The linear sampling method for anisotropic media

We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coefficients are real we also show that the set of transmission eigenvalues forms a discrete set.