Interpolatory filter banks and interpolatory wavelet packets Abstract   In classic wavelet sampling, research is generally focused on interpolatory bases in individual spaces. Consideration is seldom given to relations among different interpolatory bases, including those potentially related by filter banks. In this paper, we show that when an interpolatory basis exists in a space with a multiresolution analysis, this space can be decomposed orthogonally into two subspaces in which interpolatory bases also exist. Furthermore, similarly to standard orthogonal bases, these interpolatory bases can be related by pairs of filters, called interpolatory filter banks. For such interpolatory filter banks, it is shown that existence of interpolatory scaling functions generally leads to that of interpolatory wavelets and interpolatory wavelet packets. With this result, we further propose new algorithms for constructing such interpolatory waveletswavelet packets from corresponding scaling functions. In examples, our algorithms are applied to some typical wavelet spaces, demonstrating our theorems for interpolatory wavelets, interpolatory wavelet packets and interpolatory filter banks.

Video coding with fully separable wavelet and wavelet packet transforms Threedimensional (t2D) wavelet coding schemes have been demonstrated to be efficient techniques for video compression applications. However, the separable wavelet transform used for removing the spatial redundancy allows a limited representation of the 2D texture because of spatial isotropy of the wavelet basis functions. In this case, anisotropic transforms, such as fully separable wavelet transforms (FSWT), can represent a solution for spatial decorrelation. FSWT inherits the separability, the computational simplicity and the filter bank characteristics of the standard 2D wavelet transform, but it improves the representation of directional textures, as the ones which can be found in temporal detail frames of t  2D decompositions. The extension of both classical wavelet and waveletpacket transforms to fully separable decompositions preserve at the same time the lowcomplexity and bestbases selection algorithms of these ones. We apply these transforms in t  2D video coding schemes and compare them with classical decompositions.