Inverse Obstacle Scattering Using Reduced Data

Inverse acoustic obstacle scattering problems using multifrequency measurements

In this paper, we investigate the problem of reconstructing sound-soft acoustic obstacles using multifrequency far field measurements corresponding to one direction of incidence. The idea is to obtain a rough estimate of the obstacle’s shape at the lowest frequency using the least-squares approach, then refine it using a recursive linearization algorithm at higher frequencies. Using this approa...

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

Stability of the Solution to Inverse Obstacle Scattering Problem

It is proved that if the scattering amplitudes for two obstacles (from a large class of obstacles) differ a little, then the obstacles differ a little, and the rate of convergence is given. An analytical formula for calculating the characteristic function of the obstacle is obtained, given the scattering amplitude at a fixed frequency.

Uniqueness of the Solution to Inverse Obstacle Scattering Problem

It is proved that the scattering amplitude known at a fixed frequency, a fixed direction of the incident plane wave and all directions of the scattered wave in a solid angle, however small, determine uniquely the shape of a strictly convex obstacle with a smooth but not analytic boundary on which the Dirichlet boundary condition is assumed.