A new microwave imaging technique is proposed for reconstruction of 2-D complex permittivity profiles in dielectric samples located in a waveguide system. The spatial distributions of the dielectric constant and the loss factor are approximated by continuous functions whose functional parameters are determined using a neural network technique backed by full-wave finite-difference time-domain analysis. The profiles are reconstructed from measurements of reflection and transmission characteristics obtained with the tested sample at different locations. Operational capabilities of the technique are illustrated through a series of computational experiments for rectangular and cylindrical samples at two (original and 90deg -rotated) positions. The results demonstrate excellent agreement between the reconstructed and actual profiles approximated by linear, quadratic, and Gaussian functions: the average relative errors do not exceed 0.4%, 2.2%, and 4.8%, respectively. Finally, the assumption of functional approximation, uniqueness of the reconstruction, and prospects of practical use of the technique are thoroughly discussed.