KAIRUAIN-algorithm applied on electromagnetic imaging. For time-harmonic Maxwell equations, we consider an inverse scattering problem for the 3D imaging of the constitutive material of an unknown object from the boundary measurements of the electric field. This problem is ill-posed and nonlinear. We introduce the KAIRUAIN-algorithm which is an iterative method of Newton-Kaczmarz type, where we use the approximate inverse for regularizing the solution of the linearized equation at each Newton iteration. We study the convergence of the algorithm and develop a strategy for the choice of the regularizing parameter in a quite general setting. We apply the KAIRUAIN-algorithm to derive an efficient and stable reconstruction method for electromagnetic imaging. We use experimental data provided by the Institut Fresnel, France, to validate the capability of the reconstruction algorithm to retrieve blindly, without any a priori information, the geometry and the dielectric permittivity of the scattering object.