Resolution-Enhanced Electromagnetic Inverse Source: a Deep Learning Approach

We investigate the capabilities of Deep Learning (DL) 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) in particular. We consider a planar, scalar source and a far-zone observation domain, for which the unknown-to-data relation is provided by a 2D Fourier-like operator. The exploited a priori information is 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 non-linear processing of the 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.