This paper considers the compressive sensing framework as a way of overcoming the spatio-angular trade-off inherent to light field acquisition devices. We present a novel method to reconstruct a full 4D light field from a sparse set of data samples or measurements. The approach relies on the assumption that sparse models in the 4D Fourier domain can efficiently represent light fields. The proposed algorithm reconstructs light fields by selecting the frequencies of the Fourier basis functions that best approximate the available samples in 4D hyper-blocks. The performance of the reconstruction algorithm is further improved by enforcing orthogonality of the approximation residue at each iteration, i.e. for each selected basis function. Since sparsity is better preserved in the continuous Fourier domain, we propose to refine the selected frequencies by searching for neighboring non-integer frequency values. Experiments show that the proposed algorithm yields performance improvements of more than 1 dB compared to state-of-the-art compressive light field reconstruction methods. The frequency refinement step also significantly enhances the visual quality of reconstruction results of our method by a 1.8 dB average. © 2020