Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides**Project supported by the National Natural Science Foundation of China (Grant Nos. 61421062 and 61520106004) and the Microsoft Research Fund of Asia.

Abstract

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the near-field data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.