In this paper, we propose a Generalized Kalman Filtered Compressive Sensing (Generalized-KFCS) framework to reconstruct a video sequence, which relaxes the assumption of a slowly changing sparsity pattern in Kalman Filtered Compressive Sensing [1, 2, 3, 4]. In the proposed framework, we employ motion estimation to achieve the estimation of the state transition matrix for the Kalman filter, and then reconstruct the video sequence via the Kalman filter in conjunction with compressive sensing. In addition, we propose a novel method to directly apply motion estimation to compressively sensed samples without reconstructing the video sequence. Simulation results demonstrate the superiority of our algorithm for practical video reconstruction.