In order to remove the mixed noise of Gaussian noise and impulse noise from video data using sparse and low-rank decomposition algorithms based on norm, a nonlocal video denoising scheme is proposed. By grouping similar patches in both spatial and temporal domains, the problem of removing noise is converted into a sparse and low-rank decomposition problem. Two algorithms were designed to recover the low-rank components from a noisy video based on the related theories of regularization and norm. Algorithm 1 is based on the combination of norm and norm. Algorithm 2 is based on the combination of norm and norm. The resulting norm and norm related minimization problem can be effectively overcome by some recently developed numerical methods. Through the numerical simulation experiment, the effectiveness and precision of the two algorithms in sparse and low-rank component decomposition problems were verified. Video denoising experimental results show that the proposed scheme can effectively remove the Gaussian noise and random-valued impulse noise from the video. The denoising effect by the two algorithms, no matter the visual quality and objective evaluation criteria, were higher than that of the state-of-the-art video denoising algorithm.