﻿ 基于空间分数阶偏微分方程图像去噪的隐式差分方法 Implicit Difference Numerical Method of Image Denoising Based on Space Fractional PDE

Vol.05 No.01(2016), Article ID:17011,8 pages
10.12677/AAM.2016.51012

Implicit Difference Numerical Method of Image Denoising Based on Space Fractional PDE

Zefan Yang, Xiaozhong Yang*

Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University, Beijing

Received: Feb. 2nd, 2016; accepted: Feb. 20th, 2016; published: Feb. 26th, 2016

ABSTRACT

Image denoising numerical methods based on space fractional Partial Differential Equations is an important direction of image denoising field, and its study of numerical methods has important theoretical significance and practical value. This paper constructs implicit difference scheme for solving the space fractional partial differential equation. Through theoretical analysis and numerical experiments, we found that implicit difference scheme for solving space fractional partial differential equations is feasible, it can ensure good denoising effect.

Keywords:Image Denoising, Space Fractional Partial Differential Equations, Implicit Difference Method, Numerical Experiment

1. 引言

2. 空间分数阶偏微分方程图像去噪模型的隐式差分格式

2.1. 空间分数阶偏微分方程图像去噪模型

(1)

(2)

(3)

(4)

2.2. 隐式差分格式的构造

(5)

3. 隐式差分格式解的存在唯一性

(6)

(7)

4. 隐式差分格式解的稳定性与收敛性分析及精度分析

(8)

(9)

(10)

5. 数值试验

Table 1. SNR comparison between fractional differential mask algorithm and implicit difference method

Figure 1. Comparison of results from different order between two methods

6. 结论

Implicit Difference Numerical Method of Image Denoising Based on Space Fractional PDE[J]. 应用数学进展, 2016, 05(01): 79-86. http://dx.doi.org/10.12677/AAM.2016.51012

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*通讯作者。