A new approach based on deep learning methods is presented for reconstructing L-band brightness temperature images from the inversion of interferometric data, namely, complex visibilities here simulated from observations of the Soil Moisture and Ocean Salinity (SMOS) interferometric radiometer. A specific deep neural network (DNN) architecture composed of a fully connected layer followed by a contracting and expansive path is proposed to learn the relationship between the simulated visibilities and the brightness temperature maps. The performances of the DNN are compared with those of algebraic inversions based on Fourier theory, which are all affected by strong aliases in the synthesized field of view (FOV), as a consequence of the spacing between the elementary antennas of SMOS, which does not satisfy the Nyquist criteria. In the alias-free FOV (AFFOV) of the algebraic reconstructions, these latter are outperformed by the DNN reconstructions: average mean absolute error (MAE) of about 0.7 K for the DNN instead of 3.7 K. Outside the AFFOV of the algebraic reconstructions, the DNN reconstructions do not show significant signs of field aliasing although the MAE increases: average MAE of about 1.5 K in the whole FOV. An analysis of the role of different neurons in the hidden layers is presented, and it is shown that some neurons are specialized in reconstructing what corresponds roughly to the AFFOV region of algebraic approaches, while other neurons are specialized in dealing with the external regions of this AFFOV.