Numerical methods in inverse obstacle scattering

We consider the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic plane waves. This is a model problem for applications in radar, sonar, geophysical exploration, medical imaging and nondestructive testing. It is difficult to solve, since it is nonlinear and extremely ill-posed. Following the historical development over the last fifteen years, in this lecture we shall describe the main ideas of three different methods for the approximate numerical solution of the inverse obstacle scattering problem that acknowledge its nonlinearity and ill-posedness