}\\ \quad\quad\quad\quad\quad { \otimes _{r,y}}[\delta (r - {r_n})\delta (y - {y_n})] \hspace{8pt} \end{array}$ (13)

 $\left\{ {\begin{array}{*{20}{l}} {{k_r} = 2k\cos \theta }\\ {}\\ {{k_y} = 2k\sin \theta } \end{array}} \right.$ (14)
3.2 增强成像算法

 $\begin{array}{*{20}{l}} {{A_{{\rm{dih}}}}(k,{\theta }) = \frac{{{\rm{j}}2k{L_{{\rm{dih}}}}{H_{{\rm{dih}}}}}}{{\sqrt {\pi } }}{\rm{sinc}}\left[{k{L_{{\rm{dih}}}}\sin ({\theta } - {α} )} \right.} {\left.{\left. {\cos {\phi } } \right)} \right] \left \{\!\!\! \begin{array}{l} \sin {\phi },\ \ {\phi } \in \left[{0,{\pi } /4} \right]\\ \cos {\phi },\ \ {\phi } \in \left[{{\pi } /4,{\pi } /2} \right] \end{array} \right.} \end{array}$ (15)
 $\quad\quad\quad\quad\quad\ \begin{array}{l} {A_{{\rm{top}}}}(k,{\theta }) = {H_{{\rm{top}}}}\sqrt {{{{\rm{j}}8k{r_{{\rm{top}}}}} \mathord{\left/ {\vphantom {{{\rm{j}}8k{r_{{\rm{top}}}}} {\sqrt 2 }}} \right.} {\sqrt 2 }}} \left\{ \!\!\! \begin{array}{l} \sin {\phi },\ \ {\rm{ }}{\phi } \in \left[{0,{\pi } /4} \right]\\ \cos {\phi },\ \ {\rm{ }}{\phi } \in \left[{{\pi } /4,{\pi } /2} \right]{\rm{ }} \end{array} \right. \end{array}$ (16)

 $\begin{array}{l} {f_{{\rm{WVD}}}}(r,y;{\theta }) = \int\!\!\!\!\int {{{\tilde S}^*}({k_r},{k_r}\tan {\theta } - {{k'}\!\!_y}/2)} \\ \quad\quad\quad\quad\quad\quad \ \cdot \tilde S({k_r},{k_r}\tan {\theta } + {{k'}\!\!_y}/2)\\ \quad\quad\quad\quad\quad\quad \ \cdot \exp ({\rm{j}}{k_r}r + {\rm{j}}{{k'}\!\!_y}y){\rm{d}}{k_r}{\rm{d}}{{k'}\!\!_y} \end{array}$ (17)

WVD作为最基本的双线性时频表示方法，其主要缺点是存在交叉项的干扰，为了克服这个问题，需要对WVD进行改进，对交叉项进行抑制。Choi-Williams分布(CWD)具有好的交叉项抑制能力，与WVD相比它只需在运算中添加一个核函数[13]。基于CWD的增强成像公式可以表示为

 $\begin{array}{l} {f_{{\rm{CWD}}}}(r,y;{\theta }) = \int\!\int\!\int \Gamma \left( {k\!_y^{'},k\!_y^{'''}} \right)\tilde S\left( {{k_r},{{k''}\!\!\!_y} + \frac{{{{k'}\!\!_y}}}{2}} \right)\\ \quad\quad\quad\quad\quad\quad \ \cdot {{\tilde S}^*}\left( {{k_r},{{k''}\!\!\!_y} - \frac{{{{k'}\!\!_y}}}{2}} \right)\\ \quad\quad\quad\quad\quad\quad \ \cdot \exp \left[{{\rm{j}}{{k'''}\!\!\!\!_y}\left( {{k_r}\tan \theta - {{k''}\!\!\!_y}} \right)} \right]\\ \quad\quad\quad\quad\quad\quad \ \cdot \exp \left( {{\rm{j}}{k_r}r + {\rm{j}}k_y^{'}y} \right){\rm{d}}{k_r}{\rm{d}}{{k'}\!\!_y}{\rm{d}}{{k''}\!\!\!_y}{\rm{d}}{{k'''}\!\!\!\!_y} \end{array}$ (18)

 $\Gamma \left( {{{k'}\!\!_y}{{k'''}\!\!\!\!_y}} \ \right)=\exp \left[{ - {\beta _{{k_y}}}{{\left( {{{k'}\!\!_y}{{k'''}\!\!\!\!_y}} \ \right)}^2}} \right]$ (19)

4 实测数据验证

 图 2  FOPEN SAR成像结果 Fig. 2  FOPEN SAR imaging results
5 结论

 [1] Davis M E. Foliage Penetration Radar: Detection and Characterization of Objects under Trees[M]. SciTech Publishing, Inc, 2011: 60-92.(1) [2] Novak L M, Halversen S D, Owirka G J, et al. Effects of polarization and resolution on SAR ATR[J]. IEEE Transactions on Aerospace and Electronic Systems, 1997, 33(1): 102-116.(1) [3] 吴一戎. 多维度合成孔径雷达成像概念[J]. 雷达学报, 2013, 2(2): 135-142.Wu Yi-rong. Concept on multidimensional space joint-observation SAR[J]. Journal of Radars, 2013, 2(2): 135-142.(1) [4] Kaplan L M, McClellan J H, and Seung-Mok Oh. Prescreening during image formation for ultrawideband radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(1): 74-88.(1) [5] Carin L, Ybarra G, Bharadwaj P, et al. Physics-based classification of targets in SAR imagery using subaperture sequences[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Phoenix, AZ, USA, 1999: 3341-3344.(1) [6] Runkle P, Nguyen L H, McClellan J H, et al. Multi-aspect target detection for SAR imagery using hidden Markov models[J]. IEEE Transactions on Geoscience and Remote Sensing, 2001, 39(1): 46-55.(1) [7] Soumekh M, Gunther G, Linderman M, et al. Digitally-spotlighted subaperture SAR image formation using high performance computing[C]. Proceedings of SPIE, 2000, 4053: 260-271.(1) [8] Wong D and Carin L. Analysis and processing of ultra wide-band SAR imagery for buried landmine detection[J]. IEEE Transactions on Antennas and Propagation, 1998, 46(11): 1747-1748.(1) [9] 杨威, 陈杰, 李春升. 面向目标特性精细提取的SAR数据融合成像处理方法[J]. 雷达学报, 2015, 4(1): 29-37.Yang Wei, Chen Jie, and Li Chun-sheng. SAR data fusion imaging method oriented to target feature extraction[J]. Journal of Radars, 2015, 4(1): 29-37.(1) [10] Chaney R D, Willsky A S, and Novak L M. Coherent aspect-dependent SAR image formation[C]. Proceedings of SPIE, 1994, 2230: 256-274.(1) [11] Jackson J A, Rigling B D, and Moses R L. Canonical scattering feature models for 3D and bistatic SAR[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(2): 525-541.(1) [12] Martin W and Flandrin P. Wigner-Ville spectral analysis of nonstationary processes[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985, 33(6): 1461-1470.(1) [13] Choi H-I and Williams W J. Improved time-frequency representation of multicomponent signals using exponential kernels[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(6): 862-871.(1) [14] 洪文. 圆迹SAR成像技术研究进展[J]. 雷达学报, 2012, 1(2): 124-135.Hong Wen. Progress in circular SAR imaging technique[J]. Journal of Radars, 2012, 1(2): 124-135.(1)