Ultra-wideband SAR Tomography on asteroids : FDBP and Compressive Sensing datasets

Our knowledge of the internal structure of asteroids is currently indirect and relies on inferences from remote sensing observations of surfaces. However, it is fundamental for understanding small bodies’ history and for planetary defense missions. Radar observation of asteroids is the most mature technique available to characterize their inner structure, and Synthetic Aperture Radar Tomography (TomoSAR) allows 3D imaging by extending the synthetic aperture principle in the elevation direction. However, as the geometry of observation of small asteroids is complex, and TomoSAR studies have always been performed in the Earth observation geometry, TomoSAR results in a small body geometry must be simulated to assess the methods’ performances. Different tomography algorithms can be adopted, depending on the characteristics of the problem. While the Frequency Domain Back Projection (FDBP) is based on the correction of the Fourier transform of the received signal by an <em>ad-hoc</em> function built from the geometry of study, it can only retrieve the true position of the scatterers when applied along with ray-tracing methods, which are unreliable in the case of rough asteroid surfaces. Meanwhile, the Compressive Sensing (CS) is based on the compressive sampling theory, which relies on the hypothesis that few scatterers lie in the same direction from the subsurface. The CS can be used to retrieve the position of the scatterers, but its application in the small body geometry is questioned. Thus, both performances of the FDBP and the CS in a small body geometry are demonstrated, and the quality of the reconstruction is analyzed.当前人类对小行星内部结构的认知均为间接所得，仅能通过小行星表面的遥感观测结果进行推演。而对小行星内部结构的认知，对于理解小天体演化历史、支撑行星防御任务均具有关键意义。雷达观测是当前可用于表征小行星内部结构的最成熟技术手段，而合成孔径雷达层析成像（Synthetic Aperture Radar Tomography，TomoSAR）通过将合成孔径原理拓展至高程方向，可实现小行星的三维成像。但由于小型小行星的观测几何较为复杂，且现有层析成像研究均基于地球观测几何开展，因此需要针对小天体观测几何下的TomoSAR进行仿真，以评估相关方法的实际性能。针对该问题的不同特性，可采用多种层析成像算法。其中频域反投影算法（Frequency Domain Back Projection，FDBP）通过基于研究场景几何构建定制函数，对接收信号的傅里叶变换进行校正，但该方法仅在配合射线追踪方法使用时，才能准确反演散射体的真实位置，而在小行星表面粗糙的场景下，射线追踪方法本身可靠性不足。与此同时，压缩感知（Compressive Sensing，CS）基于压缩采样理论，其核心假设为次表层中同一方向上的散射体数量较少。该方法可用于反演散射体的位置，但在小天体观测几何下的应用效果尚存争议。因此本文通过仿真验证了频域反投影算法与压缩感知在小天体观测几何下的成像性能，并对两种方法的重建质量展开了分析。