A new structure of 3-D dual-tree discrete wavelet transform and applications to video denoising and coding

This paper introduces an anisotropic decomposition structure of a recently introduced 3-D dual-tree discrete wavelet transform (DDWT), and explores the applications for video denoising and coding. The 3-D DDWT is an attractive video representation because it isolates motion along different directions in separate subbands, and thus leads to sparse video decompositions. Our previous investigation shows that the 3-D DDWT, compared to the standard discrete wavelet transform (DWT), complies better with the statistical models based on sparse presumptions, and gives better visual and numerical results when used for statistical denoising algorithms. Our research on video compression also shows that even with 4:1 redundancy, the 3-D DDWT needs fewer coefficients to achieve the same coding quality (in PSNR) by applying the iterative projection-based noise shaping scheme proposed by Kingsbury. The proposed anisotropic DDWT extends the superiority of Isotropic DDWT with more directional subbands without adding to the redundancy. Unlike the original 3-D DDWT which applies dyadic decomposition along all three directions and produces Isotropic frequency spacing, it has a non-uniform tiling of the frequency space. By applying this structure, we can improve the denoising results, and the number of significant coefficients can be reduced further, which is beneficial for video coding.