The generalized linear sampling and factorization methods only depends on the sign of contrast on the boundary. (English) Zbl 1380.65226
Summary: We extend the applicability of the generalized linear sampling method (GLSM) [the author and H. Haddar, Inverse Probl. 30, No. 3, Article ID 035011, 20 p. (2014; Zbl 1291.35377)] and the factorization method (FM) [A. Kirsch and N. Grinberg, The factorization method for inverse problems. Oxford Lecture Series in Mathematics and Its Applications 36 (2008; Zbl 1222.35001)] to the case of inhomogeneities where the contrast changes sign. Both methods give an exact characterization of the target shapes in terms of the farfield operator (at a fixed frequency) using the coercivity property of a special solution operator. We prove this property assuming that the contrast has a fixed sign in a neighborhood of the inhomogeneities boundary. We treat both isotropic and anisotropic scatterers with possibly different supports for the isotropic and anisotropic parts. We finally validate the methods through some numerical tests in two dimensions.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35R30 | Inverse problems for PDEs |
Keywords:
inverse scattering problems; linear sampling method; factorization method; qualitative methodsReferences:
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