  This paper concerns the imaging of a complex-valued anisotropic tensor
{\gamma} = {\sigma}+{\iota}{\omega}{\epsilon} from knowledge of several inter
magnetic fields H where H satisfies the anisotropic Maxwell system on a bounded
domain with prescribed boundary conditions. We show that {\gamma} can be
uniquely reconstructed with a loss of two derivatives from errors in the
acquisition H. A minimum number of five well-chosen functionals guaranties a
local reconstruction of {\gamma} in dimension two. The explicit inversion
procedure is presented in several numerical simulations, which demonstrate the
influence of the choice boundary conditions on the stability of the
reconstruction. This problem finds applications in the medical imaging
modalities Current Density Imaging and Magnetic Resonance Electrical Impedance
Tomography.
