Wavelet Packet Decomposition and Best Basis Selection on Massively Parallel Simd Arrays

Extended Abstract Wavelet packets 14] represent a generalization of the method of multires-olution decomposition and comprise the entire family of subband coded (tree) decompositions 11, 15]. Whereas in the wavelet case the decomposition is applied recursively to the coarse scale approximations (leading to the well known (pyramidal) wavelet decomposition tree), in the wavelet packet decomposition the recursive procedure is applied to all the coarse scale approximations and detail signals, which leads to a complete binary tree and more exibility in frequency resolution. Higher dimensional wavelet packets are produced by analogy to wavelets. Wavelet packet decomposition leads in the general s-dimensional case to 2 sl frequency subbands at decomposition level l. After having generated the whole decomposition tree, there are several possibilities how to use this big set of subbands for representing the signal ((gure ??): the wavelet representation (left), the short time fourier representation (mid) and an unnamed inhomogeneous scheme (right). The wavelet packet best basis algorithm (\single tree algorithm") 2] performs an adaptive optimization of the frequency resolution of a complete binary wavelet packet decomposition tree by selecting the most suitable frequency sub-bands for signal representation (suitable in the sense of suitable for subsequent compression). The double tree algorithm generalizes this approach by selecting an optimal spatial image tiling and corresponding frequency tilings jointly. This operation is done as follows: For each leave of a spatial quadtree image partition a optimal wavelet packet basis is evaluated and its corresponding cost (either a one-or twosided costfunction) is associated with that leave in the quadtree. This basis and its cost is computed using a bottom-up search in the frequency wavelet packet tree (the rst tree). Subsequently a second bottom-up tree search is performed in the spatial quadtree resulting in the nal image partition and the corresponding wavelet packet bases in the leaves of the spatial quadtree.