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摘要: 该文提出了一种基于稀疏和低秩结构的层析SAR三维成像方法。传统基于压缩感知的层析SAR成像方法仅仅对给定方位-距离单元的高程向进行稀疏表征和重建。考虑城市和森林等区域中各自的布局分布较为类似，目标在相邻方位-距离单元的高程向分布具有较强相关性。该方法通过引入Karhunen Loeve变换来表征相邻方位-距离单元的高程向的低秩结构特性，构建稀疏和低秩结构相结合的目标区域层析SAR成像模型，采用ADMM算法对层析SAR成像模型进行求解，将复杂的原优化问题分解为若干相对简单的子问题，通过优化变量交替投影的方式进行算法求解，得到层析SAR成像结果。该方法提高了低航过数或低通道数情况下的重建精度，拥有更好的成像性能。仿真和实测数据实验表明，该重建方法能够有效分离散射体并保证重建能量的精度，且在降低航过数或通道数的情况下保持良好的成像效果，有效抑制伪影现象。
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关键词:
- 三维成像 /
- 层析SAR成像 /
- 稀疏特性 /
- 低秩结构 /
- Karhunen Loeve变换
Abstract: This paper proposes a three-dimensional tomographic SAR imaging method based on a combined sparse and low-rank structures. The traditional Compressed Sensing (CS) based tomographic SAR imaging methods only utilize the sparse representation and reconstruct along the elevation axis of a given azimuth-distance unit. Considering that the target distributions in cities, forests, and other cases are relatively similar, the elevation backscattering patterns of adjacent azimuth-range cells (pixels) are expected to be highly correlated. The proposed method introduces the Karhunen-Loeve transform to characterize the low-rank structures of the elevation of the target areas and constructs a tomographic SAR imaging model that combines sparse and low-rank structures. The ADMM algorithm is applied to solve the tomographic SAR imaging model, the complex original optimization problem is decomposed into several relatively simple sub-problems, and the tomographic SAR imaging results are obtained by the alternate projection of optimization variables. This method improves the reconstruction accuracy in the case of a few interferograms or channels and has better imaging performance. Simulations and real data experiments show that the reconstruction method can effectively separate the scatterers and ensure the accuracy of the reconstruction energy, maintain a good imaging performance under the condition of reducing the number of interferograms or channels, and effectively suppress the artifacts.-
Key words:
- Three-Dimensional (3-D) imaging /
- SAR tomography /
- Sparse /
- Low-rank /
- Karhunen Loeve transform
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图 5 航过数为9时各算法获得的高程向后向散射能量分布与仿真结果的对比
Figure 5. Comparison of the simulation result of backscattered energy distribution of the elevation obtained by each algorithm with 9 interferograms
图 6 航过数为6时各算法获得的高程向后向散射能量分布与仿真结果的对比
Figure 6. Comparison of the simulation result of backscattered energy distribution of the elevation obtained by each algorithm with 6 interferograms
图 7 航过数为9时不同信噪比情况下各算法的均方误差
Figure 7. Mean square error of each algorithm at different SNR values with 9 interferograms
图 8 航过数为6时不同信噪比情况下各算法的均方误差
Figure 8. Mean square error of each algorithm at different SNR values with 6 interferograms
图 9 航过数为9时各算法获得的森林区域重建结果
Figure 9. Reconstruction results of the forest area by each algorithm with 9 interferograms
图 10 航过数为6时各算法获得的森林区域重建结果
Figure 10. Reconstruction results of the forest area by each algorithm with 6 interferograms
图 11 通道数为12时各算法的峨眉区域重建结果
Figure 11. Reconstruction results of Emei area by each algorithm with 12 channels
图 12 通道数为8时各算法的峨眉区域重建结果
Figure 12. Reconstruction results of Emei area by each algorithm with 8 channels
图 13 各方法成像结果的距离向切片对比
Figure 13. Comparison of range slices of imaging results of each method
表 1 Ku波段雷达系统参数
Table 1. Ku-band radar system parameters
参数 数值 载波频率(GHz)
通道数N
成像场景海拔(m)
图像最近斜距(m)
航线海拔(m)
距离向像素尺寸(m)
方位向像素尺寸(m)
基线长度(m)14.5
12420
1861
2157
0.1362
0.1051
2
下载: 导出CSV
表 2 各方法耗时对比
Table 2. Time comparison of each method
方法 耗时(s) CAPON 61.844378 CS 43386.651744 本文方法 72769.757387
下载: 导出CSV
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