2026-06-08T04:21:26Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/498552024-07-10T13:00:45Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Carpio Rodríguez, Ana María
author
Rapún Banzo, María Luisa
2023-06-20T09:32:33Z
2023-06-20T09:32:33Z
2008
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.
0266-5611
10.1088/0266-5611/24/4/045014
https://hdl.handle.net/20.500.14352/49855
https//doi.org/10.1088/0266-5611/24/4/045014
http://iopscience.iop.org/0266-5611/
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.
eng
Solving inhomogeneous inverse problems by topological derivative methods
journal article
URL
https://docta.ucm.es/bitstreams/94a5b477-ca4d-49af-856a-a24b39075e9d/download
File
MD5
568662be4c15329bd912d52be3001994
3117410
application/pdf
15.pdf