Light field technology has recently been gaining traction in the research community. Several acquisition technologies have been demonstrated to properly capture light field information, and portable devices have been commercialized to the general public. However, new and efficient compression algorithms are needed to sensibly reduce the amount of data that needs to be stored and transmitted, while maintaining an adequate level of perceptual quality. In this paper, we propose a novel light field compression scheme that uses view estimation to recover the entire light field from a small subset of encoded views. Experimental results on a widely used light field dataset show that our method achieves good coding efficiency with average rate savings of 54.83% with respect to HEVC.