An increasing number of practical applications of three-dimensional microwave imaging require accurate and efficient inversion techniques. In this context, a full-wave 3D inverse-scattering method, aimed at characterizing dielectric targets, is described in this paper. In particular, the inversion approach has a Newton-based structure, in which the internal linear solver is a conjugate gradient-like algorithm in lp spaces. The presented results, which include the inversion of both numerical and experimental scattered-field data obtained in the presence of homogeneous and inhomogeneous targets, validate the reconstruction capabilities of the proposed technique.