More Web Proxy on the site http://driver.im/

research-article

An improved fractional-order differentiation model for image denoising

Authors:

Ke LuAuthors Info & Claims

Signal Processing, Volume 112, Issue C

Pages 180 - 188

https://doi.org/10.1016/j.sigpro.2014.08.025

Published: 01 July 2015 Publication History

Abstract

This paper investigates fractional order differentiation and its applications in digital image processing. We propose an improved model based on the Grünwald-Letnikov (G-L) fractional differential operator. Our improved denoising operator mask is based on G-L fractional order differentiation. The total coefficient of this mask is not equal to zero, which means that its response value is not zero in flat areas of the image. This nonlinear filter mask enhances and preserves detailed features while effectively denoising the image. Our experiments on texture-rich digital images demonstrated the capabilities of the filter. We used the information entropy and average gradient to quantitatively compare our method to existing techniques. Additionally, we have successfully used it to denoise three-dimensional magnetic resonance images. An improved fractional differential operator for image denoising is proposed.Our denoising filter operator mask based on G-L fractional is constructed.The total coefficient of filter mask is not equal to zero.This nonlinear filter mask can preserve the detail features while denoising.

References

[1]

Vishwadeep Garg, Kulbir Singh, An improved Grünwld-Letnikov fractional differential mask for image texture enhancement, Int. Adv. Comput. Sci. Appl., 3 (2012) 130-135.

[2]

Cangpin Li, Deliang Qian, YangQuan Chen, On Riemann-Liouville and Caputo derivatives, Discret. Dyn. Nat. Soc., 2011 (2011).

[3]

Kai Diethlm, Neville J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002) 229-248.

[4]

Qiangli Chen, Huang Guo, Xiu-qiong Zhang, A fractional differential approach to low contrast image enhancement, Int. J. Knowl. Lang. Process., 3 (2012) 20-29.

[5]

Dali Chen, Yangquan Chen, Dingyu Xue, Three fractional-order TV-L2 models for image denoising, J. Comput. Inf. Syst., 9 (2013) 4773-4780.

[6]

Chaobang Gao, Jiliu Zhou, Ziuqing Zheng, Fangnian Lang, Image enhancement based on improved fractional differentiation, J. Comput. Inf. Syst., 7 (2011) 257-264.

[7]

Yan Liu, Yifei Pu, Jiliu Zhou, Design of image denoising filtering based on fractional integral, J. Comput. Inf. Syst., 6 (2010) 2839-2847.

[8]

Dali Chen, Dingyu Xue, Yangquan Chen, Fractional differential-based approach for CT image enhancement, Adv. Mater. Res., 634-638 (2013) 3962-3965.

[9]

Jun Zhang, Zhihui Wei, A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising, Appl. Math. Model., 35 (2011) 2516-2528.

[10]

Q. Yu, F. Liu, I. Turner, K. Burrage, V. Vegh, The use of a Riesz fractional differential-based approach for texture enhancement in image processing, ANZIAM J., 54 (2012) C590-C607.

[11]

Dali Chen, CongRong Zheng, Dingyu Xue, Yangquan Chen, Non-local fractional differential-based approach for image enhancement, Res. J. Appl. Sci., Eng. Technol., 6 (2013) 3244-3250.

[12]

R.H. Chan, A. Lanza, S. Morigi, F. Sgallari, An adaptive strategy for the restoration of textured images using fractional order regularization, Numer. Math.: Theory, Methods Appl., 6 (2013) 276-296.

[13]

Y. Zhang, Yifei Pu, Jinrong Hu, Qingli Chen, Jiliu Zhou, Efficient CT metal artifact reduction based on fractional-order curvature diffusion, Comput. Mat. Methods Med. (2011).

[14]

Jinrong Hu, Yi-Fei Pu, Jiliu Zhou, A novel image denoising algorithm based on Riemann-Liouville definition, JCP, 6 (2011) 1332-1338.

