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摘要: 层析合成孔径雷达(TomoSAR)通过组合在不同高度上获取的多基线二维SAR数据，实现合成孔径雷达的三维成像。TomoSAR的求解本质是一维谱估计问题，基于压缩感知的方法可以在非均匀分布的少量基线观测下实现求解，逐渐成为了主流的成像方式。在经典的压缩感知算法流程中，需要将连续的高程向划分成固定的网格，并且假定目标正好位于所划分的网格上。然而该假设通常难以成立，从而引起“基失配”问题，目前该问题在TomoSAR中很少被讨论。该文首先讨论了目标不在网格(Off-grid)上的TomoSAR观测模型，提出了采用加性扰动项来修正目标偏离网格所带来影响的求解模型。在此基础之上，引入局部优化算法与
$ {L}_{1} $ 范数最小化结合的方法，求解所提出的Off-grid TomoSAR模型。最后，利用仿真数据和机载阵列干涉SAR实际飞行数据进行了验证，结果表明，对于Off-grid目标，该方法能够得到比基于$ {L}_{1} $ 范数最小化的经典方法更准确的位置、幅度和相位求解结果，证明了方法的优越性。Abstract: Synthetic Aperture Radar (SAR) Tomography (TomoSAR) is a novel technique that enables three-Dimensional (3-D) imaging using multi-baseline two-Dimensional (2-D) data. The essence of TomoSAR is actually to solve a one-dimensional spectral estimation problem. Compressed Sensing-based (CS) algorithm can retrieve solutions with only a few non-uniform acquisitions and has gradually become the main imaging method. In the conventional processing flow of CS algorithms, the continuous elevation direction is divided into a pre-set grid, and the targets are assumed to be exactly on the grid.$ {{L}}_{1} $ minimization has been proven to be effective in TomoSAR imaging. In the conventional processing flow, the continuous elevation axis is divided into fixed grids, and scatters are assumed to be exactly on the pre-set grid. However, this hypothesis is generally untenable, and will lead to a problem called “Basis Mismatch”, which is rarely discussed in TomoSAR. In this letter, we first discuss the model of Off-grid TomoSAR, and then propose an addictive perturbation model to compensate for the errors caused by the grid effect. We utilize the local optimization thresholding algorithm to solve the complex-valued$ {{L}}_{1} $ minimization problem of TomoSAR. We conducted experiments both on simulation data and actual airborne flight data. Our simulation results indicate that the proposed method can estimate a more accurate position of scatters, which leads to better original signal recovery. The reconstruction results of actual data verify that the impact of grid mismatch can be mostly eliminated. -
图 2 高程向目标重建结果的简单示意图
Figure 2. Sketch map of the reconstruct results in the elevation direction
图 4 散射点位置估计值与真值距离的统计平均值
Figure 4. The average distance between the estimated scattering point position and the true value
图 5 本文方法优于传统方法的概率与SNR的关系
Figure 5. Probability of the proposed algorithm providing better estimation versus SNR
图 6 获得更精确估计的概率与观测数量的关系
Figure 6. Probability of the proposed algorithm providing better estimation versus number of acquisitions
图 8 从谷歌地球获取的实验地区于2015年的光学影像和对应的SAR图像
Figure 8. Optical image of the experiment area obtained from Google Earth in 2015 and SAR image of the corresponding area
图 11 本文方法与传统L1范数最小化的方法对图8中红线标记的方位向切片的成像结果比较
Figure 11. Comparison of our method and the conventional process of
$ {L}_{1} $ minimization in the slant range plane for the azimuth-bin marked in Fig. 8表 1 BPLOT的流程
Table 1. The process of BPLOT
算法 : BPLOT (1) 输入: $\boldsymbol{A},{\boldsymbol{A} }',\boldsymbol{g},\Delta s{\text{，}}\mathrm{稀}\mathrm{疏}\mathrm{度}K$
(2) $ {L}_{1} $范数求解:
$\mathrm{argmin} \left\{ {\left|\left|{ { {\boldsymbol{g} } } }-{{ {\boldsymbol{A} } } }_{\mathit{g} }{\boldsymbol\varGamma }\right|\right|}_{2}^{2}+\mu {\left|\left|{\boldsymbol\varGamma }\right|\right|}_{1}\right\}$
$\boldsymbol{\varGamma }={\left[\boldsymbol{\gamma }\;\;{\boldsymbol{\gamma } }'\right]}^{t},{\boldsymbol{A} }_{\mathit{g} }=\left[\begin{array}{cc}\boldsymbol{A}& {\boldsymbol{A} '} \end{array}\right]$
(3) For count t=1: K,
(4) $ {\alpha }_{t} $=${\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x} }_{p}\{\left|{\mathit{\gamma } }_{p}\right|+\left|{\mathit{\gamma } }_{p}\right|/|2\pi {\Delta }s\left|\right\}$, $ p\notin \left({S}^{t-1}\right) $
(5) $ {S}^{t}={S}^{t-1}\cup \left\{{\alpha }_{t}\right\} $
(6) 计算网格偏差 $\Delta k\Delta s=\mathfrak{R}e({{\boldsymbol{\gamma}} }'/({\rm{j} }2\pi {\boldsymbol{\gamma}} \left)\right)$
(7) 计算散射值
${\hat{\boldsymbol{A} } }_{f}={{\boldsymbol{A}}}(S+\Delta k\Delta s)$
${\hat{\gamma } }_{f}={\left({ {\hat{ \boldsymbol{A} } }_{f} }^{\rm{H} }{\hat{ \boldsymbol{A} } }_{f}\right)}^{-1}{ {\hat{ \boldsymbol{A} } }_{f} }^{\rm{H} }\boldsymbol{g}$
(8) 输出：${\hat{\gamma } }_{f},S,\Delta k$
下载: 导出CSV
表 2 仿真参数
Table 2. Simulation parameters
参数 参数值 载波频率(GHz) 14.5 信号带宽(MHz) 500 通道数N 8 基线宽度(m) 0.084 脉冲重复频率(Hz) 480 平台高度(m) 1200 平台速度(m/s) 70 下视角(°) 45
下载: 导出CSV
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