A distributed source method for inverse acoustic scattering

We develop a new algorithm for solving inverse acoustic scattering problems. In particular we show that this algorithm can reproduce scattering shapes efficiently, using synthetic data, from only one incident wave in the acoustically hard case and using at most two incident waves for the acoustically soft problem. In order to test the inversion algorithm we generate synthetic data using a technique which combines the distributed source method and the fundamental solution of the Helmholtz equation in order to calculate the scattered field for each of these problems. Numerical results for three-dimensional axially symmetric shapes are compared with those obtained previously by other authors.