[15]

Yifei Pu, Jiliu Zhou, Xiao Yuan, Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement, IEEE Trans. Image Process., 19 (2010) 491-511.

Digital Library

[16]

Yifei Pu, Weixing Wang, Jiliu Zhou, Yiyang Wang, Huading Jia, Fractional differential approach to detecting texture features of digital image and its fractional differential filter implementation, Sci. China Ser. F: Inf. Sci., 51 (2008) 1319-1339.

[17]

Yue Gao, Meng Wang, Zheng-Jun Zha, Qi Tian, Naiyao Zhaang, Less is more: efficient 3-D object retrieval with query view selection, IEEE Trans. Multimed., 13 (2011) 1007-1018.

Digital Library

[18]

Y. Gao, M. Wang, D. Tao, R. Ji, Q. Dai, 3-D object retrieval and recognition with hypergraph analysis, IEEE Trans. Image Process., 21 (2012) 4290-4303.

Digital Library

[19]

P.S. Mukherjee, P. Qiu, 3-D image denoising by local smoothing and nonparametric regression, Technometrics, 53 (2011) 196-208.

[20]

Yue Gao, Meng Wang, Rongrong Ji, Zindong Wu, Qionghai Dai, 3-D object retrieval with Hausdorff distance learning, IEEE Trans. Ind. Electron., 61 (2014) 2088-2098.

[21]

Yue Gao, Meng Wang, Zheng-Jun Zha, Jialie Shen, Xuelong Li, Zindong Wu, Visual-textual joint relevance learning for tag-based social image search, IEEE Trans. Image Process., 22 (2013) 363-376.

Digital Library

[22]

L. Ruding, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D: Nonlinear Phenom., 60 (1992) 259-268.

Digital Library

[23]

A. Chanbolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis., 20 (2004) 89-97.

[24]

J. Mairal, M. Elad, G. Sapiro, Sparse representation for color image restoration, IEEE Trans. Image Process., 17 (2008) 53-69.

Digital Library

[25]

F. Bach, R. Jenatton, J. Mairal, G. Obozinski, Structured sparsity through convex optimization, Stat. Sci., 27 (2012) 450-468.

[26]

J. Mairal, F. Bach, J. Ponce, G. Sapiro, A. Zisserman, Non-local sparse models for image restoration, in: Proceedings of the International Conference on Computer Vision (ICCV), 2009.

[27]

P. Getreuer, 2007, tvdenoise.m (a MATLAB program) {http://www.mathworks.nl/matlabcentral/fileexchange/16236}.

[28]

P. Coupe, P. Yger, S. Prima, P. Hellier, C. Kervrann, C. Barillot, An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images, IEEE Trans. Med. Imaging, 27 (2008) 425-441.

[29]

A. Buades, B. Coll, J.-M. Morel, Image denoising method. A new nonlocal principle, Soc. Ind. Appl. Math., 52 (2010) 113-147.

[30]

. {http://life.nthu.edu.tw/~b831658/MRI-Brain.html}

[31]

. {http://overcode.yak.net/15?size=M}

Cited By

Gaur SKhan ASuthar D(2024)Optimization of parameters for image denoising algorithm pertaining to generalized Caputo-Fabrizio fractional operatorJournal on Image and Video Processing10.1186/s13640-024-00632-52024:1Online publication date: 13-Sep-2024
https://dl.acm.org/doi/10.1186/s13640-024-00632-5
Limami FHadri AAfraites LLaghrib A(2024)Tensor-guided learning for image denoising using anisotropic PDEsMachine Vision and Applications10.1007/s00138-024-01532-435:3Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1007/s00138-024-01532-4
Gupta AKumar S(2022)Generalized framework for the design of adaptive fractional-order masks for image denoisingDigital Signal Processing10.1016/j.dsp.2021.103305121:COnline publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1016/j.dsp.2021.103305
Show More Cited By

