Publication Cover
Applicable Analysis
An International Journal
Volume 76, 2000 - Issue 3-4
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Original Articles

New characterizations of solutions in inverse scattering theory

Pages 319-350 | Received 01 May 2000, Published online: 10 May 2007
 

Abstract

This paper introduces a new approach to characterize the shape ω of a scattering medium (either an acoustically soft obstacle or an inhomogeneous medium) by the far field data. In contrast to the Linear Sampling Method normality of the far field operator is not needed. Therefore, also scattering by limited far field data and absorbing media can be treated. While in the Linear Sampling Method the points in the interior of ω are characterized by the solution of an integral equation of the first kind, for our new method a constrained optimization problem has to be solved. Although this new approach is more time consuming some numerical experiments at the end of this paper show the practicability of the method.

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