Huygens’ principle and iterative methods in inverse obstacle scattering

Huygens' principle and iterative methods in inverse obstacle scattering

The main purpose of this paper is to establish relations between three iterative numerical methods based on Huygen’s principle that arose almost simultaneously to solve a particular inverse problem. The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scatter...

Iterative Regularization Methods in Inverse Scattering

We consider the problem of reconstructing the shape of an acoustic or electromagnetic scatterer from far eld measurements of the scattered wave corresponding to one incident time harmonic wave in the resonance region. This problem is di cult to solve since it is nonlinear and severely ill-posed. The characterization of the Fr echet derivatives, which has been accomplished some years ago by Kirs...

Uniqueness and numerical methods in inverse obstacle scattering

The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for i...

Inverse obstacle scattering in the time domain

This work is a study of the extension of an inverse obstacle scattering algorithm for fixed, single-frequency data to multi-frequency time-dependent settings. The inversion algorithm is based on the point source method, which reconstructs scattered fields pointwise with respect to frequency. We use Fourier transforms to obtain the time-dependent scattered fields as superpositions of single-freq...

Inverse obstacle scattering for elastic waves