An inverse scattering problem (ISP) for synthetic aperture radar (SAR) data in application to through-the-wall imaging is addressed. In contrast with the conventional algorithms of SAR imaging, which work with the linearized mathematical model based on the Born approximation, the fully nonlinear case is considered here. To avoid the local minima problem, the so-called “convexification” globally convergent inversion scheme is applied to approximate the distribution in the slant range (SR) plane of a function that is associated with the dielectric constant. It is demonstrated that this function estimates quite well both the value of the dielectric constant and the location of the target. The benchmark scene of this article comprises a homogeneous dielectric wall and different dielectric targets hidden behind it. The results comprise 2-D images of the SR dielectric constant of the scene of interest. Numerical results are obtained by the proposed inversion method for both the computationally simulated and experimental data. Our results show that the values, cross-range sizes, and locations of SR dielectric constants for targets hidden behind the wall are close to those of real targets. Numerical comparison with the solution of the linearized ISP provided by the Born approximation, commonly used in conventional SAR imaging, shows a significantly better accuracy of our results.

中文翻译：

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穿墙非线性 SAR 成像

解决了应用于穿墙成像的合成孔径雷达 (SAR) 数据的逆散射问题 (ISP)。与使用基于 Born 近似的线性化数学模型的 SAR 成像的传统算法相比，这里考虑的是完全非线性的情况。为了避免局部最小值问题，应用所谓的“凸化”全局收敛反演方案来近似与介电常数相关的函数在斜距 (SR) 平面中的分布。证明该函数可以很好地估计介电常数的值和目标的位置。本文的基准场景包括一个均质电介质墙和隐藏在其后面的不同电介质目标。结果包括感兴趣场景的 SR 介电常数的二维图像。对于计算模拟和实验数据，通过所提出的反演方法获得了数值结果。我们的结果表明，隐藏在墙后的目标的 SR 介电常数的值、跨距大小和位置接近真实目标的值。与常规 SAR 成像中常用的 Born 近似提供的线性化 ISP 解的数值比较表明，我们的结果具有明显更好的准确性。隐藏在墙后的目标的 SR 介电常数位置接近真实目标。与常规 SAR 成像中常用的 Born 近似提供的线性化 ISP 解的数值比较表明，我们的结果具有明显更好的准确性。隐藏在墙后的目标的 SR 介电常数位置接近真实目标。与常规 SAR 成像中常用的 Born 近似提供的线性化 ISP 解的数值比较表明，我们的结果具有明显更好的准确性。