Light field imaging is limited in its computational processing demands of high sampling for both spatial and angular dimensions. Single-shot light field cameras sacrifice spatial resolution to sample angular viewpoints, typically by multiplexing incoming rays onto a 2D sensor array. While this resolution can be recovered using compressive sensing, these iterative solutions are slow in processing a light field. We present a deep learning approach using a new, two branch network architecture, consisting jointly of an autoencoder and a 4D CNN, to recover a high resolution 4D light field from a single coded 2D image. This network decreases reconstruction time significantly while achieving average PSNR values of 26-32 dB on a variety of light fields. In particular, reconstruction time is decreased from 35 minutes to 6.7 minutes as compared to the dictionary method for equivalent visual quality. These reconstructions are performed at small sampling/compression ratios as low as 8%, allowing for cheaper coded light field cameras. We test our network reconstructions on synthetic light fields, simulated coded measurements of real light fields captured from a Lytro Illum camera, and real coded images from a custom CMOS diffractive light field camera. The combination of compressive light field capture with deep learning allows the potential for real-time light field video acquisition systems in the future.