用几次后向散射测量恢复多面体障碍物
Recovering a polyhedral obstacle by a few backscattering measurements
摘要：
本文提出了一种仅通过少量的高频声后向散射测量来恢复$\mathbb{R}^n$中多面体障碍物的逆散射方案，即$n=2,3$。障碍物可以是听起来软的或听起来硬的。结果表明，后向散射孔径中的远场模具有一定的局部极大值，由此可以确定前表面的外法线方向。然后，通过使用对应于具有适当选择的入射方向的几个入射平面波的无相位后向散射数据，可以确定障碍物的每个侧面/面的外部单元法向量。在确定外部单元法线之后，恢复被简化为确定障碍物的位置点和每个侧面/面远离位置点的距离的有限维问题。对于后一种重建，需要利用远场相位数据。数值实验也说明了所提出的方法的有效性。
英文摘要：
We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
