  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.
