Resolution-Enhanced Electromagnetic Inverse Source: A Deep Learning Approach

We investigate the capabilities of deep learning based on a convolutional neural network (CNN) to improve the solution of an electromagnetic inverse source problem against a classical regularization scheme, the truncated singular value decomposition (TSVD). We consider a planar, scalar source and a far-zone observation domain, for which the unknown-to-data relation is provided by a two-dimensional Fourier-like operator. The exploited a priori information is a weak geometrical information for TSVD, whereas for CNN a priori information is the one embedded during the training stage. As long as the objects belong to a subset matching the information used for the training stage, the nonlinear processing of the neural network (NN) outperforms the linear processing of the TSVD by extrapolating out-of-band harmonics. On the other side, the NN performs poorly when the object does not match the a priori information. The results are of general interest for problems where the Fourier inversion is considered.