Compressive sampling matching pursuit （CoSaMP） algorithm integrates the idea of combining algorithm to ensure running speed and provides rigorous error bounds which provide a good theoretical guarantee to convergence. And compressive sensing （CS） can help us ease the pressure of hardware facility from the requirements of the huge amount in information processing. Therefore, a new video coding framework was proposed, which was based on CS and curvelet transform in this paper. Firstly, this new framework uses curvelet transform and CS to the key frame of test sequence, and then gains recovery frame via CoSaMP to achieve data compress. In the classic CoSaMP method, the halting criterion is that the number of iterations is fixed. Therefore, a new stopping rule is discussed to halting the algorithm in this paper to obtain better performance. According to a large number of experimental results, we ran see that this new framework has better performance and lower RMSE. Through the analysis of the experimental data, it is found that the selection of number of measurements and sparsity level has great influence on the new framework. So how to select the optimal parameters to gain better performance deserves worthy of further study.
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