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We investigate image and video denoising using adaptive dual-tree discrete wavelet packets (ADDWP), which is extended from the dual-tree discrete wavelet transform (DDWT). With ADDWP, DDWT subbands are further decomposed into wavelet packets with anisotropic decomposition, so that the resulting wavelets have elongated support regions and more orientations than DDWT wavelets. To determine the decomposition structure, we develop a greedy basis selection algorithm for ADDWP, which has significantly lower computational complexity than a previously developed optimal basis selection algorithm, with only slight performance loss. For denoising the ADDWP coefficients, a statistical model is used to exploit the dependency between the real and imaginary parts of the coefficients. The proposed denoising scheme gives better performance than several state-of-the-art DDWT-based schemes for images with rich directional features. Moreover, our scheme shows promising results without using motion estimation in video denoising. The visual quality of images and videos denoised by the proposed scheme is also superior.