Full Text:   <3352>

Summary:  <1674>

CLC number: O241.82

On-line Access: 2020-06-12

Received: 2020-02-10

Revision Accepted: 2020-04-01

Crosschecked: 2020-05-06

Cited: 0

Clicked: 5041

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Xing-ran Liao

https://orcid.org/0000-0003-3721-403X

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.6 P.856-865

http://doi.org/10.1631/FITEE.2000067


An improved ROF denoising model based on time-fractional derivative


Author(s):  Xing-ran Liao

Affiliation(s):  School of Mathematics, Sichuan University, Chengdu 610065, China

Corresponding email(s):   xrliao_scu@163.com

Key Words:  Improved ROF denoising model, Time-fractional derivative, Caputo derivative, Image denoising


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.

@article{title="An improved ROF denoising model based on time-fractional derivative",
author="Xing-ran Liao",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="6",
pages="856-865",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2000067"
}

%0 Journal Article
%T An improved ROF denoising model based on time-fractional derivative
%A Xing-ran Liao
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 6
%P 856-865
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2000067

TY - JOUR
T1 - An improved ROF denoising model based on time-fractional derivative
A1 - Xing-ran Liao
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 6
SP - 856
EP - 865
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2000067


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 O(τ2−α+h2), where τ, α, and h 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.

基于时间分数阶导数的改进ROF去噪模型

廖星冉
四川大学数学学院,中国成都市,610065

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O(τ2−α+h2)收敛于精确解,其中ταh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。

关键词:改进ROF去噪模型;时间分数阶导数;Caputo导数;图像去噪

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Abirami A, Prakash P, Thangavel K, 2018. Fractional diffusion equation-based image denoising model using CN-GL scheme. Int J Comput Math, 95(6-7):1222-1239.

[2]Bai J, Feng XC, 2018. Image denoising using generalized anisotropic diffusion. J Math Imag Vis, 60(7):994-1007.

[3]Bergounioux M, Piffet L, 2010. A second-order model for image denoising. Set-Valued Var Anal, 18(3-4):277-306.

[4]Blomgren P, Chan TF, Mulet P, et al., 1997. Total variation image restoration: numerical methods and extensions. Proc Int Conf on Image Processing, p.384-387.

[5]Bredies K, Kunisch K, Pock T, 2010. Total generalized variation. SIAM J Imag Sci, 3(3):492-526.

[6]Knoll F, Bredies K, Pock T, et al., 2011. Second order total generalized variation (TGV) for MRI. Mag Reson Med, 65(2):480-491.

[7]Podlubny I, 1998. Fractional Differential Equations. Academic Press, Cambridge, USA.

[8]Rosen JB, 1961. The gradient projection method for nonlinear programming. Part II. Nonlinear constraints. J Soc Ind Appl Math, 9(4):514-532.

[9]Rudin LI, Osher S, Fatemi E, 1992. Nonlinear total variation based noise removal algorithms. Phys D, 60(1-4):259- 268.

[10]Vogel CR, 2002. Computational Methods for Inverse Problems. SIAM, Philadelphia, USA.

[11]Wu GC, Baleanu D, Bai YR, 2019. Discrete fractional masks and their applications to image enhancement. In: Bǎleanu D, Lopes AM (Eds.), Applications in Engineering, Life and Social Sciences, Part B. De Gruyter, Berlin, Boston, p.261-270.

[12]Zhang L, Zhang L, Mou XQ, et al., 2011. FSIM: a feature similarity index for image quality assessment. IEEE Trans Imag Process, 20(8):2378-2386.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE