A Numerical Study of the Probe Method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source $\Phi(\cdot,z)$ with source point z to define an indicator function $\hat{I}(...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2006-01, Vol.28 (5), p.1597-1612
Main Authors: Erhard, Klaus, Potthast, Roland
Format: Article
Language:English
Subjects:
Acoustics
Algorithms
Applied mathematics
Boundary value problems
Integral equations
Methods
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Summary:The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source $\Phi(\cdot,z)$ with source point z to define an indicator function $\hat{I}(z)$ which can be reconstructed from Cauchy data or far field data. The indicator function $\hat{I}(z)$ can be shown to blow off when the source point z tends to the boundary $\partial D$, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.
ISSN:1064-8275
1095-7197
DOI:10.1137/040607149