  This paper concerns the simultaneous reconstruction of a sound-soft cavity
and its excitation sources from the total-field data. Using the single-layer
potential representations on two measurement curves, this co-inversion problem
can be decoupled into two inverse problems: an inverse cavity scattering
problem and an inverse source problem. This novel decoupling technique is fast
and easy to implement since it is based on a linear system of integral
equations. Then the uncoupled subproblems are respectively solved by the
modified optimization and sampling method. We also establish the uniqueness of
this co-inversion problem and analyze the stability of our method. Several
numerical examples are presented to demonstrate the feasibility and
effectiveness of the proposed method.
