A second degree Newton method for an inverse obstacle scattering problem

A regularized second degree Newton method is proposed and implemented for the inverse problem for scattering of time-harmonic acoustic waves from a sound-soft obstacle. It combines ideas due to Johansson and Sleeman [18] and Hettlich and Rundell [8] and reconstructs the obstacle from the far field pattern for scattering of one incident plane wave.

A linearized second degree Newton method is proposed for the inverse scattering problem.
► It proposes a new possibility for the regularization of the inverse problem which leads to a finer reconstruction.
► The reconstruction via this method is more stable.