Imaging with electromagnetic waves in terminating waveguides

Liliana  Borcea; Dinh-Liem  Nguyen

doi:10.3934/ipi.2016027

Article Contents

2016, Volume 10, Issue 4: 915-941. Doi: 10.3934/ipi.2016027

This issue Previous Article The localized basis functions for scalar and vector 3D tomography and their ray transforms Next Article FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems

Imaging with electromagnetic waves in terminating waveguides

Liliana Borcea^1, and
Dinh-Liem Nguyen^1,

1.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043

Received: October 2015

Revised: July 2016

Published: November 2016

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Abstract

We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered returns. The mathematical formulation of the inverse scattering problem is based on the electromagnetic Lippmann-Schwinger integral equation and an explicit calculation of the Green tensor. The image formation is carried with reverse time migration and with $\ell_1$ optimization.

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Mathematics Subject Classification: Primary: 35R30, 78A46; Secondary: 35Q61.

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