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

2020/06/05 by David Franklin, Franklin, David, Jeffrey A. Hogan +3
Computer Science · Mathematics · #42C40 (Primary) 42B99 #47N10 #65K10 #65T60 #65T60 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2006.03302

openalex publication_date 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^-1f(t/a) (t∈\mathbb Rⁿ, a>0).

Citations

• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Orthonormal bases of compactly supported wavelets

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