A method of inverse scattering problem solution for penetrable objects using back-scattering data

This paper is dedicated to creating a method of inverse scattering problem solution, which uses back-scattering data for reconstructing the boundary of penetrable scatterers. The method belongs to sampling-style methods that exploit an indicator function possessing a blow-up property that enables to identify the interface between two materials. The indicator function is derived by solving a conditional minimization problem to establish a special linear transformation applied to initial data. A condition used for the minimization is set according to Born approximation as a solution of the corresponding inverse scattering problem.