Non-separable multidimensional multiresolution wavelets: A Douglas-Rachford approach

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: x
Language: eng
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