An improved fractional-order differentiation model for image denoising
1. Computing methodologies
  1. Artificial intelligence
  2. Computer graphics

Recommendations

Image Denoising Using Fractional-Order Non-Local TV Model
ICIMCS '14: Proceedings of International Conference on Internet Multimedia Computing and Service

A fractional order non-local denoising algorithm and the implementation of fractional order non-local filter are introduced and discussed in this paper. The proposed regularize image denoising problem using a total variation (TV) prior on a graph, which ...
Fully fractional anisotropic diffusion for image denoising

This paper introduces a novel Fully Fractional Anisotropic Diffusion Equation for noise removal which contains spatial as well as time fractional derivatives. It is a generalization of a method proposed by Cuesta which interpolates between the heat and ...
Generalized framework for the design of adaptive fractional-order masks for image denoising
Abstract
This paper proposes a generalized fractional differential (GFD) mask which incorporates various fractional-order kernels such as power-law kernel, exponentional kernel, and Mittag-Leffler kernel, corresponding to Riemann-Liouville (RL)/...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Signal Processing

Signal Processing Volume 112, Issue C

July 2015

209 pages

ISSN:0165-1684

Issue’s Table of Contents

Copyright © Elsevier B.V.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 July 2015

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

12
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 01 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Gaur SKhan ASuthar D(2024)Optimization of parameters for image denoising algorithm pertaining to generalized Caputo-Fabrizio fractional operatorJournal on Image and Video Processing10.1186/s13640-024-00632-52024:1Online publication date: 13-Sep-2024
https://dl.acm.org/doi/10.1186/s13640-024-00632-5
Limami FHadri AAfraites LLaghrib A(2024)Tensor-guided learning for image denoising using anisotropic PDEsMachine Vision and Applications10.1007/s00138-024-01532-435:3Online publication date: 8-Apr-2024
https://dl.acm.org/doi/10.1007/s00138-024-01532-4
Gupta AKumar S(2022)Generalized framework for the design of adaptive fractional-order masks for image denoisingDigital Signal Processing10.1016/j.dsp.2021.103305121:COnline publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1016/j.dsp.2021.103305
Zhou JZhang DZhang W(2022)Underwater image enhancement method via multi-feature prior fusionApplied Intelligence10.1007/s10489-022-03275-z52:14(16435-16457)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1007/s10489-022-03275-z
Mortazavi MGachpazan MAmintoosi MSalahshour S(2022)Fractional derivative approach to sparse super-resolutionThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-022-02509-y39:7(3011-3028)Online publication date: 30-May-2022
https://dl.acm.org/doi/10.1007/s00371-022-02509-y
Gupta AKumar S(2022)Design of Mittag–Leffler Kernel-Based Fractional-Order Digital Filter Using Fractional Delay InterpolationCircuits, Systems, and Signal Processing10.1007/s00034-021-01942-z41:6(3415-3445)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s00034-021-01942-z
Aboutabit N(2021)A new construction of an image edge detection mask based on Caputo–Fabrizio fractional derivativeThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-020-01896-437:6(1545-1557)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s00371-020-01896-4
Jin CLuan N(2020)An image denoising iterative approach based on total variation and weighting functionMultimedia Tools and Applications10.1007/s11042-020-08871-079:29-30(20947-20971)Online publication date: 1-Aug-2020
https://dl.acm.org/doi/10.1007/s11042-020-08871-0
Shukla APandey RReddy P(2020)Generalized fractional derivative based adaptive algorithm for image denoisingMultimedia Tools and Applications10.1007/s11042-020-08641-y79:19-20(14201-14224)Online publication date: 1-May-2020
https://dl.acm.org/doi/10.1007/s11042-020-08641-y
Shukla APandey RYadav SPachori R(2020)Generalized Fractional Filter-Based Algorithm for Image DenoisingCircuits, Systems, and Signal Processing10.1007/s00034-019-01186-y39:1(363-390)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1007/s00034-019-01186-y
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents