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arXiv · 2006.03302

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

David Franklin·Jeffrey A. Hogan·Matthew K. Tam
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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 $D_af(t)=a^{-1}f(t/a)$ $(t\in{\mathbb R}^n, a>0)$.

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BibTeXRIS

David Franklin, Jeffrey A. Hogan, Matthew K. Tam. 2020-06-05. A Douglas-Rachford construction of non-separable continuous compactly supported multidimensional wavelets. https://arxiv.org/abs/2006.03302

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