A novel compression framework called distributed compressed hyper spectral image sensing (DCHIS) is proposed in this paper. In our framework, the random measurements of each spectral band are obtained using compressed sensing (CS) encoding independently at the encoder. At the decoder, a new reconstruction algorithm with the proposed initialization and stopping criterion is applied to reconstruct the non-key frames with the assistance of the estimated side information, which is derived from the previous reconstructed key frames using the prediction method. Experimental results show that the proposed algorithm not only improves the reconstruction quality, but also increases convergence rate. Our algorithm has a very low-complexity encoder and is hardware friendly.