Modeling-Backed Microwave Imaging in Closed Systems: Reconstruction of a Spherical Inhomogeneity

This project contributes to the field of computational techniques for processing data in microwave imaging inside closed cavities. A computational procedure for imaging of a spherical inhomogeneity in a dielectric sample is outlined. It uses an artificial neural network capable of reconstructing geometrical and material parameters. The network uses data from an FDTD model. Computational experiments are reported for the 4-port waveguide element containing a Teflon sample with a hidden inclusion. The error in reconstruction of four geometrical parameters of a dielectric sphere is 3.3%; the error in finding complex permittivity of the inclusion is 9.8%. The project makes a solid theoretical background for the experimental program dedicated to multiport systems for practical applications

Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide

We consider an inverse medium scattering problem for the Helmholtz equation in a closed cylindrical waveguide with penetrable compactly supported scattering objects. We develop novel monotonicity relations for the eigenvalues of an associated modified near field operator, and we use them to establish linearized monotonicity tests that characterize the support of the scatterers in terms of near field observations of the corresponding scattered waves. The proofs of these shape characterizations rely on the existence of localized wave functions, which are solutions to the scattering problem in the waveguide that have arbitrarily large norm in some prescribed region, while at the same time having arbitrarily small norm in some other prescribed region. As a byproduct we obtain a uniqueness result for the inverse medium scattering problem in the waveguide. Numerical examples are presented to document the potentials and limitations of this approach

Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce incident plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coefficients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a constructive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.Comment: 20 pages, 7 figure