Transform-based Distributed Data Gathering

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These transforms can be computed as data is routed towards the collection (or sink) node in the tree and exploit data correlation between nodes in the tree. Moreover, when used in wireless sensor networks, these transforms can also leverage data received at nodes via broadcast wireless communications. Various constructions of unidirectional transforms are also provided for use in data gathering in wireless sensor networks. New wavelet transforms are also proposed which provide significant improvements over existing unidirectional transforms

Multi-dimensional real Fourier transform

Four subroutines compute one-dimensional and multi-dimensional Fourier transforms for real data, multi-dimensional complex Fourier transforms, and multi-dimensional sine, cosine and sine-cosine transforms. Subroutines use Cooley-Tukey fast Fourier transform. In all but one-dimensional case, transforms are calculated in up to six dimensions

Wavelets and Wavelet Packets on Quantum Computers

We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.Comment: 11 pages, 10 postscript figure, to appear in Proc. of Wavelet Applications in Signal and Image Processing VI