A fast explicit diffusion algorithm of fractional order anisotropic diffusion for image denoising

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/IPI.2021018

Zhiguang Zhang, Qiang Liu, Tianling Gao

引用次数: 1

Abstract

In this paper, we mainly show a novel fast fractional order anisotropic diffusion algorithm for noise removal based on the recent numerical scheme called the Fast Explicit Diffusion. To balance the efficiency and accuracy of the algorithm, the truncated matrix method is used to deal with the iterative matrix in the model and its error is also estimated. In particular, we obtain the stability condition of the iteration by the spectrum analysis method. Through implementing the fast explicit format iteration algorithm with periodic change of time step size, the efficiency of the algorithm is greatly improved. At last, we show some numerical results on denoising tasks. Many experimental results confirm that the algorithm can more quickly achieve satisfactory denoising results.

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一种用于图像去噪的分数阶各向异性快速显式扩散算法

本文主要在快速显式扩散的基础上，提出了一种新的快速分数阶各向异性扩散去噪算法。为了平衡算法的效率和准确性，采用截断矩阵法处理模型中的迭代矩阵，并对其误差进行了估计。特别地，我们用谱分析法得到了迭代的稳定性条件。通过实现时间步长周期性变化的快速显式格式迭代算法，大大提高了算法的效率。最后给出了去噪任务的一些数值结果。大量实验结果表明，该算法能够更快地获得满意的去噪效果。

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

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.