The linear sampling method for three-dimensional inverse scattering problems

Abstract

The inverse scattering problem under consideration is to determine the shape of an obstacle in R 3 from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods. Numerical examples are given showing the practicality of this new approach.