Light field imaging has recently known a regain of interest due to the availability of practical light field capturing systems that offer a wide range of applications in the field of computer vision. However, capturing high-resolution light fields remains technologically challenging since the increase in angular resolution is often accompanied by a significant reduction in spatial resolution. This paper describes a learning-based spatial light field super-resolution method that allows the restoration of the entire light field with consistency across all angular views. The algorithm first uses optical flow to align the light field and then reduces its angular dimension using low-rank approximation. We then consider the linearly independent columns of the resulting low-rank model as an embedding, which is restored using a deep convolutional neural network (DCNN). The super-resolved embedding is then used to reconstruct the remaining views. The original disparities are restored using inverse warping where missing pixels are approximated using a novel light field inpainting algorithm. Experimental results show that the proposed method outperforms existing light field super-resolution algorithms, achieving PSNR gains of 0.23 dB over the second best performing method. The performance is shown to be further improved using iterative back-projection as a post-processing step.