Full Text:   <2152>

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CLC number: TP391

On-line Access: 2020-10-14

Received: 2019-12-24

Revision Accepted: 2020-03-14

Crosschecked: 2020-08-28

Cited: 0

Clicked: 4622

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Li Xu

https://orcid.org/0000-0002-1376-1779

Guo Huang

https://orcid.org/0000-0001-8109-7833

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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.10 P.1485-1493

http://doi.org/10.1631/FITEE.1900727


An improved method for image denoising based on fractional-order integration


Author(s):  Li Xu, Guo Huang, Qing-li Chen, Hong-yin Qin, Tao Men, Yi-fei Pu

Affiliation(s):  College of Electronics and Materials Engineering, Leshan Normal University, Leshan 614000, China; more

Corresponding email(s):   huangguoxuli@163.com

Key Words:  Fractional-order integral, Cauchy integral, Image denoising, Fractional gradient, Texture protection


Li Xu, Guo Huang, Qing-li Chen, Hong-yin Qin, Tao Men, Yi-fei Pu. An improved method for image denoising based on fractional-order integration[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(10): 1485-1493.

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publisher="Zhejiang University Press & Springer",
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Abstract: 
Given that the existing image denoising methods damage the texture details of an image, a new method based on fractional integration is proposed. First, the fractional-order integral formula is deduced by generalizing the cauchy integral, and then the approximate value of the fractional-order integral operator is estimated by a numerical method. Finally, a fractional-order integral mask operator of any order is constructed in eight pixel directions of the image. Simulation results show that the proposed image denoising method can protect the edge texture information of the image while removing the noise. Moreover, this method can obtain higher image feature values and better image vision after denoising than the existing denoising methods, because a texture protection mechanism is adopted during the iterative processing.

一种基于分数阶积分的图像去噪改进方法

许黎1,2,黄果3,陈庆利3,秦洪英3,门涛3,蒲亦非2
1乐山师范学院电子与材料工程学院,中国乐山市,614000
2四川大学计算机学院,中国成都市,610064
3乐山师范学院,互联网自然语言智能处理四川省高等学校重点实验室,中国乐山市,614000

摘要:针对现有图像去噪方法容易造成图像纹理细节丢失的现象,提出一种基于分数积分的去噪新方法。首先,通过拓展柯西积分推导分数阶积分公式,然后利用数值方法估计分数阶积分算子的近似值。最后,在图像8个像素方向构造一个任意阶次的分数阶积分掩模算子。仿真结果表明,本文提出的图像去噪方法在去除噪声的同时,能够保护图像的边缘和纹理信息。并且,由于在迭代过程中采用了纹理保护机制,该方法在去噪后可获得更高的图像特征值和更好的视觉效果。

关键词:分数阶积分;柯西积分;图像去噪;分数梯度;纹理保护

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Reference

[1]Amoako-Yirenkyi P, Appati JK, Dontwi IK, 2016. A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative. Adv Differ Equat, 2016:238.

[2]Bai YR, Baleanu D, Wu GC, 2018. A novel shuffling technique based on fractional chaotic maps. Optik, 168:553-562.

[3]Bhrawy AH, Zaky MA, 2017. An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations. Appl Numer Math, 111:197-218.

[4]Chen DL, Sun SS, Zhang CR, 2013. Fractional-order TV-L2 model for image denoising. Cent Eur J Phys, 11(10):1414-1422.

[5]Chen E, Min LQ, Chen GR, 2017. Discrete chaotic systems with one-line equilibria and their application to image encryption. Int J Bifurc Chaos, 27(3):1750046.

[6]Ding HF, Li CP, Yi Q, 2017. A new second-order midpoint approximation formula for Riemann-Liouville derivative: algorithm and its application. IMA J Appl Math, 82(5):909-944.

[7]He N, Wang JB, Zhang LL, et al., 2014. An improved fractional-order differentiation model for image denoising. Signal Process, 112:180-188.

[8]Huang G, Pu YF, Chen QL, et al., 2011. Research on image denoising based on fractional order integral. Syst Eng Electron, 33(4):925-932 (in Chinese).

