Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation

We consider the problem of the reconstruction of dielectrics from blind backscattered experimental data. The reconstruction is done from time domain data, as opposed to a more conventional case of frequency domain data. Experimental data were collected using a microwave scattering facility which was built at the University of North Carolina at Charlotte. This system sends electromagnetic pulses into the medium and collects the time-resolved backscattered data on a part of a plane. The spatially distributed dielectric constant ε_r (x), x ∈ ℝ³ is the unknown coefficient of a wave-like PDE. This coefficient is reconstructed from those data in blind cases. To do this, a globally convergent numerical method is used.