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 eld 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 rst kind and avoids the use of nonlinear optimization methods. Numerical examples are given showing the practicality of this new approach.

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

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