This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data.

翻译：本文研究从散射场测量中确定可穿透散射对象位置与形状的反介质问题。我们提出一种采样指示函数，用于快速鲁棒地重构散射目标。该指示函数的灵活性在于其可适用于近场或远场测量数据，且实现简便，无需求解任何不适定问题。通过结合远场算子的因子化分析与Funk-Hecke公式，研究了该指示函数的分辨率分析与稳定性估计。数值模拟与实验数据均验证了该方法的有效性。