The light field camera array can be regarded as distributed source. The image sequence captured by a camera array contains the inter-correlation and intra-correlation. In order to utilize the correlation, a joint sparsity model was established to combine the light field with distributed compressive sensing, and a recovery algorithm was proposed for the model -- simultaneous regularized orthogonal matching pursuit algorithm (SROMP), which uses the correlation to reconstruct the light field image sequences. Several light field images could be approximate at once using different linear combinations of elementary signals. Experimental results show that SROMP algorithm could be used to achieve high accuracy reported in the literatures.