Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements

We consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. We consider the case of acoustic boundary measurements, with different types of boundary conditions to be prescribed, and we prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally we treat applications of these results to the case of inverse scattering