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

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Abstract
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 corresponding to observation angle and plane waves incident at angle is known for all . From this information, the support of the scattering obstacle is obtained by solving the integral equation where k is the wavenumber and is on a rectangular grid containing the scatterer. The support is found by noting that is unbounded as approaches the boundary of the scattering object from inside the scatterer. Numerical examples are given showing the practicality of this method.