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A numerical method is developed for recovering both the source locations andthe obstacle from the scattered Cauchy data of the time-harmonic acousticfield. First of all, the incident and scattered components are decomposed fromthe coupled Cauchy data by the representation of the single-layer potentialsand the solution to the resulting linear integral system. As a consequence ofthis decomposition, the original problem of joint inversion is reformulatedinto two decoupled subproblems: an inverse source problem and an inverseobstacle scattering problem. Then, two sampling-type schemes are proposed torecover the shape of the obstacle and the source locations, respectively. Thesampling methods rely on the specific indicator functions defined ontarget-oriented probing domains of circular shape. The error estimates of thedecoupling procedure are established and the asymptotic behaviors of theindicator functions are analyzed. Extensive numerical experiments are alsoconducted to verify the performance of the sampling schemes.

Jointly determining the point sources and obstacle from Cauchy data