Multifrequency inverse obstacle scattering: the point source method and generalized filtered backprojection

We outline two methods for obstacle reconstruction from multifrequency far field scattering data, the first built upon the point source method proposed by Potthast for solving inverse scattering problems with single frequency data in the resonance region, and the second based on filtered backprojection techniques using the physical optics approximation for high frequency scattering. Our implementation using the point source method can be viewed as a generalized filtered backprojection algorithm, the key to which is the construction of the filter used in the backprojection operator. Numerical examples illustrate that the critical factor for reconstructions in multifrequency settings is the frequency dependence of the filter.