Remote sensing radar techniques provide highly detailed imaging. Nevertheless, radar images do not offer directly retrievable representations of shape within the scene. Therefore, shape reconstruction from radar typically relies on applying post-processing computer vision techniques, originally designed for optical images, to radar imaging products. Shape reconstruction directly from raw data would be desirable in many applications, e.g. in computer vision and robotics. In this perspective, inversion seems an attractive approach. Nevertheless, inversion has seldom been attempted in the radar context, as high frequency signals lead to energy functionals dominated by tightly packed narrow local minima. In this paper, we take the first step in developing a framework in which radar signals and images can be jointly used for shape reconstruction. In particular, we investigate the feasibility of shape reconstruction by inversion of pulse-compressed radar signals alone, collected at sparse locations. Motivated by geometric methods that have matured within the fields of image processing and computer vision, we pose the problem in a variational context obtaining a partial differential equation for the evolution of an initial shape towards the shape-reflectivity combination that best reproduces the data. While doing so, we highlight several non-obvious difficulties encountered and discuss how to surpass them. We illustrate the potential of this approach through three simulated examples and discuss several implementation choices, including boundary conditions, reflectivity estimation, and radiative models. The success of our simulations shows that this variational approach can naturally accommodate radar inversion and has the potential for further expansion towards active surfaces and level set applications, where we believe it will naturally complement current applications with optical images.

遥感雷达技术可提供高度详细的成像。但是，雷达图像无法提供场景中形状的直接可检索表示。因此，雷达的形状重建通常依赖于将最初设计用于光学图像的后处理计算机视觉技术应用于雷达成像产品。直接从原始数据进行形状重构在许多应用中（例如在计算机视觉和机器人技术中）将是理想的。从这个角度来看，反演似乎是一种有吸引力的方法。尽管如此，很少在雷达环境中尝试进行反演，因为高频信号导致能量功能主要由紧密堆积的狭窄局部极小值主导。在本文中，我们迈出了开发框架的第一步，在该框架中雷达信号和图像可以联合用于形状重构。特别是，我们研究了通过在稀疏位置收集的单独脉冲压缩雷达信号反演来进行形状重构的可行性。在图像处理和计算机视觉领域内成熟的几何方法的推动下，我们在变分环境中提出了该问题，该问题获得了偏微分方程，该方程使初始形状向形状-反射率组合演化，从而最好地再现了数据。在此过程中，我们重点介绍了遇到的一些非显而易见的困难，并讨论了如何克服这些困难。我们将通过三个模拟示例来说明这种方法的潜力，并讨论几种实现选择，包括边界条件，反射率估计和辐射模型。