A microwave imaging technique for the detection and monitoring of brain stroke is presented in this paper. The imaging algorithm, which operates in the framework of L ^p Banach spaces, iteratively solves a nonlinear inverse scattering problem. This allows to reconstruct the differential dielectric properties of a horizontal slice of the patient's head. The proposed approach is validated by means of a set of numerical simulations with three-dimensional anatomically-realistic phantoms of the human head, in presence of different measurement configurations.