In this paper, a compressing and reconstruction method for a noise video based on Compressed Sensing (CS) theory is proposed. At first, the CS theory is presented. Then the noise video is estimated from noisy measurement by solving the convex minimization problem. The video recovery algorithms based on gradient-based method is used to compressing and reconstructing the noise signal. And a compressive sensing algorithm with gradient-based method is proposed. At last, the performance of the proposed approach is shown and compared with some conventional algorithms. Our method can obtain best resu...