Department of Mathematics
We propose an inverse scattering scheme of recovering a polyhedral obstacle in Rn, n= 2, 3, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need to make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme.
Backscattering, Inverse scattering, Phaseless, Polyhedral obstacle
Source Publication Title
Journal of Differential Equations
Copyright © 2015 Elsevier Inc. All rights reserved.
This work was supported by the NSFC under the grants No. 11201453 and No. 11371115, and the FRG and startup funds from Hong Kong Baptist University.
Link to Publisher's Edition
Li, Jingzhi, and Hongyu Liu. "Recovering a polyhedral obstacle by a few backscattering measurements." Journal of Differential Equations 259.5 (2015): 2101-2120.