We describe a local low rank approximation method based on super-rays for light field compression. Super-rays can be seen as a set of super-pixels that are coherent across all light field views. A super-ray based disparity estimation method is proposed using a low rank prior, in order to be able to align all the super-pixels forming each super-ray. A dedicated super-ray construction method is described that constrains the super-pixels forming a given super-ray to be all of the same shape and size, dealing with occlusions. This constraint is needed so that the super-rays can be used as a support of angular dimensionality reduction based on low rank matrix approximation. A low rank matrix approximation is then computed on the disparity compensated super-rays using a singular value decomposition (SVD). A coding algorithm is then described for the different components of the resulting low rank approximation. Experimental results show performance gains compared with two reference light field coding schemes (HEVC-based scheme and JPEG-Pleno VM 1.1).