Authors: Dorn, Oliver; Lesselier, Dominique

Source: Inverse Problems, Volume 22, Number 4, August 2006 , pp. R67-R131(65)

Publisher: IOP Publishing

Abstract:

We give an overview of recent techniques which use a level set representation of shapes for solving inverse scattering problems. The main focus is on electromagnetic scattering using different popular models, such as for example Maxwell's equations, TM-polarized and TE-polarized waves, impedance tomography, a transport equation or its diffusion approximation. These models are also representative of a broader class of inverse problems. Starting out from the original binary approach of Santosa for solving the corresponding shape reconstruction problem, we successively develop more recent generalizations, such as for example using colour or vector level sets. Shape sensitivity analysis and topological derivatives are discussed as well in this framework. Moreover, various techniques for incorporating regularization into the shape inverse problem using level sets are demonstrated, which also include the choice of subclasses of simple shapes, such as ellipsoids, for the inversion. Finally, we present various numerical examples in two dimensions and in three dimensions for demonstrating the performance of level set techniques in realistic applications.

Document Type: Research article

DOI: http://dx.doi.org/10.1088/0266-5611/22/4/R01

Publication date: 2006-08-01

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• In this Subject: General & Civil Engineering ,  Mathematics and Statistics
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