Identification of sound-soft 3D obstacles from phaseless data

Abstract

The inverse problem for time-harmonic acoustic wave scattering to recover a sound-soft obstacle from agiven incident field and the far field pattern of the scattered field is considered. We split this problem into twosubproblems; first to reconstruct the shape from the modulus of the data and this is followed byemploying the full far fieldpattern in a few measurement points to find the location of the obstacle.We extend a nonlinear integral equation approach for shape reconstruction from the modulus of the far fielddata [6] to the three-dimensional case. It is known, see [13], that the locationof the obstacle cannot be reconstructed from only the modulus of the far field pattern since it is invariant undertranslations. However, employing the underlying invariance relationand using only few far field measurements in the backscattering direction wepropose a novel approach for the localization of the obstacle.The efficient implementation of the method is described and the feasibility of the approach is illustrated by numericalexamples.