Topological optimality condition for the identification of the center of an inhomogeneity

Topological optimality condition for the identification of the center of an inhomogeneity Full article

Journal

Inverse Problems
ISSN: 0266-5611

Output data

Year: 2018, Volume: 34, Number: 3, Article number : 035009, Pages count : DOI: 10.1088/1361-6420/aaa997

Tags

asymptotic analysis; inverse problem for inhomogeneous media; topological derivative; topology optimization; zero-order optimality condition

Authors

Cakoni Fioralba ¹ , Kovtunenko Victor A ^2,3

Affiliations

1	Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, United States of America
2	Department of Mathematics, University of Graz, NAWI Graz
3	Siberian Division of the Russian Academy of Sciences, Lavrent’ev Institute of Hydrodynamics

The inverse scattering problem for inhomogeneous media is considered within the topology optimization framework. Varying the complex-valued refractive index we derive a zero-order necessary optimality condition in minimizing the L 2 misfit cost functional of the far-field measurement. The topology asymptotic expansion of the optimality condition leads to an imaging operator, which is used to identify the center of the unknown inhomogeneity using few far-field measurements. Numerical tests show high precision and stability in the reconstruction using our optimality condition based imaging both in two and three dimensions.

Cakoni F. , Kovtunenko V.A.
Topological optimality condition for the identification of the center of an inhomogeneity
Inverse Problems. 2018. V.34. N3. 035009 . DOI: 10.1088/1361-6420/aaa997 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000424903900002
Scopus:	2-s2.0-85042161442
Elibrary:	35515534
OpenAlex:	W2789839610

DB	Citing
Scopus	22
OpenAlex	22
Web of science	20