  Traveltime tomography is a very effective tool to reconstruct acoustic,
seismic or electromagnetic wave speed distribution. To infer the velocity image
of the medium from the measurements of first arrivals is a typical example of
ill-posed problem. In the framework of Tikhonov regularization theory, in order
to replace an ill-posed problem by a well-posed one and to get a unique and
stable solution, a stabilizing functional (stabilizer) has to be introduced.
The stabilizer selects the desired solution from a class of solutions with a
specific physical and/or geometrical property; e.g., the existence of sharp
boundaries separating media with different petrophysical parameters. Usually
stabilizers based on maximum smoothness criteria are used during the inversion
process; in these cases the solutions provide smooth images which, in many
situations, do not describe the examined objects properly. Recently a new
algorithm of direct minimization of the Tikhonov parametric functional with
minimum support stabilizer has been introduced; it produces clear and focused
images of targets with sharp boundaries. In this research we apply this new
technique to real radar tomographic data and we compare the obtained result
with the solution generated by the more traditional minimum norm stabilizer.
