We consider the problem of imaging of objects buried under the ground using experimental backscattering time-dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric constants of these objects using the globally convergent inverse algorithm of Beilina and Klibanov. Our algorithm is tested on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. There are two main challenges in working with this type of experimental data: (i) there is a huge misfit between these data and computationally simulated data, and (ii) the signals scattered from the targets may overlap with and be dominated by the reflection from the ground's surface. To overcome these two challenges, we propose new data preprocessing steps to make the experimental data look similar to the simulated data, as well as to remove the reflection from the ground's surface. Results of a total of 25 data sets of both nonblind and blind targets indicate good accuracy.