The Operator Factorization Method in Inverse Obstacle Scattering
The Operator Factorization Method in Inverse Obstacle Scattering
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DOI：
10.1007/s00020-004-1355-z
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发表时间：
2006-03
影响因子：
0.8
通讯作者：
N. Grinberg
中科院分区：
文献类型：
--
作者：
N. Grinberg
The standard factorization method from inverse scattering theory allows to reconstruct an obstacle pointwise from the normal far field operatorF. The kernel of this method is the study of the first kind Fredholm integral equation (F*F)1/4f= Φzwith the right-hand partIn this paper we extend the factorization method to cover some kinds of boundary conditions which leads to non-normal far field operators. We visualize the scatterer explicitly in terms of the singular system of the selfadjoint positive operatorF#= [(ReF)*(ReF)]1/2+ ImF. The following characterization criterium holds: a given pointzis inside the obstacle if and only if the function Φzbelongs to the range ofF#1/2. Our operator approach provides the tool for treatment of a wide class of inverse elliptic problems.
