Focusing inversion technique applied to radar tomographic data

Palermo, Italy

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.

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