On the numerical solution of the three-dimensional inverse obstacle scattering problem

AbstractThe inverse problem under consideration is to determine the shape of an impenetrable sound-soft obstacle from the knowledge of a time-harmonic incident plane acoustic wave and far-field or near-field measurements of the scattered wave. We present a method for the approximate solution which avoids the solution of the corresponding direct problem and stabilizes the ill-posed inverse problem by reformulating it as a nonlinear optimization problem. The numerical implementation of the method is described and some three-dimensional examples of reconstructions are given