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In this paper, a new spatiotemporal filtering scheme is described for noise reduction in video sequences. For this purpose, the scheme processes each group of three consecutive sequence frames in two steps: 1) estimate motion between frames and 2) use motion vectors to get the final denoised current frame. A family of adaptive spatiotemporal L-filters is applied. A recursive implementation of these filters is used and compared with its nonrecursive counterpart. The motion trajectories are obtained recursively by a region-recursive estimation method. Both motion parameters and filter weights are computed by minimizing the kurtosis of error instead of mean squared error. Using the kurtosis in the algorithms adaptation is appropriate in the presence of mixed and impulsive noises. The filter performance is evaluated by considering different types of video sequences. Simulations show marked improvement in visual quality and SNRI measures cost as well as compared to those reported in literature.