Perturbative numeric approach in microwave imaging

TL;DR

This paper extends an elastic deformation imaging method to Helmholtz equations using multi-frequency measurements and ultrasound perturbations, enabling simultaneous reconstruction of conductivity and permittivity under certain conditions.

Contribution

It introduces a perturbative numeric approach for microwave imaging that combines ultrasound perturbations with multi-frequency data to reconstruct electrical properties.

Findings

Successfully extends elastic deformation imaging to Helmholtz equations.

Enables simultaneous reconstruction of conductivity and permittivity.

Applicable under non-resonant frequency conditions.

Abstract

In this paper, we show that using measurements for different frequencies, and using ultrasound localized perturbations it is possible to extend the method of the imaging by elastic deformation developed by Ammari and al. [Electrical Impedance Tomography by Elastic Deformation SIAM J. Appl. Math., 68(6), (2008), 1557-1573.] to problems for the Helmholtz equations with Neumann boundary conditions, and to reconstruct by a perturbation method both the conductivity and the permittivity, provided that the conductivity function is coercive and the wave number in the Helmholtz equation is not a resonant frequency.