This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We show that a smallest strip containing the unknown object can be approximately determined by the multi-frequency backscattering far field data at two opposite observation directions. The proof is based on the Kirchhoff approximation and Fourier transform. Such a strip is then reconstructed by an indicator, which is the absolute value of an integral of the product of the data and some properly chosen function over the frequency interval. With the increase of the number of the backscattering data, the location and shape of the underlying object can be reconstructed. Numerical examples are conducted to show the validity and robustness of the proposed sampling method. The numerical examples also show that the concave part of the underlying object can be well reconstructed, and the different connected components of the underlying object can be well separated.

中文翻译：

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具有多频稀疏反向散射远场数据的逆电磁障碍物散射问题

本文致力于设计一种逆电磁散射问题的直接采样方法，该方法利用多频稀疏反向散射远场数据重建完美传导障碍物的边界。我们表明，可以通过两个相反观察方向的多频反向散射远场数据来近似确定包含未知物体的最小条带。证明基于基尔霍夫近似和傅立叶变换。然后由指示符重建这样的条带，该指示符是数据的积分的绝对值，并且在频率间隔上的一些正确选择的功能。随着后向散射数据数量的增加，可以重建出底层物体的位置和形状。数值例子表明了所提出的抽样方法的有效性和鲁棒性。数值算例还表明，可以很好地重构下层物体的凹面部分，能够很好地分离下层物体的不同连通分量。