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摘要: 低过采样Staggered SAR利用变脉冲重复间隔技术有效分散盲区，可实现连续观测的高分宽幅成像，同时采用低过采样率可降低系统对数据存储的要求，因此具有重要的研究价值。然而，低过采样Staggered SAR存在的非均匀采样、回波丢失和非理想方位天线方向图(AAP)问题会导致成像结果中出现严重的方位模糊。该文提出了一种基于压缩感知的成像方法，可解决已有方法模糊抑制性能差和效率低的问题。首先，建立了准确描述低过采样Staggered SAR非均匀采样、回波丢失和距离徙动的创新性频域模型(IFDM)，利用二维快速迭代收缩阈值算法对基于该IFDM构造的优化问题进行迭代求解可抑制非均匀采样和回波丢失造成的方位模糊；然后，利用选择滤波方法处理迭代结果可抑制非理想AAP造成的方位模糊。实验结果表明该文方法在成像性能和效率上均优于已有方法。Abstract: Low-oversampled staggered synthetic aperture radar can achieve continuously observed high-resolution and wide-swath imaging by utilizing the variable pulse repetition interval to distribute blind ranges. Moreover, adopting a low oversampling ratio can reduce the data storage requirements, contributing to its research significance. However, non-uniform sampling, echo data loss, and non-ideal Azimuth Antenna Pattern (AAP) cause severe azimuth ambiguities in a directly focused image. This study proposes a compressive sensing-based method with better ambiguity removal performance and higher efficiency compared to existing methods. First, an Innovative Frequency-Domain Model (IFDM) is constructed, which accurately describes the non-uniform sampling, echo data loss, and coupled range cell migration. Based on the IFDM, an optimization problem is constructed and solved by the two-dimensional fast iterative shrinkage thresholding algorithm to remove the ambiguity caused by non-uniform sampling and echo data loss. Subsequently, selective filtering is used to suppress the ambiguity caused by the AAP. The experiments demonstrate that the proposed method can more effectively and efficiently suppress the azimuth ambiguities compared to existing methods.
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图 1 Staggered SAR 天线方向图混叠示意图
Figure 1. Map of azimuth antenna pattern aliasing for Staggered SAR
图 2 点目标成像结果方位剖面图
Figure 2. Azimuth profiles of reconstructed results for a point target
图 3 覆盖范围为20 km×20.5 km场景的模拟回波数据处理结果
Figure 3. Imaging result of the simulated data of the 20 km×20.5 km scene
图 4 20 km×20.5 km场景中“区域1”成像结果放大图及剖面图对比
Figure 4. Larger image of imaging result of “Zone 1” in the 20 km×20.5 km scene and comparison of azimuth profiles
图 5 20 km×20.5 km场景中“区域2”成像结果放大图
Figure 5. Larger image of reconstructed result of “Zone 2” in the 20 km×20.5 km scene
表 1 IFDM-FISTA-SF流程
Table 1. The process of IFDM-FISTA-S
输入：距离压缩后的Staggered SAR回波数据${\boldsymbol{S}}$，稀疏算子$\Psi $ 输出：方位模糊被抑制的高质量成像结果${{\boldsymbol{X}}_{ {\text{final} } } }$ 初始化：${\lambda _1},\bar \lambda > 0$, $\beta \in \left( {0,1} \right)$, ${\sigma _0} = {\sigma _1} = 1$, $L > 0$, $l = 0$,
${{\boldsymbol{\varGamma}} ^{(0)} } = {{\boldsymbol{\varGamma}} ^{(1)} } = {\boldsymbol{0} }$IFDM-FISTA：当满足$l \le L$时，进行以下迭代
