We present a new method for reconstructing a 4D light field from a random set of measurements. A 4D light field block can be represented by a sparse model in the Fourier domain. As such, the proposed algorithm reconstructs the light field, block by block, by selecting frequencies of the model that best fits the available samples, while enforcing orthogonality with the approximation residue. The method achieves a very high reconstruction quality, in terms of Peak Signal-to-Noise Ratio (PSNR). Experiments on several datasets show significant quality improvements of more than 1dB compared to state-of-the-art algorithms.