The alpha matting algorithm can effectively separate the foreground and background information of two-dimensional images to realize object extraction, alpha image compositing, and other computational imaging processing. A light field alpha matting propagation model satisfying spatial-angular consistency is established through the sparse representation of light field data based on the spatial-angular interaction of four-dimensional light field data. The alpha closed form solution of the central sub-aperture image is propagated to other sub-aperture image plane by the propagation model, and the alpha images of light field with spatial-angular consistency can be obtained efficiently. In addition, a quantitative evaluation metric of spatial-angular consistency for light field alpha images based on epipolar plane image (EPI) is proposed. The numerical experiments are conducted on synthetic data sets and real light field data. The results show that compared with each sub-aperture image matting algorithm, the proposed algorithm can reduce redundant computation and quickly obtain high-quality light field alpha images with better spatial-angular consistency.