In the context of sea state monitoring, reconstructing the wave field and estimating the sea state parameters from radar data is a challenging problem. To reach this goal, this paper proposes a fully data-driven, deep learning approach based on a convolutional neural network. The network takes as input the radar image spectrum and outputs the sea wave directional spectrum. After a 2D fast Fourier transform, the wave elevation field is reconstructed, and accordingly, the sea state parameters are estimated. The reconstruction strategy, herein presented, is tested using numerical data generated from a synthetic sea wave simulator, considering the spectral proprieties of the Joint North Sea Wave Observation Project model. A performance analysis of the proposed deep-learning estimation strategy is carried out, along with a comparison to the classical modulation transfer function approach. The results demonstrate that the proposed approach is effective in reconstructing the directional wave spectrum across different sea states.