Iterative solution of the inverse scattering problem from transient scattered field

摘要

The realm of inverse scattering problems is to determine proprieties of unknown objects from the measurements of the scattered fields. Most popular strategy for solving this ill-posed problem is to reconstruct the parameter of interest iteratively by minimizing a cost functional involving the discrepancy between the measurements and that would be obtained via a forward model with the estimation of the parameter. In the frequency domain a theoretical analysis (A.G. Tijhuis et al, Theoretical and Comput. Aspect of 2D Inverse Profiling, vol. 39, 2001) of the dynamic convergence and of the resolution of these iterative approaches shows that the convergence is enhanced at low frequency while the resolution is superior at high frequency. To circumvent these two antagonistic criteria, a multiple frequency approach is proposed (frequency hopping approach), i.e. start the iterative inversion process at low frequencies in order to get a trend that is used as an initial guess for the inversion at higher frequency making it thus possible to retrieve the object under test with high resolution. Successful results have been obtained on synthetic data as well as experimental data. Another way to circumvent the foreseen difficulties encountered in the frequency-domain inversion is to use time-domain data. In this paper, we compare both approaches.