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

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-07-10 DOI:10.1016/j.acha.2024.101684

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

引用次数: 0

Abstract

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.

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不可分离的多维多分辨率小波：道格拉斯-拉赫福德方法

在将小波构造问题重铸成一个可行性问题，并在其中加入由紧凑支撑、平滑性和正交性要求所产生的约束条件之后，在沿整数网格平移和各向同性二向扩张的情况下，采用道格拉斯-拉赫福德算法来寻找多维、不可分离、紧凑支撑、平滑、正交、多分辨率的小波。本文介绍了数值构造这种小波的算法。通过应用该算法，可以生成新的一维小波以及真正不可分离的二维小波。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.