Signal sparse decomposition is one of critical issues in compressed sensing. Redundant dictionary provides much more sparse decomposition than using conventional orthonormal basis function. In this paper, we propose jointly sparse model of light field based on the features of light camera arraythe images with intersignal and intrasignal correlation, and then sparse represent the signals using different linear combinations of redundant dictionary trained from original signals, and next reconstruct the sparse signals with Simultaneously stagewise Orthogonal Matching Persuit, which runs much faster than other greedy algorithms and reconstructs images simultaneously. Finally, we give several examples showing the methods are rapid and reliable in light field images.