[9]Jain S, Bajaj V, Kumar A, 2018. Riemann Liouvelle fractional integral based empirical mode decomposition for ECG denoising. IEEE J Biomed Health Inform, 22(4):1133-1139.

[10]Jalab HA, Ibrahim RW, 2015. Fractional Alexander polynomials for image denoising. Signal Process, 107:340-354.

[11]Jalab HA, Ibrahim RW, Ahmed A, 2017. Image denoising algorithm based on the convolution of fractional Tsallis entropy with the Riesz fractional derivative. Neur Comput Appl, 28(S1):217-223.

[12]Jiang W, Wang ZX, 2012. Image denoising new method based on fractional partial differential equation. Adv Mater Res, 532-533:797-802.

[13]Li B, Xie W, 2016. Image enhancement and denoising algorithms based on adaptive fractional differential and integral. Syst Eng Electron, 38(1):185-192 (in Chinese).

[14]Liu ST, Yu L, Zhu BH, 2001. Optical image encryption by cascaded fractional Fourier transforms with random phase filtering. Opt Commun, 187(1-3):57-63.

[15]Liu Y, Pu YF, Zhou JL, 2011. A digital image denoising method based on fractional calculus. J Sichuan Univ (Eng Sci Ed), 43(3):90-95, 144 (in Chinese).

[16]Liu ZJ, Liu ST, 2007. Double image encryption based on iterative fractional Fourier transform. Opt Commun, 275(2):324-329.

[17]Nandal A, Gamboa-Rosales H, Dhaka A, et al., 2018. Image edge detection using fractional calculus with feature and contrast enhancement. Circ Syst Signal Process, 37(9):3946-3972.

[18]Podlubny I, 1999. Fractional Differential Equations. Academic Press, New York, NY, USA, p.16-45.

[19]Pu YF, Wang WX, Zhou JL, et al., 2008. Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci China Ser F, 51(9):1319-1339.

[20]Pu YF, Siarry P, Zhou JL, et al., 2014. A fractional partial differential equation based multiscale denoising model for texture image. Math Meth Appl Sci, 37(12):1784-1806.

[21]Pu YF, Zhang N, Zhang Y, et al., 2016. A texture image denoising approach based on fractional developmental mathematics. Patt Anal Appl, 19(2):427-445.

[22]Pu YF, Siarry P, Chatterjee A, et al., 2018. A fractional-order variational framework for retinex: fractional-order partial differential equation-based formulation for multi-scale nonlocal contrast enhancement with texture preserving. IEEE Trans Image Process, 27(3):1214-1229.

[23]Shao L, Yan RM, Li XL, et al., 2014. From heuristic optimization to dictionary learning: a review and comprehensive comparison of image denoising algorithms. IEEE Trans Cybern, 44(7):1001-1013.

[24]Tian D, Xue DY, Wang DH, 2015. A fractional-order adaptive regularization primal–dual algorithm for image denoising. Inform Sci, 296:147-159.

[25]Wu GC, Zeng DQ, Baleanu D, 2019a. Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Frac Calc Appl Anal, 22(1):180-192.

[26]Wu GC, Deng ZG, Baleanu D, 2019b. New variable-order fractional chaotic systems for fast image encryption. Chaos, 29(8):083103.

[27]Wu XJ, Li Y, Kurths J, 2015. A new color image encryption scheme using CML and a fractional-order chaotic system. PLoS ONE, 10(3):e0119660.

[28]Yu JM, Tan LJ, Zhou SB, et al., 2017. Image denoising algorithm based on entropy and adaptive fractional order calculus operator. IEEE Access, 5:12275-12285.

[29]Zhang GM, Sun XX, Liu JX, 2016. Fractional total variation denoising model based on adaptive projection algorithm. Patt Recogn Artif Intell, 29(11):1009-1018 (in Chinese).

[30]Zhang J, Wei ZH, Xiao L, 2012. Adaptive fractional-order multi-scale method for image denoising. J Math Imag Vis, 43(1):39-49.

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