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A reconstruction algorithm is detailed for three-dimensional full-vectorial microwave imaging based on Newton-type optimization. The goal is to reconstruct the three-dimensional complex permittivity of a scatterer in a homogeneous background from a number of time-harmonic scattered field measurements. The algorithm combines a modified Gauss-Newton optimization method with a computationally efficient forward solver, based on the fast Fourier transform method and the marching-on-in-source-position extrapolation procedure. A regularized cost function is proposed by applying a multiplicative-additive regularization to the least squares datafit. This approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non-linearity of the optimization problem. It is furthermore shown that the modified Gauss-Newton method converges much faster than the Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. Promising quantitative reconstructions from both simulated and experimental data are presented. The latter data are bi-static polarimetric free-space measurements provided by Institut Fresnel, Marseille, France.