Olphert, Sean and Power, Stephen (2011) Higher Rank Wavelets. Canadian Journal of Mathematics, 63. pp. 689-720. ISSN 0008-414X
Full text not available from this repository.Abstract
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in . While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct \emph{Latin square wavelets} as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Canadian Journal of Mathematics |
| Uncontrolled Keywords: | wavelet ; multi-scaling ; higher rank ; multiresolution ; Latin squares |
| Subjects: | Q Science > QA Mathematics |
| Departments: | Faculty of Science and Technology > Mathematics and Statistics |
| ID Code: | 59562 |
| Deposited By: | ep_importer_pure |
| Deposited On: | 26 Oct 2012 16:32 |
| Refereed?: | Yes |
| Published?: | Published |
| Last Modified: | 26 Oct 2012 16:33 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/59562 |
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