Anisotropic Wavelet Packet Research Articles

Efficient and Rate-Distortion Optimal Wavelet Packet Basis Selection in JPEG2000

This paper discusses optimal wavelet packet basis selection within JPEG2000. Algorithms for rate-distortion optimal wavelet packet basis selection in JPEG2000 are presented and compared to more efficient wavelet packet basis selection schemes. Both isotropic and anisotropic wavelet packet bases are considered. For the first time, computationally efficient heuristics are compared to the best bases in the standardized coding framework of JPEG2000. For the first time, the maximum performance gains of custom wavelet packets in JPEG2000 can be assessed. The algorithms are evaluated on a wide range of highly textured image data.

Methods and Tools for Wavelet-Based Scalable Multiview Video Coding

A wavelet-based multiview video coding scheme is presented in this paper. It uses a 4-D wavelet transform, which is composed of a 1-D temporal wavelet transform, namely motion compensated temporal filtering, a 1-D view-directional wavelet transform, namely disparity compensated view filtering and a 2-D spatial wavelet transform. Since the presented framework can make use of the inherent scalability properties of the wavelet transforms involved, it allows full scalability of the coded bitstream in the temporal, view, spatial, and quality dimensions. Coding performance close to the H.264/advanced video coding based standard multiview video codec is shown. Enhancements of the view transform, in order to better account for brightness and color variations across views are introduced. Additionally, the use of a signal adaptive anisotropic wavelet packet (WP) transform as a generalization of WP transforms for the spatial decomposition is proposed. Both enhancements lead to a decrease of bit rate of up to 11% compared with the baseline version of the codec.

Methods for the anisotropic wavelet packet transform

Anisotropic wavelet packets present a flexible transform with interesting properties and applications. While certain aspects of this transform have been investigated in conjunction with applications, this paper aims at providing a basic theoretical framework for working with anisotropic wavelet packets. Random decompositions are developed which have distributions with different average decomposition depths and degrees of anisotropy. They can be used in cryptographic applications or to test other algorithms. For the uniform distribution, it is necessary to determine the number of possible bases for all decomposition depths. A best basis algorithm for anisotropic decompositions is developed. A graph theoretical representation of the anisotropic decomposition structure is presented, which is unique for each decomposition and, thus, free of redundancy, which is important for compression purposes. A compression algorithm based on these techniques is developed and tested on random decompositions.

On the Number of Rectangular Tilings

Adaptive multiscale representations via quadtree splitting and two-dimensional (2-D) wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their one-dimensional counterparts, in particular, by coupling of the two dimensions and restricting to only one possible further partition of each block into four subblocks. In this paper, we consider more flexible schemes that exploit more variations of multidimensional data structure. In the meantime, we restrict to tree-based decompositions that are amenable to fast algorithms and have low indexing cost. Examples of these decomposition schemes are anisotropic wavelet packets, dyadic rectangular tilings, separate dimension decompositions, and general rectangular tilings. We compute the numbers of possible decompositions for each of these schemes. We also give bounds for some of these numbers. These results show that the new rectangular tiling schemes lead to much larger sets of 2-D space and frequency decompositions than the commonly-used quadtree-based schemes, therefore bearing the potential to obtain better representation for a given image.

Fast Algorithm for Best Anisotropic Walsh Bases and Relatives

We introduce a new family of Nlog Nbest basis search algorithms for functions of more than one variable. These algorithms search the collection of anisotropic wavelet packet and cosine packet bases and output a minimum entropy basis for a given function. These algorithms are constructed after treating the model problem of computing best Walsh packet bases. Several intermediate algorithms for conducting mixed isotropic/anisotropic best basis searches in the function's various coordinate directions are also presented.