Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air-soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user-defined parameter, $\delta$, which scales the resolution by $\sqrt{\delta}$ allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrate the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.

翻译：受基于无人机的探地雷达在埋地雷探测中的应用启发，我们研究在随机粗糙表面下损耗介质中对微小点状散射体进行成像的问题。随机粗糙表面和损耗介质中的吸收均显著阻碍目标检测与成像过程。利用主成分分析，我们有效消除了空气-土壤界面的反射。随后，采用经典合成孔径雷达成像函数的改进形式对目标进行成像。该成像方法引入用户自定义参数$\delta$，可将分辨率缩放$\sqrt{\delta}$倍，从而实现亚波长精度的目标定位。二维数值结果展示了该方法对多目标成像的鲁棒性。然而，由于损耗介质中的吸收作用，目标可探测深度受到限制。