This article introduces and evaluates numerically a multigrid solver for non-linear tomographic radar imaging. Our goal is to enable the fast and robust inversion of sparse time-domain data with a mathematical full-wave approach utilizing a higher-order Born approximation (BA). Full-wave inversion is computationally expensive, hence techniques to speed up the numerical procedures are needed. To model the wave propagation effectively, we use the finite element time-domain (FETD) method, which is equipped with a multigrid scheme to enable the rapid evaluation of the higher-order BA. As a potential application, we consider the tomography of small solar system bodies (SSSBs) and asteroid interiors particular, the latter of which can contain internal details observable by radar, e.g., layers, voids and cracks. In the numerical experiments, we investigated monostatic, bistatic and multistatic measurement configurations. The results obtained suggest that, with a relevant noise level, the tomographic reconstruction quality can be improved by applying the higher-order BA in comparison to the first-order case, which we interpret as a linearization of the inverse problem. Our open multigrid-FETD solver for Matlab (The Mathworks Inc.) is available online. It applies Matlabs features for graphics computing unit acceleration to enhance computational performance.

中文翻译：

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用于复杂形状目标全波雷达断层扫描的具有高阶Born近似的时域多重网格求解器

本文介绍并数值评估了非线性层析成像雷达成像的多重网格求解器。我们的目标是通过使用高阶 Born 近似 (BA) 的数学全波方法实现稀疏时域数据的快速和稳健反演。全波反演在计算上是昂贵的，因此需要加速数值程序的技术。为了有效地模拟波的传播，我们使用有限元时域 (FETD) 方法，该方法配备了多重网格方案，可以快速评估高阶 BA。作为一个潜在的应用，我们考虑了小型太阳系天体 (SSSB) 和小行星内部的层析成像，后者可以包含雷达可观察到的内部细节，例如层、空隙和裂缝。在数值实验中，我们研究了单基地、双基地和多基地测量配置。获得的结果表明，在相关噪声水平下，与一阶情况相比，可以通过应用高阶 BA 来提高断层扫描重建质量，我们将其解释为逆问题的线性化。我们用于 Matlab (The Mathworks Inc.) 的开放式多重网格 FETD 求解器可在线获取。它将 Matlabs 功能应用于图形计算单元加速，以提高计算性能。我们用于 Matlab (The Mathworks Inc.) 的开放式多重网格 FETD 求解器可在线获取。它将 Matlabs 功能应用于图形计算单元加速，以提高计算性能。我们用于 Matlab (The Mathworks Inc.) 的开放式多重网格 FETD 求解器可在线获取。它将 Matlabs 功能应用于图形计算单元加速，以提高计算性能。