Construction of Parseval wavelets from redundant filter systems
Abstract
We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.
Cite
@article{arxiv.math/0405301,
title = {Construction of Parseval wavelets from redundant filter systems},
author = {L. W. Baggett and P. E. T. Jorgensen and K. D. Merrill and J. A. Packer},
journal= {arXiv preprint arXiv:math/0405301},
year = {2007}
}
Comments
34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more references