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We propose a video denoising algorithm based on a spatiotemporal Gaussian scale mixture model in the wavelet transform domain. This model simultaneously captures the local correlations between the wavelet coefficients of natural video sequences across both space and time. Such correlations are further strengthened with a motion compensation process, for which a Fourier domain noise-robust cross correlation algorithm is proposed for motion estimation. Bayesian least square estimation is used to recover the original video signal from the noisy observation. Experimental results show that the performance of the proposed approach is competitive when compared with state-of-the-art video denoising algorithms based on both peak signal-to-noise-ratio and structural similarity evaluations.