Recovery of singularities for formally determined inverse problems
Recovery of singularities for formally determined inverse problems
复制标题
形式确定的反问题的奇点恢复
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
G. Uhlmann
中科院分区：
文献类型：
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作者：
Ziqi Sun;G. Uhlmann
在本文中，我们考虑了几个正式确定的问题，在两个层面。这些问题没有全局可识别性结果。然而，我们可以恢复这些函数的一个重要特征，即它们的奇异性。更精确地说，我们证明了在一定能量下，只要知道相应的散射振幅，就可以确定L ∞紧支势的奇点位置和强度.我们还证明了，一个可以确定的位置和强度的奇异性的声速的介质的边界上进行测量。
In this paper we considered several formally determined problems in two dimensions. There are no global identifiability results for these problems. However, we can recover an important feature of these functions, namely their singularities. More precisely, we prove that one can determine the location and strength of singularities of anL∞ compactly supported potential by knowing the associated scattering amplitude at a fixed energy. Also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium.