Tomographic reconstruction allows for the recovery of 3D information from 2D projection data. This commonly requires a full angular scan of the specimen. Angular restrictions that exist, especially in technical processes, result in reconstruction artifacts and unknown systematic measurement errors. We investigate the use of neural networks for extrapolating the missing projection data from holographic sound pressure measurements. A bias flow liner was studied for active sound dampening in aviation. We employed a dense U-Net trained on synthetic data and compared reconstructions of simulated and measured data with and without extrapolation. In both cases, the neural network based approach decreases the mean and maximum measurement deviations by a factor of two. These findings can enable quantitative measurements in other applications suffering from limited angular access as well.