The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.Mathematics subject classification: (MSC2010) 35Q61, 78M10, 35R30, 65M32, 65M60. J = f ∈ (L 2 (Ω)) 2 | div f = 0 in Ω ,