用于消除乘法噪声的变阶分数 1-Laplacian 扩散方程

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-10-08 DOI:10.1007/s13540-024-00345-6

Yuhang Li, Zhichang Guo, Jingfeng Shao, Yao Li, Boying Wu

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引用次数: 0

摘要

本文论述了一类具有可变阶数的分数 1-拉普拉斯扩散方程，并将其作为消除图像中乘法噪声的模型。本文证明了所提模型弱解的良好拟合性。为了克服近似过程中遇到的基本困难，我们特别强调研究变阶分数 Sobolev 空间的密度特性。数值实验证明，我们的模型在整个图像中表现出良好的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal$

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Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal

This paper deals with a class of fractional 1-Laplacian diffusion equations with variable orders, proposed as a model for removing multiplicative noise in images. The well-posedness of weak solutions to the proposed model is proved. To overcome the essential difficulties encountered in the approximation process, we place particular emphasis on studying the density properties of the variable-order fractional Sobolev spaces. Numerical experiments demonstrate that our model exhibits favorable performance across the entire image.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.