Distributed compressed video sensing (DCVS), combining advantages of compressed sensing and distributed video coding, is developed as a novel and powerful system to get an encoder with low complexity. Nevertheless, it is still unclear how to explore the method to achieve an effective video recovery through utilizing realistic signal characteristics as much as possible. Based on this, we present a novel spatiotemporal dictionary learning (DL) based reconstruction method for DCVS, where both the DL model and the l1-analysis based recovery with correlation constraints are included in the minimization problem to achieve the joint optimization of sparse representation and signal reconstruction. Besides, an alternating direction method with multipliers (ADMM) based numerical algorithm is outlined for solving the underlying optimization problem. Simulation results demonstrate that the proposed method outperforms other methods, with 0.03-4.14 dB increases in PSNR and a 0.13-15.31 dB gain for non-key frames.