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In this paper, we propose a novel, temporally-adaptive maximum a posteriori (MAP) estimation algorithm for the reduction of additive video noise in the wavelet domain. We have exploited the fact that the spatial and temporal redundancies, which exist in a video sequence in the time domain, also persist in the wavelet domain. This allows the video motion to be captured in the wavelet domain. A new statistical model for video sequences is proposed, where the subband coefficients in individual frames as well as the wavelet coefficient difference occurring between two consecutive frames are modeled using the generalized Laplacian distribution. Based on this model, a MAP estimator is developed that estimates the noise-free wavelet coefficients in the current frame, conditioned on the noisy coefficients in the current frame and the filtered coefficients in the past frame. The proposed algorithm has been tested using several different test sequences and corrupting noise powers and the experimental results show that the proposed scheme outperforms several state-of-the-art spatio-temporal filters in time and wavelet domains in terms of quantitative performance as well as visual quality.