Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
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DOI：
10.1137/20m1319309
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Rakesh;M. Salo
中科院分区：
文献类型：
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作者：
Rakesh;M. Salo
我们考虑了固定角度逆散射问题，并证明了紧支撑势在两个相对固定角度下的散射振幅是唯一决定的。我们还证明了几乎对称或水平控制的电位是由它们的固定角度散射数据唯一决定的。这是通过建立问题的频域和时域公式之间的等价性来实现的，并通过扩展[RS19]的方法来解决时域问题，该方法采用了[BK81]和[IY01]中介绍的关于使用Carleman估计求解逆问题的思想。
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [RS19] which adapts the ideas introduced in [BK81] and [IY01] on the use of Carleman estimates for inverse problems.