Application of the Hybrid Stochastic - Deterministic Minimization Method to a Surface Data Inverse Scattering Problem

A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this inverse problem to an identification of the positions of the small scatterers. These positions are found by a global minimization search. Such a search is implemented by a novel Hybrid Stochastic-Deterministic Minimization method. The method combines random tries and a deterministic minimization. The effectiveness of this approach is illustrated by numerical experiments. In the modeling part our method is valid when the Born approximation fails. In the numerical part, an algorithm for the estimate of the number of the small scatterers is proposed.