Imaging an acoustic obstacle and its excitation sources from phaseless near-field data

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can be decoupled into two inverse problems: an inverse obstacle scattering problem and an inverse source problem, and the corresponding uniqueness can be established. This novel decoupling technique requires some extra data but brings in several salient benefits. First, our method is fast and easy to implement. Second, the boundary condition of the obstacle is not needed. Finally, this approximate decoupling method can be applied to other co-inversion problems, such as determining the medium and its excitation sources. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.