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.