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

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 $D_{a}f(t)=a^{-1}f(t/a)$ $(t\in {\mathbb{R}}^n,a>0)$.

arXiv comment36 pages, 4 figures

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