New interior transmission problem applied to a single Floquet-Bloch mode imaging of local perturbations in periodic media

Fioralba Cakoni, Houssem Haddar, Thi Phong Nguyen

Research output: Contribution to journalArticle

Abstract

This paper considers the imaging of local perturbations of an infinite penetrable periodic layer. A cell of this periodic layer consists of several bounded inhomogeneities situated in a known homogeneous media. We use a differential linear sampling method to reconstruct the support of perturbations without using the Green's function of the periodic layer nor reconstruct the periodic background inhomogeneities. The justification of this imaging method relies on the well-posedeness of a nonstandard interior transmission problem, which until now was an open problem except for the special case when the local perturbation did not intersect the background inhomogeneities. The analysis of this new interior transmission problem is the main focus of this paper. We then complete the justification of our inversion method and present some numerical examples that confirm the theoretical behavior of the differential indicator function determining the reconstructable regions in the periodic layer.

Original languageEnglish (US)
Article number015009
JournalInverse Problems
Volume35
Issue number1
DOIs
StatePublished - Jan 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Applied Mathematics
  • Computer Science Applications
  • Mathematical Physics

Keywords

  • generalized linear sampling
  • inverse scattering
  • periodic layer
  • transmission eigenvalues problem

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