A regularized sampling method for solving three-dimensional inverse scattering problems

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