The factorization method for inhomogeneous medium with an impenetrable obstacle

This paper is concerned with the inverse scattering problem of time-harmonic acoustic waves by a mixed-type scatterer. Such a scatterer is given as the union of an inhomogeneous medium with unknown buried objects inside and an impenetrable obstacle. Having established the well-posedness of the direct problem by the variational method, we study the factorization method for recovering the support of the inhomogeneous medium and the shape of the impenetrable obstacle simultaneously. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the inverse algorithm.