The denoising of video data should take into account both temporal and spatial dimensions, however, separable 3-D transforms have artifacts that degrade their performance in applications. True 3-D transforms are rarely used for video denoising. We describe the design and application of the non-separable 3-D dual-tree complex wavelet transform for video denoising. We show that this expansive transform gives a motion-based multi-scale decomposition for video - it isolates in its subbands motion along different directions. The development of this transform depends on the design of pairs of wavelet bases where the wavelet associated with the second basis is the Hilbert transform of the wavelet associated with the first basis. We also illustrate the modeling of the wavelet coefficients as mixtures of Laplacian random variables.