  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.
