- Title
- Non-separable multidimensional multiresolution wavelets: A Douglas-Rachford approach
- Creator
- Franklin, David; Hogan, Jeffrey A.; Tam, Matthew K.
- Relation
- ARC.DP160101537 http://purl.org/au-research/grants/arc/DP160101537
- Relation
- Applied and Computational Harmonic Analysis Vol. 73, Issue November 2024, no. 101684
- Publisher Link
- http://dx.doi.org/10.1016/j.acha.2024.101684
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2024
- Description
- After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas–Rachford algorithm is employed in the search for multi-dimensional, non-separable, compactly supported, smooth, orthogonal, multiresolution wavelets in the case of translations along the integer lattice and isotropic dyadic dilations. An algorithm for the numerical construction of such wavelets is described. By applying the algorithm, new one-dimensional wavelets are produced as well as genuinely non-separable two-dimensional wavelets.
- Subject
- wavelets; multiresolution analysis; optimisation; Douglas-Rachford algorithm; projection algorithm; feasibility problem
- Identifier
- http://hdl.handle.net/1959.13/1508950
- Identifier
- uon:56171
- Identifier
- ISSN:1063-5203
- Rights
- © 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
- Language
- eng
- Full Text
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