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A survey on sampling and probe methods for inverse problems

Potthast, R. (2006) A survey on sampling and probe methods for inverse problems. Inverse Problems, 22 (2). R1-R47. ISSN 0266-5611

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Abstract/Summary

The goal of the review is to provide a state-of-the-art survey on sampling and probe methods for the solution of inverse problems. Further, a configuration approach to some of the problems will be presented. We study the concepts and analytical results for several recent sampling and probe methods. We will give an introduction to the basic idea behind each method using a simple model problem and then provide some general formulation in terms of particular configurations to study the range of the arguments which are used to set up the method. This provides a novel way to present the algorithms and the analytic arguments for their investigation in a variety of different settings. In detail we investigate the probe method (Ikehata), linear sampling method (Colton-Kirsch) and the factorization method (Kirsch), singular sources Method (Potthast), no response test (Luke-Potthast), range test (Kusiak, Potthast and Sylvester) and the enclosure method (Ikehata) for the solution of inverse acoustic and electromagnetic scattering problems. The main ideas, approaches and convergence results of the methods are presented. For each method, we provide a historical survey about applications to different situations.

Item Type:Article
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:4890
Uncontrolled Keywords:FAR-FIELD OPERATOR ELECTROMAGNETIC SCATTERING PROBLEM SINGULAR SOURCES METHOD BOUNDARY-VALUE-PROBLEMS POINT-SOURCE METHOD NO-RESPONSE TEST OBSTACLE SCATTERING ENCLOSURE METHOD FACTORIZATION METHOD ACOUSTIC SCATTERING

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