RT Journal Article
T1 Solving inhomogeneous inverse problems by topological derivative methods
A1 Carpio Rodríguez, Ana María
A1 Rapún Banzo, María Luisa
AB 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.
PB IOP Publishing
SN 0266-5611
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/49855
UL https://hdl.handle.net/20.500.14352/49855
LA eng
NO Carpio Rodríguez, A. M., Rapún Banzo, M. L. «Solving inhomogeneous inverse problems by topological derivative methods». Inverse Problems, vol. 24, n.o 4, agosto de 2008, p. 045014. DOI.org (Crossref), https://doi.org/10.1088/0266-5611/24/4/045014.
NO Ministerio de Educación, Formación Profesional y Deportes (España)
NO Universidad Complutense de Madrid/Banco de Santander
DS Docta Complutense
RD 10 abr 2025