An improved ROF denoising model based on time-fractional derivative

Xing-ran LIAO

doi:10.1631/FITEE.2000067

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An improved ROF denoising model based on time-fractional derivative

Special Feature on New Trends in Fractional Calculus for Information Science | Updated：2022-05-19

- An improved ROF denoising model based on time-fractional derivative
- 基于时间分数阶导数的改进ROF去噪模型
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 6, Pages: 856-865(2020)
- Affiliations：
  
  School of Mathematics, Sichuan University, Chengdu 610065, China
- Author bio：
  
  [ "Xing-ran LIAO, E-mail: xrliao_scu@163.com" ]
- Funds：
- DOI：10.1631/FITEE.2000067
  CLC： O241.82
- Received：10 February 2020，
  
  Revised：2020-;5-;6，
  
  Published：2020-06
- Accepted：
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Xing-ran LIAO. An improved ROF denoising model based on time-fractional derivative[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 856-865.
DOI：

Xing-ran LIAO. An improved ROF denoising model based on time-fractional derivative[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 856-865. DOI： 10.1631/FITEE.2000067.

摘要

本文主要讨论图像去噪和纹理保持问题。时间分数阶导数通常具有可调的分数阶控制扩散过程，应用于图像去噪时，其记忆效果能很好保留图像纹理。因此，在经典Rudin-Osher-Fatemi（ROF）模型基础上，设计一个新的时间分数阶导数ROF模型，空间上的离散化基于整数阶差分格式，时间上的离散化是Caputo导数的近似（即，用类Caputo差分法离散Caputo导数）。详细分析这种显式格式的稳定性和收敛性，证明该模型的数值解以阶数

(

2−

)收敛于精确解，其中

，

和

分别为时间步长、分数阶和空间步长。最后，采用信噪比、特征相似度、直方图恢复度评价指标综合评价新模型性能。数值试验结果表明，改进的模型比现有模型具有更强去噪和纹理保持能力。

Abstract

In this study

we discuss mainly the image denoising and texture retention issues. Usually

the time-fractional derivative has an adjustable fractional order to control the diffusion process

and its memory effect can nicely retain the image texture when it is applied to image denoising. Therefore

we design a new Rudin-Osher-Fatemi model with a time-fractional derivative based on a classical one

where the discretization in space is based on the integer-order difference scheme and the discretization in time is the approximation of the Caputo derivative (i.e.

Caputo-like difference is applied to discretize the Caputo derivative). Stability and convergence of such an explicit scheme are analyzed in detail. We prove that the numerical solution to the new model converges to the exact solution with the order of

(

)

where

and

are the time step size

fractional order

and space step size

respectively. Finally

various evaluation criteria including the signal-to-noise ratio

feature similarity

and histogram recovery degree are used to evaluate the performance of our new model. Numerical test results show that our improved model has more powerful denoising and texture retention ability than existing ones.

关键词

Keywords

references

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