A simple method for solving inverse scattering problems in the resonance region

This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer. It is assumed that the far field pattern u(infinity)(phi; theta) corresponding to observation angle rp and plane waves incident at angle theta is known for all phi, theta is an element of [-pi, pi]. From this information, the support of the scattering obstacle is obtained by solving the integral equation integral(-pi)(pi) u(infinity)(phi;theta)g(theta)d theta = e(ik rho cos(phi-alpha)) phi is an element of [-pi,pi] where k is the wavenumber and y(0) = (rho cos alpha, rho sin alpha) is on a rectangular grid containing the scatterer. The support is found by noting that parallel to g parallel to(L2(-pi,pi)) is unbounded as y(0) approaches the boundary of the scattering object from inside the scatterer. Numerical examples are given showing the practicality of this method.