Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space

IF 1.3 4区数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-05-10 DOI:10.1155/2024/9932668

Hui-Min Liu, Yu Tian

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Abstract

Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space . We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results.

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索波列夫空间中不规则小波/Gabor 帧的一些条件和扰动定理

由于其在图像复原和深度卷积神经网络中的潜在应用，一些研究人员对不规则帧的研究产生了兴趣。本文探讨了 Sobolev 空间中的不规则小波系统（IWS）和不规则 Gabor 系统（IGS）。我们得到了 IWS 和 IGS 成为框架的充分条件和必要条件。通过应用这些条件，我们还得出了 IWS 和 IGS 成为框架的特征。最后，我们讨论了不规则小波框架（IWF）和不规则 Gabor 框架（IGF）的扰动定理。我们还提供了一些实例来支持我们的结果。

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

Journal of Mathematics Mathematics-General Mathematics

CiteScore

2.50

自引率

14.30%

发文量

期刊介绍： Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.