Image Synthesis for Inverse Obstacle Scattering Using the Eigenfunction Expansion Theorem

Image synthesis for inverse obstacle scattering using the eigenfunction expansion theorem

In recent years several new inverse scattering techniques have been developed that determine the boundary of an unknown obstacle by reconstructing the surrounding scattered field. In the case of sound soft obstacles, the boundary is usually found as the minimum contour of the total field. In this note we derive a different approach for imaging the boundary from the reconstructed fields based on...

Image processing for limited aperture inverse acoustic obstacle scattering

Inverse acoustic scattering by small-obstacle expansion of misfit function

This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems, whereby the featured cost function J is expanded in powers of the characteristic size ε of a sound-hard scatterer about ε = 0. The O(ε) approximation of J is established for a small scatterer of arbitrary shape of given location embedded in an arbitrary acoustic domain, and gene...

Inverse obstacle scattering for elastic waves

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...