American Institute of Mathematical Sciences

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February  2009, 3(1): 123-138. doi: 10.3934/ipi.2009.3.123

The factorization method is independent of transmission eigenvalues

Armin Lechleiter 1,

1. 

DEFI, INRIA Scalay Ile de France / Ecole polytechnique (CMAP), Ecole Polytechnique, 91128 Palaiseau Cedex, France

Received  November 2008 Revised  January 2009 Published  February 2009

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.
Keywords: transmission eigenvalues, Factorization method, range identity., electromagnetics, acoustics, inverse medium scattering.
Mathematics Subject Classification: Primary 78A46; Secondary 74J2.
Citation: Armin Lechleiter. The factorization method is independent of transmission eigenvalues. Inverse Problems & Imaging, 2009, 3 (1) : 123-138. doi: 10.3934/ipi.2009.3.123
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