An investigation of the efficiency of 3-D dual-tree discrete wavelet transforms and its variants for video representation

This paper proposes two new approaches for video representation using 3-D dual-tree discrete wavelet transform (DDWT), and explores their applications for video coding. The DDWT is an attractive video representation because it isolates object features with different spatial orientations and motion directions in separate subbands. Furthermore, this directionality can be achieved with the same computation efficiency as the standard separable discrete wavelet transform (DWT). Our prior investigation has shown that the 3-D DDWT, even with 4:1 redundancy, needs fewer coefficients than the non-redundant 3-D DWT to achieve the same reconstruction quality (in terms of PSNR). In this paper, we explore extensions of the DDWT to achieve more efficient video representation. The first approach applies an anisotropic packet decomposition of the 3-D DDWT, to achieve more directional subbands without adding to the redundancy. Considering the DDWT loses the vertical and horizontal orientations in pursuit of other directions, the second approach combines the 3-D DDWT and DWT to capture directions represented by both 3-D DDWT and DWT. Our simulation results show that the anisotropic DDWT can provide significantly better representation over isotropic DDWT under the same number of retained coefficients. However, combining DWT with DDWT only yields limited gains.