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2019 | OriginalPaper | Chapter

Application in Image Denoising Using Fractional Total Variation Theory

Authors : Guo Huang, Qing-li Chen, Tao Men, Xiu-Qiong Zhang, Hong-Ying Qin, Li Xu

Published in: The Proceedings of the International Conference on Sensing and Imaging

Publisher: Springer International Publishing

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Abstract

Aiming at the existing problems that the image denoising algorithm based on integer-order partial differential equation could lost part of edge and texture information. This image denoising algorithm based on fractional variational theory was proposed by the theory of fractional calculus and partial differential equation. The denoising model proposed in this paper introduces and implements the numeric computation of the fractional variation partial differential equations by constructing the fractional differential mask operators along eight directions of image. The simulation data prove that the image denoising algorithm based on fractional variation theory compared with the traditional image denoising algorithm could better retain the edge and texture detail information, obtain visual effect, and properly improve the signal-to-noise ratio.

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Literature
1.
go back to reference Tschumperle D, Deriche R (2005) Vector-valued image regularization with PDEs: a common framework for different applications [J]. IEEE Trans Pattern Anal Mach Intell 27(4):506–517CrossRef Tschumperle D, Deriche R (2005) Vector-valued image regularization with PDEs: a common framework for different applications [J]. IEEE Trans Pattern Anal Mach Intell 27(4):506–517CrossRef
2.
go back to reference Gilboa G, Sochen N, Zeevi YY (2006) Variational denoising of partly textured images by spatially varying constraints [J]. IEEE Trans Image Process 15(8):2281–2289CrossRef Gilboa G, Sochen N, Zeevi YY (2006) Variational denoising of partly textured images by spatially varying constraints [J]. IEEE Trans Image Process 15(8):2281–2289CrossRef
3.
go back to reference Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion [J]. IEEE Trans Pattern Anal Machine Intell 12(7):629–639CrossRef Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion [J]. IEEE Trans Pattern Anal Machine Intell 12(7):629–639CrossRef
4.
go back to reference Ruding L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms [J]. Physical D 60(1–4):259–268MathSciNetCrossRef Ruding L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms [J]. Physical D 60(1–4):259–268MathSciNetCrossRef
5.
go back to reference Osher S, Rudin LI, Fatemi E (1992) Nonlinear total variation based noise removal algorithms [J]. Physica D Nonlinear Phenomena 60(3):259–268MathSciNetMATH Osher S, Rudin LI, Fatemi E (1992) Nonlinear total variation based noise removal algorithms [J]. Physica D Nonlinear Phenomena 60(3):259–268MathSciNetMATH
6.
go back to reference Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models [J]. Int J Comput Vis 1(4):321–331CrossRef Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models [J]. Int J Comput Vis 1(4):321–331CrossRef
7.
go back to reference Pu Y-F, Zhou J-L, Siarry P (2013) Fractional extreme value adaptive training method: fractional steepest descent approach. IEEE Trans Neural Netw Learn Syst 26(4):653–663MathSciNetCrossRef Pu Y-F, Zhou J-L, Siarry P (2013) Fractional extreme value adaptive training method: fractional steepest descent approach. IEEE Trans Neural Netw Learn Syst 26(4):653–663MathSciNetCrossRef
8.
go back to reference Pu YF, Siarry P, Zhou JL (2014) Fractional partial differential equation denoising models for texture image [J]. Science China Inf Sci 57(7):1–19MathSciNetCrossRef Pu YF, Siarry P, Zhou JL (2014) Fractional partial differential equation denoising models for texture image [J]. Science China Inf Sci 57(7):1–19MathSciNetCrossRef
9.
go back to reference Bai J, Feng X-C (2007) Fractional-order anisotropic diffusion for image Denoising [J]. IEEE Trans Image Process 16:2492–2502MathSciNetCrossRef Bai J, Feng X-C (2007) Fractional-order anisotropic diffusion for image Denoising [J]. IEEE Trans Image Process 16:2492–2502MathSciNetCrossRef
10.
go back to reference Zhang J, Wei Z (2011) A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising [J]. Appl Math Model 35(5):2516–2528MathSciNetCrossRef Zhang J, Wei Z (2011) A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising [J]. Appl Math Model 35(5):2516–2528MathSciNetCrossRef
11.
go back to reference Zhang J, Wei Z (2010) Fractional-order multi-scale variation PDE model and adaptive algorithm for SAR image denoising [J]. J Electron Inf Technol 32(7):1654–1659 Zhang J, Wei Z (2010) Fractional-order multi-scale variation PDE model and adaptive algorithm for SAR image denoising [J]. J Electron Inf Technol 32(7):1654–1659
12.
go back to reference Wu C, Tai XC (2010) Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models [J]. Siam J Imaging Sci 3(3):300–339MathSciNetCrossRef Wu C, Tai XC (2010) Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models [J]. Siam J Imaging Sci 3(3):300–339MathSciNetCrossRef
13.
go back to reference Ren Z, He C, Zhang Q (2013) Fractional order total variation regularization for image super-resolution [J]. Signal Process 93(9):2408–2421CrossRef Ren Z, He C, Zhang Q (2013) Fractional order total variation regularization for image super-resolution [J]. Signal Process 93(9):2408–2421CrossRef
14.
go back to reference Ortigueira MD, Rodríguez-Germá L, Trujillo JJ (2011) Complex Grünwald–Letnikov, Liouville, Riemann–Liouville, and Caputo derivatives for analytic functions [J]. Commun Nonlinear Sci Numerical Simulation 16(11):4174–4182MathSciNetCrossRef Ortigueira MD, Rodríguez-Germá L, Trujillo JJ (2011) Complex Grünwald–Letnikov, Liouville, Riemann–Liouville, and Caputo derivatives for analytic functions [J]. Commun Nonlinear Sci Numerical Simulation 16(11):4174–4182MathSciNetCrossRef
15.
go back to reference Tomovski Ž (2012) Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator [J]. Nonlinear Anal 75(7):3364–3384MathSciNetCrossRef Tomovski Ž (2012) Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator [J]. Nonlinear Anal 75(7):3364–3384MathSciNetCrossRef
16.
go back to reference Jiang W, Wang ZX (2012) Image denoising new method based on fractional partial differential equation [J]. Adv Mater Res 532-533:797–802CrossRef Jiang W, Wang ZX (2012) Image denoising new method based on fractional partial differential equation [J]. Adv Mater Res 532-533:797–802CrossRef
Metadata
Title
Application in Image Denoising Using Fractional Total Variation Theory
Authors
Guo Huang
Qing-li Chen
Tao Men
Xiu-Qiong Zhang
Hong-Ying Qin
Li Xu
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-91659-0_15