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This paper is concerned with reconstructing an acoustic obstacle and itsexcitation sources from the phaseless near-field measurements. By supplementingsome artificial sources to the inverse scattering system, this co-inversionproblem can be decoupled into two inverse problems: an inverse obstaclescattering problem and an inverse source problem, and the correspondinguniqueness can be established. This novel decoupling technique requires someextra data but brings in several salient benefits. First, our method is fastand easy to implement. Second, the boundary condition of the obstacle is notneeded. Finally, this approximate decoupling method can be applied to otherco-inversion problems, such as determining the medium and its excitationsources. Several numerical examples are presented to demonstrate thefeasibility and effectiveness of the proposed method.

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