An optimization method for acoustic inverse obstacle scattering problems with multiple incident waves

The inverse problem considered in this article is to determine the shape of a two-dimensional time-harmonic acoustic scatterer with Dirichlet boundary conditions from the knowledge of some far field patterns. Based on the optimization method due to Kirsch and Kress for the inverse scattering problem, we propose a new scheme by reformulating the cost functional via a technique of piecewise integration with respect to incident directions. Convergence analysis of this method is given. Numerical experiments show that our method accelerates the computations without losing the accuracy of the reconstructions for the fullaperture problems. The method is extended to the limited-aperture case by weighting the total fields with special factors. Numerical examples for limitedaperture problems are also presented which show that our method produces satisfactory results efficiently in the illuminated regions.