Seismic exploration in complex geologic settings and shallow geologic targets has led to a demand for higher spatial and temporal resolution in the final migrated image. Conventional marine seismic and wide-azimuth data acquisition lack near-offset coverage, which limits imaging in these settings. A new marine source-over-cable survey, with split-spread configuration, known as TopSeis, was introduced in 2017 to address the shallow-target problem. However, wavefield reconstruction in the near offsets is challenging in the shallow part of the seismic record due to the high temporal frequencies and coarse sampling that leads to severe spatial aliasing. We have investigated deep learning as a tool for the reconstruction problem, beyond spatial aliasing. Our method is based on a convolutional neural network (CNN) approach trained in the wavelet domain that is used to reconstruct the wavefield across the streamers. We determine the performance of the proposed method on broadband synthetic data and TopSeis field data from the Barents Sea. From our synthetic example, we find that the CNN can be learned in the inline direction and applied in the crossline direction, and that the approach preserves the characteristics of the geologic model in the migrated section. In addition, we compare our method to an industry-standard Fourier-based interpolation method, in which the CNN approach shows an improvement in the root-mean-square (rms) error close to a factor of two. In our field data example, we find that the approach reconstructs the wavefield across the streamers in the shot domain, and it displays promising characteristics of a reconstructed 3D wavefield.