  In this paper we consider the inverse acoustic scattering (in \mathbb{R}^3)
or electromagnetic scattering (in \mathbb{R}^2, for the scalar TE-polarization
case) problem of reconstructing possibly multiple defective penetrable regions
in a known anisotropic material of compact support. We develop the
factorization method for a non-absorbing anisotropic background media
containing penetrable defects. In particular, under appropriate assumptions on
the anisotropic material properties of the media we develop a rigorous
characterization for the support of the defective regions from the given far
field measurements. Finally we present some numerical examples in the two
dimensional case to demonstrate the feasibility of our reconstruction method
including examples for the case when the defects are voids (i.e. subregions
with refractive index the same as the background outside the inhomogeneous
hosting media).
