Work

A Douglas-Rachford construction of non-separable continuous compactly supported multidimensional wavelets

Year: 2020

Type: preprint

Abstract: After re-casting the $n$-dimensional 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 one- and two-dimensional wavelets. New one-dimensional wavelets are produced as well as genuinely non-separable two-dimensional wavelets in the case where the dilation on the plane is the standard $D_af(t)=a^{-1}f(t/a)$ $(t\in{\mathbb R}^n, a>0)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2006.03302

Authors: Franklin, David, Hogan, Jeffrey A., Tam, Matthew K.

Institutions: University of Newcastle Australia, The University of Melbourne

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3033802190

Cites: 30

Cited by: 3

Related to: 10