Compressed sensing (CS) has great potential for use in video data acquisition and storage because it makes it unnecessary to collect an enormous amount of data and to perform the computationally demanding compression process. We propose an effective CS algorithm for video that consists of two iterative stages. In the first stage, frames containing the dominant structure are estimated. These frames are obtained by thresholding the coefficients of similar blocks. In the second stage, refined residual frames are reconstructed from the original measurements and the measurements corresponding to the frames estimated in the first stage. These two stages are iterated until convergence. The proposed algorithm exhibits superior subjective image quality and significantly improves the peak-signal-to-noise ratio and the structural similarity index measure compared to other state-of-the-art CS algorithms.