步骤1 ${{\boldsymbol{Z}} ^{(l)} } = {{\boldsymbol{\varGamma}} ^{(l)} } + \left( { {\sigma _{l - 1} } - 1} \right)/{\sigma _l} \cdot \left( { {{\boldsymbol{\varGamma}} ^{(l)} } - {{\boldsymbol{\varGamma}} ^{(l - 1)} } } \right)$步骤2 ${\hat {\boldsymbol{X}}^{(l)} } = {\Psi ^{ - 1} }\left( { {{\boldsymbol{\varGamma}} ^{(l)} } } \right)$ 步骤3 ${\boldsymbol{E} } = {\boldsymbol{B} } \odot \left\{ { {\tilde {\boldsymbol F} }_{\text{t} }^{\text{H} }\left[ {\left( {({ {\boldsymbol{F} }_{\text{a} } }{\boldsymbol{X} }) \circ { { { {\tilde {\boldsymbol F} } } }_{\text{r} } } } \right) \odot {\boldsymbol{D} } } \right]{\boldsymbol{F} }_{{\tau } }^{\text{H} } } \right\} - {\boldsymbol{S} }$ 步骤4 $\nabla g\left( {\boldsymbol{\varGamma} } \right) = \Psi \left\{ { {\boldsymbol{F} }_{\text{a} }^{\text{H} }\left[ {\left( {\left( { { {\tilde {\boldsymbol{F}}}_{\text{t} } }{\boldsymbol{E}}{{\boldsymbol{F}}_{ {\tau } } } } \right) \odot {{\boldsymbol{D}}^*} } \right) \circ \tilde {\boldsymbol{F}}_{\text{r} }^{\text{H} } } \right]} \right\}$ 步骤5 ${ {\boldsymbol{U} }^{(l)} } = { {\boldsymbol{Z} }^{(l)} } - 1/{\ell _{\rm{f} } } \cdot \nabla g\left({ {\boldsymbol{\varGamma} } ^{(l)} }\right)$ 步骤6 ${ {\boldsymbol{\varGamma} } ^{(l + 1)} } = { {\rm{soft} } } \left( { { {\boldsymbol{U} }^{(l)} },{\lambda _l}/{\ell _{\rm{f}}} } \right)$ 步骤7 ${\sigma _{l + 1} } = \left(1 + \sqrt {4\sigma _l^2 + 1} \right)/2$ 步骤8 ${\lambda _{l + 1}} = \max \left( {\beta {\lambda _l},\bar \lambda } \right)$ 步骤9 $l = l + 1$ SF：${{\boldsymbol{X}}_{ {\text{final} } } }{\text{ = SF} }\left( {\tilde {\boldsymbol{X}}} \right) = {\text{SF} }\left( { { {\hat {\boldsymbol{X}}}^{(L)} } } \right)$ 
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表 2 低过采样Staggered SAR仿真参数
Table 2. Simulation parameters for low-oversampled Staggered SAR
参数 数值 参数 数值 轨道高度(km) 760 最大PRI (s) 1/1500 平台速度(m/s) 7473 最小PRI (s) 1/1800 参考斜距史(km) 981.8 发射过采样率 1.1 发射信号带宽(MHz) 20 有效接收采样率 0.9 多普勒带宽(Hz) 1495 中心频率(GHz) 10
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表 3 不同方法对点目标模糊抑制性能的评估结果
Table 3. Evaluation results of the azimuth-ambiguity-removal performance for different methods
Method ATR (dB) ISLR (dB) $\omega {\text{K}}$ –18.04 –7.20 MIAA-MCR –18.65 –11.34 IFDM-FISTA –20.17 –12.58 IFDM-FISTA-SF –33.56 –14.18
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表 4 各方法计算复杂度以及处理图3对应宽幅场景耗时
Table 4. Different methods’ computation complexity and time for the scene given by Fig. 3
Method 计算复杂度 耗时 (min) $ \omega {\text{K}} $ $ O\left( {MN{\text{lo}}{{\text{g}}_2}\left( {MN} \right)} \right) $ 1 MIAA-MCR $O\left( {LMNM_{\text{d}}^2} \right)$ 273 IFDM-FISTA by NUDFT $ O\left( {LMN\left( {M + N} \right)} \right) $ 1676 IFDM-FISTA/IFDM-FISTA-SF $ O\left( {LMN{\text{lo}}{{\text{g}}_2}\left( {MN} \right)} \right) $ 47
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