  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.
