Scattering data inversion through Interval Analysis under Rytov approximation

The solution of inverse scattering problems where the unknown scatterer respects the Rytov approximation is addressed in this paper by means of an innovative strategy based on Interval Analysis. Firstly, the approach recast the inverse problem as an optimization one by defining a suitable cost function that measures the discrepancy between the measured and the reconstructed scattered field in the Interval Arithmetic framework. Successively, the cost function is minimized by means of a branch-and-bound algorithm based on the exploitation of the rules of Interval Analysis. Such a solution guarantees the presence of the optimal solution in the list of candidate solutions obtained when the termination conditions are satisfied.