In this paper, we focus on the problem of compressing dense light fields which represent very large volumes of highly redundant data. In our scheme, view synthesis based on convolutional neural networks (CNN) is used as a first prediction step to exploit interview correlation. Super-rays are then constructed to capture the interview and spatial redundancy remaining in the prediction residues. To ensure that the super-ray segmentation is highly correlated with the residues to be encoded, the super-rays are computed on synthesized residues (the difference between the four transmitted corner views and their corresponding synthesized views), instead of the synthesized views. Neighboring super-rays are merged into a larger super-ray according to a rate-distortion cost. A 4D shape adaptive discrete cosine transform (SA-DCT) is applied per super-ray on the prediction residues in both the spatial and angular dimensions. A traditional coding scheme consisting of quantization and entropy coding is then used for encoding the transformed coefficients. Experimental results show that the proposed coding scheme outperforms HEVC-based schemes at low bitrate.