Identifying convex obstacles from backscattering far field data
Jialei Li, Xiaodong Liu, Qingxiang Shi
从反向散射远场数据中恢复异常是逆散射理论中长期存在的开放问题。 我们朝着这个方向迈出了第一步,通过从反散远场测量中确定凸不平的障碍的独特可识别性。 具体来说,我们证明凸障碍物的边界和边界条件都是由所有频率的背散方向测量的远场模式唯一确定的。 关键工具是Majda对高频机制中远场模式的渐近估计。 此外,我们引入了一个快速稳定的数值算法,用于重建边界和计算边界条件。 该算法的一个关键特征是,即使边界不为已知,也可以计算边界条件,反之亦然。 数字实验证明了拟议算法的有效性和稳健性。
The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles from backscattering far field measurements. Specifically, we prove that both the boundary and the boundary conditions of the convex obstacle are uniquely determined by the far field pattern measured in backscattering directions for all frequencies. The key tool ...