The factorization and monotonicity method for the defect in an open periodic waveguide

Abstract

In this paper, we consider the inverse scattering problem to reconstruct the defect in an open periodic waveguide from near field data. Our first aim is to mention that there is a mistake in the factorization method of Lechleiter 2008. By this we can not apply it to solve this inverse problem. Our second aim is to give ways to understand the defect from inside (Theorem 1.1) and outside (Theorem 1.2) based on the monotonicity method.

23 pages, 6 figures, arXiv admin note: text overlap with arXiv:1906.01180

References in corpus (5)

• Monotonicity based shape reconstruction in electrical impedance tomography
• Local uniqueness for an inverse boundary value problem with partial data
• Dimension bounds in monotonicity methods for the Helmholtz equation
• The monotonicity method for the inverse crack scattering problem
• Scattering by the local perturbation of an open periodic waveguide in the half plane

Cited by in corpus (1)

• Remarks on the factorization and monotonicity method for inverse acoustic scatterings