Single measurement experimental data for an inverse medium problem inverted by a multi-frequency globally convergent numerical method

TL;DR

This paper tests a globally convergent numerical method for inverse medium problems on experimental data, addressing data discrepancies with a heuristic preprocessing step, and achieves accurate reconstructions of targets.

Contribution

It introduces a heuristic data preprocessing procedure to adapt experimental data for a multi-frequency inverse Helmholtz problem, enabling effective reconstructions.

Findings

Good accuracy in reconstructing refractive indices and target locations

Reconstruction errors are lower than direct measurements for dielectric targets

Preprocessing enables the use of experimental data with the method

Abstract

The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the frequency domain with the multi-frequency data. Due to a huge discrepancy between the collected and computationally simulated data, the straightforward Fourier transform of the experimental data does not work. Hence, it is necessary to develop a heuristic data preprocessing procedure. This procedure is described. The preprocessed data are used as the input for the inversion algorithm. Numerical results demonstrate good accuracy in the reconstruction of both refracive indices and locations of targets. Furthermore, the reconstruction errors for refractive indices of dielectric targets are significantly less than errors of a posteriori direct measurements.