A linear image reconstruction algorithm for solving the Magnetic Induction Tomography inverse problem is presented. It's an optimization process to determine a reconstruction matrix that does the best mapping between a set of training parameter vectors and their respective measurements dictated by a forward model. It allows the simultaneous 3D reconstructions of the electric conductivity, electric permittivity and magnetic permeability. The results were compared with the ones obtained from a single-step regularized Gauss-Newton method and a reduction of 15% in the image error was verified. The behavior of the developed algorithm in a simulated clinical environment was also assessed using a realistic bio-impedance model of the human head, derived from a high resolution magnetic resonance image.