Newton's method for inverse obstacle scattering meets the method of least squares

Abstract

The inverse scattering problem of how to image the shape of a scatterer D from the far-field pattern u(infinity) for the scattering of time-harmonic waves can be interpreted as a nonlinear ill-posed operator equation F(partial derivativeD) = u(infinity) with the operator F mapping the boundary onto the far field. We will review recent results on regularized Newton iteration methods as applied to the above equation and present first ideas of an alternative approach that resembles a least-squares method for the solution of inverse obstacle scattering problems due to Kirsch and Kress and does not require a forward solver.