B-spline quarklets and biorthogonal multiwavelets

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2023-06-21 DOI:10.1142/s0219691323500297

Marc Hovemann, Anne Kopsch, Thorsten Raasch, Dorian Vogel

引用次数: 1

Abstract

In this paper, we show that B-spline quarks and the associated quarklets fit into the theory of biorthogonal multiwavelets. Quark vectors are used to define sequences of subspaces [Formula: see text] of [Formula: see text] which fulfill almost all conditions of a multiresolution analysis. Under some special conditions on the parameters, they even satisfy all those properties. Moreover, we prove that quarks and quarklets possess modulation matrices which fulfill the perfect reconstruction condition. Furthermore, we show the existence of generalized dual quarks and quarklets which are known to be at least compactly supported tempered distributions from [Formula: see text]. Finally, we also verify that quarks and quarklets can be used to define sequences of subspaces [Formula: see text] of [Formula: see text] that yield non-orthogonal decompositions of [Formula: see text].

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b样条夸克与双正交多小波

本文证明了b样条夸克及其相关夸克符合双正交多小波理论。夸克矢量用于定义[公式:见文本]的子空间序列[公式:见文本]，这些子空间序列几乎满足多分辨率分析的所有条件。在某些特殊条件下，它们甚至满足所有这些性质。此外，我们还证明了夸克和夸克具有满足完美重构条件的调制矩阵。此外，我们证明了广义对偶夸克和夸克的存在性，这些夸克和夸克至少是紧支持的调质分布，来自[公式:见原文]。最后，我们还验证了夸克和夸克可以用来定义[公式:见文]的子空间序列[公式:见文]，从而产生[公式:见文]的非正交分解。

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

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.

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