We present a method for GPU accelerated compression of light fields. The approach is by using a dictionary learning framework for compression of light field images. The large amount of data storage by capturing light fields is a challenge to compress and we seek to accelerate the encoding routine by GPGPU computations. We compress the data by projecting each data point onto a set of trained multi-dimensional dictionaries and seek the most sparse representation with the least error. This is done by a parallelization of the tensor-matrix product computed on the GPU. An optimized greedy algorithm to suit computations on the GPU is also presented. The encoding of the data is done segmentally in parallel for a faster computation speed while maintaining the quality. The results shows an order of magnitude faster encoding time compared to the results in the same research field. We conclude that there are further improvements to increase the speed, and thus it is not too far from an interacti ve compression speed.