Universidad Complutense de Madrid
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Solving inhomogeneous inverse problems by topological derivative methods



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Carpio, Ana y Rapún, M.L. (2008) Solving inhomogeneous inverse problems by topological derivative methods. Inverse problems, 24 (4). ISSN 0266-5611

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URL Oficial: http://iopscience.iop.org/0266-5611/

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We introduce new iterative schemes to reconstruct scatterers buried in a medium and their physical properties. The inverse scattering problem is reformulated as a constrained optimization problem involving transmission boundary value problems in heterogeneous media. Our first step consists in developing a reconstruction scheme assuming that the properties of the objects are known. In a second step, we combine iterations to reconstruct the objects with iterations to recover the material parameters. This hybrid method provides reasonable guesses of the parameter values and the number of scatterers, their location and size. Our schemes to reconstruct objects knowing their nature rely on an extended notion of topological derivative. Explicit expressions for the topological derivatives of the corresponding shape functionals are computed in general exterior domains. Small objects, shapes with cavities and poorly illuminated obstacles are easily recovered. To improve the predictions of the parameters in the successive guesses of the domains we use a gradient method.

Tipo de documento:Artículo
Palabras clave:Level set methods; Transmission problems; Obstacle scattering; Helmotz-equation; Shape optimization; Integral-equations; Tomography; Uniqueness; Reconstruction; Approximation
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:14934
Depositado:20 Abr 2012 11:37
Última Modificación:28 Oct 2016 08:30

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