Focusing inversion technique applied to radar tomographic data

摘要

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