zbMATH — the first resource for mathematics

The factorization method is independent of transmission eigenvalues. (English) Zbl 1184.78020
Summary: As a rule of thumb, sampling methods for inverse scattering problems suffer from interior eigenvalues of the obstacle. Indeed, throughout the history of such algorithms one meets the phenomenon that if the wave number meets some resonance frequency of the scatterer, then those methods can only be shown to work under suitable modifications. Such modifications often require a-priori knowledge, corrupting thereby the main advantage of sampling methods. It was common belief that transmission eigenvalues play a role corresponding to Dirichlet or Neumann eigenvalues in this respect. We show that this is not the case for the Factorization method: when applied to inverse medium scattering problems this method is stable at transmission eigenvalues.

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
74J25 Inverse problems for waves in solid mechanics
76Q05 Hydro- and aero-acoustics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78M25 Numerical methods in optics (MSC2010)
Full Text: DOI